source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-39497 | harpazo
#### harpazo
##### Pure Mathematics
Sure you do...you know that the number $$54$$ has a value of $$5\cdot10+4$$, right?
Yes but???
#### MarkFL
##### La Villa Strangiato
Staff member
Moderator
Math Helper
Yes but???
But what? If a number has the two digits from left to right as x and y, then the value of the number (assuming base 10) is 10x + y. If y is twice x, then the number's value is 10x + 2x. Switching the digits gives the number a value of 20x + x.
Does that make sense?
harpazo
#### harpazo
##### Pure Mathematics
But what? If a number has the two digits from left to right as x and y, then the value of the number (assuming base 10) is 10x + y. If y is twice x, then the number's value is 10x + 2x. Switching the digits gives the number a value of 20x + x.
Does that make sense?
You said:
"If y is twice x, then the number's value is 10x + 2x. Switching the digits gives the number a value of 20x + x."
How does switching the digits yield
20x + x?
Staff member
The following is multiple choice question (with options) to answer.
If the digits of a two-digit number are interchanged, the number so obtained is greater than the original number by 18. If the sum of the two digits of the number is 14. What is the original number ? | [
"68",
"77",
"95",
"86"
] | A | Explanation :
Let the no. be 10x + y.
No. formed by the interchange of digits = 10y + x
We have y - x = 2 .....(i)
y + x = 14 .....(ii)
Solving (i) and (ii), we get x = 6, and y = 8
∴ the no. is 68.
Answer : Option A |
AQUA-RAT | AQUA-RAT-39498 | Now find the time Rick spends running.
$\displaystyle t_{r,R}=\frac{D}{2v_r}$
Now just add the two times up and you’re done.
$\displaystyle t_R=\frac{D}{2v_w}+\frac{D}{2v_r}=\frac{D}{2v_wv_r}\left(v_w+v_r\right)$
#### PART B. Find Rick’s average speed for covering the distance D.
You were given the total distance and have calculated the total time. Recall that average speed is equal to the total distance traveled divided by the amount of time it took to travel this distance.
$\displaystyle v_{ave,\:R}=\frac{2v_rv_w}{v_w+v_r}$
#### PART C. How long does it take Tim to cover the distance?
Tim walks at speed $\displaystyle v_w$ half the time and runs at speed $\displaystyle v_r$ for the other half.
$\displaystyle v_{ave,\:T}=\frac{v_w+v_r}{2}$
The time is just the distance divided by the average speed.
$\displaystyle t_T=\frac{D}{\frac{v_w+v_r}{2}}=\frac{2D}{v_r+v_w}$
#### PART D. Who covers the distance D more quickly?
Imagine that both Rick and Tim do all of their walking before they start to run. Rick will start running when he has covered half of the total distance. When Tim reaches half of the total distance, will he already have started running?
#### PART E. In terms of given quantities, by what amount of time, Δt, does Tim beat Rick?
$\displaystyle \Delta t=\frac{D\left(v_w-v_r\right)^2}{2v_rv_w\left(v_r-v_w\right)}$
This is just simple subtraction between the two computed times.
The following is multiple choice question (with options) to answer.
Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 20mph, what was his average speed over the three hour portion of his ride? | [
"14 mph",
"20/3 mph",
"70/3 mph",
"80/3 mph"
] | B | Average speed for first two hours, S1 = 40 mph
Distance travelled in these two hours, D1 = 80 miles
Average speed for the entire 5 hour ride, S = 20 mph
Total Distance traveller in the entire 5 hour ride, D = 20 x 5 = 100 miles.
Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 100 - 80 = 20
Average speed for the latter 3 hour period S2 = D2/3 = 20/3
Hence, the correct answer is B |
AQUA-RAT | AQUA-RAT-39499 | # If $n$ is a positive integer, does $n^3-1$ always have a prime factor that's 1 more than a multiple of 3?
It appears to be true for all $n$ from 1 to 100. Can anyone help me find a proof or a counterexample?
If it's true, my guess is that it follows from known classical results, but I'm having trouble seeing it.
In some cases, the prime factors congruent to 1 mod 3 are relatively large, so it's not as simple as "they're all divisible by 7" or anything like that.
It's interesting if one can prove that an integer of a certain form must have a prime factor of a certain form without necessarily being able to find it explicitly.
EDITED TO ADD: It appears that there might be more going on here!
$n^2-1$ usually has a prime factor congruent to 1 mod 2 (not if n=3, though!)
$n^3-1$ always has a prime factor congruent to 1 mod 3
$n^4-1$ always has a prime factor congruent to 1 mod 4
$n^5-1$ appears to always have a prime factor congruent to 1 mod 5.
Regarding $n^2-1$: If $n>3$, then $n^2-1=(n-1)(n+1)$ is a product of two numbers that differ by 2, which cannot both be powers of 2 if they are bigger than 2 and 4. Therefore at least one of $n-1,n+1$ is divisible by an odd prime.
The following is multiple choice question (with options) to answer.
If n=4p where p is a prime number greater than 1, how many different positive even divisors does n have, including n? | [
"1",
"2",
"3",
"4"
] | C | We're told that N = 4P and that P is a prime number greater than 1. Let's TEST P = 2; so N = 8
The question now asks how many DIFFERENT positive EVEN divisors does 8 have, including 8?
8:
1,8
4,2
How many of these divisors are EVEN? 2,4,8…..3 even divisors.
ANSWER:C |
AQUA-RAT | AQUA-RAT-39500 | Show Tags
18 Jun 2014, 06:09
Thanks much Bunuel
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1820
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The perimeter of square S is 40. Square T is inscribed in square S. [#permalink]
Show Tags
18 Jun 2014, 20:26
1
maggie27 wrote:
Can anybody please explain me that why are we not considering the option of a 7 * 7 square inscribed into the square S as dis would give us the area less than 50.
Also note that area of inscribed square is always half than that of the original square
As Bunuel pointed out, if it goes less than 50, it means some of the vertex is not touching side of the original square.
_________________
Kindly press "+1 Kudos" to appreciate
Senior Manager
Joined: 15 Sep 2011
Posts: 321
Location: United States
WE: Corporate Finance (Manufacturing)
Re: The perimeter of square S is 40. Square T is inscribed in square S. [#permalink]
Show Tags
01 Jul 2015, 18:04
If $$x^{2}$$ is area of square, then find x, one side of the square. If square is inscribed, then diagonal is the length of larger square and therefore the diagonal is $$10$$. To determine the side, the formula also includes the area of the square, $$x^{2}$$. So, if $$2x^{2} = 100$$ then $$x^{2}=50$$
D.
Thanks,
A
Director
Joined: 04 Jun 2016
Posts: 568
GMAT 1: 750 Q49 V43
Re: The perimeter of square S is 40. Square T is inscribed in square S. [#permalink]
Show Tags
31 Jul 2016, 20:43
Fabino26 wrote:
The perimeter of square S is 40. Square T is inscribed in square S. What is the least possible value of the area of square T ?
A. 45
B. 48
C. 49
D. 50
E. 52
The following is multiple choice question (with options) to answer.
The perimeter of one square is 24m & that of another is 32m. Perimeter of a square whose area is equal to the sum of the areas of the 2 squares will be | [
"20 m",
"24 m",
"28 m",
"40 m"
] | D | Perimeter of square = 4 * Side
Perimeter of first square = 24 m.
Side of first square =
∴ Area of first square =
Perimeter of second square = 32 m.
Side of second square =
∴ Area of second square =
Sum of the areas of two squares = 36 + 64 = 100 m2
∴ Side of square =
∴ Perimeter of square = 4 * 10 = 40 m.
D |
AQUA-RAT | AQUA-RAT-39501 | (1) Kevin spent a total of $18.00 on beer. (2) Kevin bought 3 more cans of beer than bottles of beer. Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that Kevin bought Let B = the NUMBER of Bottles that Kevin bought So, we can write: C + B = 15 Statement 1: Kevin spent a total of$18.00 on beer
The COST of C cans = ($1.00)C = 1C The COST of B bottles = ($1.50)B = 1.5B
So, we can write: 1C + 1.5B = 18.00
When we combine this equation with the equation we created from the given information, we have:
C + B = 15
1C + 1.5B = 18.00
Since we COULD solve this system for C and B, we COULD determine the number of bottles of beer that Kevin bought.
(of course, we won't solve the system, since that would be a waste of our valuable time!)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: Kevin bought 3 more cans of beer than bottles of beer
We can write: C = B + 3
When we combine this equation with the equation we created from the given information, we have:
C + B = 15
C = B + 3
Since we COULD solve this system for C and B, we COULD determine the number of bottles of beer that Kevin bought.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
The following is multiple choice question (with options) to answer.
The price of a gallon of gasoline was $30 on the 15th of March. By the 15th of April, the price per gallon had increased by 20%, and by the 15th of May the price had increased again to a total of $45 per gallon. What was the percent change in the price of a gallon of gasoline between the 15th of April and the 15th of May? | [
"20%",
"25%",
"30%",
"35%"
] | B | Price of a gallon of gasoline was $30 on the 15th of March
Price of a gallon of gasoline increased by 20 %so the price on 15th of April = 1.2*30 = $36
Price of a gallon of gasoline was $45 on 15th of May
so there was a increase of $9 from 15th of april to 15 th of may
% increase = 9/36 * 100 = 25 %
Correct answer - B |
AQUA-RAT | AQUA-RAT-39502 | # Thread: Trig. with ratio question
1. ## Trig. with ratio question
Hello,
$\triangle$ABC is an acute triangle and H is the triangle's orthocenter.
Express the ratio of $\triangle$ABH's area to $\triangle$ABC's area through the triangle's angles.
(No sketch is given)
According to the answer key, the answer is supposed to be:
$\frac{\triangle ABH}{\triangle ABC} = \cot\alpha * \cot\beta$
Any help?
Thanks in advance.
2. Please consider the attached figure, given any acute $\triangle ABC$ where $AH_A, BH_B$ and $CH_C$ are three altitudes from the vertices $A,B$ and $C$. And $H$ is the triangle's orthocenter. Also let $\angle A = \alpha$, $\angle B=\beta$ and $\angle C=\gamma$. Also note that $\angle 1+\angle 3=\alpha$ and $\angle 2 + \angle 4=\beta$.
By definition, we have
$\frac{\triangle ABH}{\triangle ABC}=\frac{\frac{1}{2}\cdot HH_C\cdot AB}{\frac{1}{2}\cdot CH_C\cdot AB}=\frac{HH_C}{CH_C}$
Consider the right triangle $\triangle ACH_C$, we have $\cot\alpha =\frac{AH_C}{CH_C}$, which implies that $CH_C=\frac{AH_C}{\cot\alpha}$
Now consider the two right triangles $\triangle ACH_A$ and $\triangle BCH_B$, we have $\angle 1 + \angle\gamma =90$ and $\angle 2 +\angle \gamma =90$, hence $\angle 1 = \angle 2=90-\angle \gamma$
The following is multiple choice question (with options) to answer.
In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases. | [
"2:3",
"4:5",
"16:9",
"7:9"
] | C | Sol. Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.
Then,
((1/2) X xX 3h)/(1/2) X y X 4h) =4/3 x/y =(4/3 X 4/3)=16/9
Required ratio = 16 : 9.
Ans: C |
AQUA-RAT | AQUA-RAT-39503 | # How to combine ratios? If $a:b$ is $2:5$, and $c:d$ is $5:2$, and $d:b$ is $3:2$, what is the ratio $a:c$?
How would I go about solving this math problem?
if the ratio of $a:b$ is $2:5$ the ratio of $c:d$ is $5:2$ and the ratio of $d:b$ is $3:2$, what is the ratio of $a:c$?
I got $a/c = 2/5$ but that is not a correct answer.
-
Hint: Ratio $\,a:b = 2:5\,$ is the same as $$\frac{a}{b}=\frac{2}{5}$$ – DonAntonio Aug 20 '12 at 15:48
First thing, your c:d is not clear, – Rahul Taneja Aug 20 '12 at 16:46
Thanks, I fixed it. – jbman223 Aug 20 '12 at 16:48
Maybe it helps you to simply set e.g. $a=30$ and figure out what the other numbers must be in that case. – celtschk Aug 20 '12 at 17:01
These ratios are just simple equations. For example $a:b=2:5$ is $$a= \frac{2}{5}b$$ No need for confusing tricks here. Just substitutions : $$a = \frac{2}{5}b = \frac{2}{5}\frac{2}{3} d = \frac{2}{5}\frac{2}{3}\frac{2}{5} c = \frac{8}{75} c$$ So that $$a:c = 8:75$$
-
The following is multiple choice question (with options) to answer.
Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=4/5, what is the ratio of rectangle A’s area to rectangle B’s area? | [
"5/4",
"25/16",
"4/5",
"16/25"
] | D | The area of rectangle A is ab.
c=5a/4 and d=5b/4.
The area of rectangle B is cd=25ab/16.
The ratio of rectangle A's area to rectangle B's area is ab / (25ab/16) = 16/25.
The answer is D. |
AQUA-RAT | AQUA-RAT-39504 | We are given: .a
5 = 120 .and .a6 = 720
Then: .r .= .a
6/a5 .= .720/120 .= .6
. . The "rule" is multiply-by-six.
Therefore, the preceding term is: .a
4 = 20.
See? .We could have eyeballed the problem . . .
5. Originally Posted by Soroban
. . There is a simpler solution.
I always tell my students that I have a tendancy to make things harder than they have to be.
-Dan
The following is multiple choice question (with options) to answer.
There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 18, then find the smaller number? | [
"30",
"66",
"77",
"88"
] | A | Let the two positive numbers be 5x and 8x respectively.
8x - 5x = 18
3x = 18 => x = 6
=> Smaller number = 5x = 30.
Answer: A |
AQUA-RAT | AQUA-RAT-39505 | ### Show Tags
23 Dec 2016, 09:03
2x+50/5x+40=4/6, find x, then don't get into decimals, approx 17.something then 2(17)+5(17)= approx 122
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9558
Location: Pune, India
Re: Two mixtures A and B contain milk and water in the ratios [#permalink]
### Show Tags
09 Nov 2017, 02:28
4
bmwhype2 wrote:
Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?
A. 144
B. 122.5
C. 105.10
D. 72
E. 134
Responding to a pm:
Here is the weighted average method of solving it:
Concentration of milk in the first mixture = 2/7 = 18/63 = 90/315
Concentration of milk in the second mixture = 5/9 = 35/63 = 175/315
Concentration of milk in the resultant mixture = 2/5 = 126/315
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (175/315 - 126/315) / (126/315 - 90/315) = 49 / 36
So 36 gallons of mixture B needs 49 gallons of A
90 gallons of B will need (49/36)*90 = 122.5 gallons
The numbers in the question are hard to work with. In most GMAT questions, the numbers fall easily in place. It is the concept that you have to focus on.
_________________
Karishma
Veritas Prep GMAT Instructor
Senior SC Moderator
Joined: 22 May 2016
Posts: 3284
Two mixtures A and B contain milk and water in the ratios [#permalink]
### Show Tags
09 Nov 2017, 11:23
1
1
bmwhype2 wrote:
Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?
The following is multiple choice question (with options) to answer.
A 100-litre mixture of milk and water contains 49 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x? | [
"27.5 litres",
"26.67 litres",
"27.67 litres",
"28.57 litres"
] | D | Working formula ...
Initial Concentration*Initial Volume=Final Concentration*Final Volume.
Let X is the part removed from 100 lts.
49%(1-X/100)^2 = 25% * 100%
(1-x/100)^2=25/49------>(1-x/100)^2=(5/7)^2
100-X=500/7
x=28.57...
Ans D |
AQUA-RAT | AQUA-RAT-39506 | Thanks for any help. I am totally confused.
1. 👍 0
2. 👎 0
## Similar Questions
1. ### Probability
jeff has 8 red marbles, 6 blue marbles, and 4 green marbles that are the same size and shape. he puts the marbles into a bag, mixes the marbles, and randomly picks one marble. what is the probability that the marble will be blue?
2. ### math
A bag contains 5 red marbles, 6 white marbles, and 8 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red? The probability that all the marbles are red is? What
3. ### Math ~ Check Answers ~
1. There are 35 marbles in a bag: 9 blue marbles, 8 green marbles, 4 red marbles, 8 white marbles, and 6 yellow marbles. Find P (red). Write the probability as a fraction in simplest form, a decimal, and a percent. a.) 4/31,
4. ### math
there are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag. what is the theoretical probability of randomly drawing either a red marble or a blue marble?
1. ### math check probability
5. A bag contains 7 green marbles and 4 white marbles. You select a marble at random. What are the odds in favor of picking a green marble? A. 7:11**? B. 7:4 C. 4:7 D. 3:7 ------------------------------------ 6. Food Express is
2. ### Math
There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag. What is the theoretical probability of randomly drawing a red marble and then a green marble? 10%
3. ### math
A bag contains 8 red marbles, 5 blue marbles, 8 yellow marbles, and 6 green marbles. What is the probability of choosing a red marble if a single choice is made from the bag? is it 8/27 ?
4. ### statistics
The following is multiple choice question (with options) to answer.
A marble shop contains 6 blue marbles, 7 red marbles, and 7 green marbles. If 4 marbles are purchased at random from the shop, what is the probability that the 4 marbles will be blue? | [
"5/19",
"9/20",
"1/57",
"15/57"
] | C | It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 6/20
Probability of choosing 2nd card of the same type: 5/19
Probability of choosing 3rd card of the same type: 4/18
Multiply and you get 1/57
Answer C. |
AQUA-RAT | AQUA-RAT-39507 | speed-of-light, measurements, si-units, metrology, length
Title: How is the Length of a Meter Physically Measured? I have two parts to this question.
First, I understand that the meter is defined as the distance light travels in 1/299,792,458 seconds. But how is this distance actually measured? The second is obviously from an atomic clock, but Wikipedia makes it appear that the distance is calculated by the counting of wavelengths. For the count of wavelength to be useful you must calculate the physical length of it, which is dependent on the speed of light, which is defined with meters and to increase the accuracy of the measurement, NIST recommends the use of a specific wavelength of laser (which is in meters). Does this not make the actual measurement of the length of the meter circular? Or does the fact that the speed of light is a constant defined in meter/second over come the appearance of the circular logic? The way I see the circular logic would be if the speed of light ever changed, the length of the meter would also change, which make it impossible for us to know the speed of light changed without referencing it back to an older physical object.
Further, the measurement is done in a vacuum but we can not actually create a perfect vacuum, so I assume there would be a pressure range allowed on the vacuum, and pressure measurements are also based on the definition of a meter (I would think this would further add circular logic to laboratory measurements performed in air and adjusted for refraction).
Second, how is this measurement for the meter actually used to calibrate physical objects? I.e. If I buy a meter stick that has been calibrated against the national standard, how do they actually compare the length of the stick vs the wavelength measurements? The length of a meter bar can be measured using a HeNe laser. The laser used is chosen because we are very good at stabilizing the frequencies it outputs. This means that if we can measure the frequencies before the testing, they will remain steady during the testing. A cesium clock can be used to determine the frequencies of light used with great precision, as the second is defined from said clocks.
Once you have a good measurement of frequency, you have a good measurement of wavelength (assuming a reasonable medium... a vacuum is best, as the speed of light is defined in a vacuum, thus no uncertainty). With a wavelength in hand, you can do interferometry.
The following is multiple choice question (with options) to answer.
Which greatest possible length can be used to measure exactly 12 meter 65 cm, 15 meter 25 cm and 10 meter 65 cm | [
"45cm",
"5cm",
"4cm",
"15cm"
] | B | Explanation:
Convert first all terms into cm.
i.e. 1265 cm, 1525cm, 1065cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 5.
Option B |
AQUA-RAT | AQUA-RAT-39508 | We're asked for the price at which the TOTAL PROFIT from the sale of these units = $42,000. Since there are 600 units, then each unit has to bring in$42,000/600 = $70 in profit. The COST of each unit is$90, so to hit that total profit, we just need to increase that $90 by$70 on each unit.
$90 +$70 = $160 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at: Rich.C@empowergmat.com The Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★ SVP Joined: 03 Jun 2019 Posts: 1739 Location: India Re: A television manufacturer produces 600 units of a certain model each [#permalink] ### Show Tags 16 Sep 2019, 09:23 RSOHAL wrote: A television manufacturer produces 600 units of a certain model each month at a cost to the manufacturer of$90 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus the manufacturer's cost to produce) on the sales of these units will be at least $42,000? A$110
B$120 C$140
D$160 E$180
A television manufacturer produces 600 units of a certain model each month at a cost to the manufacturer of $90 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus the manufacturer's cost to produce) on the sales of these units will be at least$42,000?
Let the selling price per unit be $x 600 (x - 90) >= 42,000 x -90 >= 70 x>=$160
IMO D
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."
Please provide kudos if you like my post. Kudos encourage active discussions.
My GMAT Resources: -
The following is multiple choice question (with options) to answer.
Albert buys 4 cows and 9 cows for $13,400. If he sells the cows at 10% profit and the cows at 20% profit, then he earns a total profit of $1880. The cost of a cow is: | [
"1000",
"3000",
"2000",
"4000"
] | C | C
2000
Let C.P. of each cow be $x and C.P. of each cow be $y.
Then, 4x + 9y = 13400 -- (i)
And, 10% of 4x + 20% of 9y = 1880
2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)
Solving (i) and (ii), we get : x = 2000 and y = 600.
Cost price of each cow = $2000. |
AQUA-RAT | AQUA-RAT-39509 | In solving many kinematic problems for gears, there is a key rule to key in mind: When two gears are meshing, the tangential velocities of both gears at the point of meshing are equal.
(Also, as said in EMiller's answer, gear C seems to be the smaller orange gear, and gear D the larger yellow gear, contrary to the diagram's labelling).
This rule will help provide the equations we need to solve this problem. Note that there are 2 pairs of meshing gears (A meshes with C and B meshes with D). The points of meshing for each pair are $P$ and $Q$ respectively. Therefore, this gives us 2 equations to work with. It is then a matter of relating the tangential velocities at the point of meshing with the velocity of the centre of gear C and D. I will define the following terms:
Let $v_{a,p}, v_{c,p}$ be the tangential velocities of gears A and C, respectively, at point P.
Let $v_{b,q}, v_{d,q}$ be the tangential velocities of gears A and C, respectively, at point P.
Let $V$ be the velocity of the centre of gear C and D.
(The following diagrams represents gears A and C, and then B and D, as circles that are in pure rolling with one another:)
According to the rule above, we get the following two equations:
$$v_{a,p}=v_{c,p} \qquad (Eq.1)$$ $$v_{b,q}=v_{d,q} \qquad (Eq.2)$$
$v_{a,p}$ and $v_{b,q}$ are simple enough to determine since the centres of gears A and B don't move:
$$v_{a,p}=\omega_a R_a = 0.4\text{m/s} \qquad v_{b,q}=\omega_b R_b = 0.4\text{m/s}$$
The following is multiple choice question (with options) to answer.
A wheel that has 4 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is: | [
"49",
"4",
"12",
"6"
] | D | Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 4 :: 21 : x 14 * x = 4 x 21
x = (4 x 21)/14
x = 6.
Answer is D. |
AQUA-RAT | AQUA-RAT-39510 | # Simple and Compound Interest Problem
• January 14th 2011, 01:41 AM
dumluck
Simple and Compound Interest Problem
Hi All,
Q:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received$605 as interest. What was the value of his total savings before investing in these two bonds?
1. $5500 2.$ 11000
3. $22000 4.$ 2750
5. $44000 Answer Explanation... 1. Interest for the first year of the simple compound bond is 275/2 -$275.
2. So we need to determine the rate of interest based on this so...
605 - 550 = 55. That's the difference between the interest earned on the simple vs compound interest bonds.
55/275 * 100/1 = 11/55 * 100/1 = 20% Interest
3. 275 represents 20% interest of a number
275/20 * 100/1 = 55/4 * 100/1 = $1375. 4. This represents half the money so 1375*2 =$2750. (D).
My questions is: Why are we using 55. I.E. The difference between the two interest to determine the interest in 2. What does this 55 represent (besides the difference between the two?)
• January 14th 2011, 09:20 AM
Soroban
Hello, dumluck!
I'm not impressed with their explanation.
Quote:
Q: Shawn invested one half of his savings in a bond
that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, compounded annually, for the same 2 years at the same rate of interest and received$605 as interest.
What was the value of his total savings before investing in these two bonds?
. . $1.\;\5500 \qquad 2.\;\11000 \qquad 3.\;\22000 \qquad 4.\;\2750 \qquad 5.\;\44000$
Let $\,r$ be the annual interest rate for both accounts.
Let $\,P$ be the amount invested in each account.
The following is multiple choice question (with options) to answer.
A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate? | [
"10",
"99",
"87",
"66"
] | A | P ---- 2P ---- 8 years
2 1/4 P ---- 10 years
Answer: A |
AQUA-RAT | AQUA-RAT-39511 | shortest-path
Description:
Tentative distances to B and D determined. C not yet visible.
Shortest distance from previous step taken. No new information on shortest path to B. Tentative distance to C now known. No new information on D.
We choose to backtrack to A, and then move to D because the distance to D (2) is smaller than that to C (4). We update the tentative distance to C because via D it is shorter than via B.
We choose to move to C directly from D because it is shorter (3) than backtracking and going via A (4). Moving to C gives us no new shorter distances. All nodes visited, so end. It's more traditional to describe dijkstra with the open and closed sets:
You start with an empty closed set and an open set containing $ \{ (A,0) \}$
You select the node with the lowest cost and remove it from the open set, then you expand the neighbours and add them to the open set $ \{ \{B,1\} \{D,2\} \}$ or update the elements in the open set and Add the selected node to the closed set
step1:
open = $ \{ (B,1, A), (D,2, A) \}$
closed = $\{(A)\}$
step2:
open = $ \{ (C,4, B), (D,2, A) \}$
closed = $\{(A),(B,A)\}$
step3:
open = $ \{ (C,3, D) \}$
closed = $\{(A),(B,A),(D,A)\}$
There is no actual sense of "backtracking" because you are considering all the open nodes in parallel.
Many other search algorithms work in the same way with the only difference in how a node is selected from the open set. Breadth-first takes the oldest node in the set, depth-first takes the youngest, Dijkstra takes the node with the lowest cost, A* takes the node with the lowest cost+heuristic.
The following is multiple choice question (with options) to answer.
Two children want to walk together to visit their aunt, who lives exactly 8 blocks north and 7 blocks east of their current location. If they travel only along streets and do not travel diagonally, the shortest possible route connecting the two points is exactly 15 blocks. How many different 15-block routes may they take to travel the shortest possible distance to their aunt’s house? | [
"15!*8!*7!",
"15!*8*7",
"23!/(8!*7!)",
"15!/(8!*7!)"
] | D | If they need to walk 8 blocks north and 7 blocks east, we can express this route as NNNNNNNNEEEEEEE. The question thus asks us how many ways we can arrange those letters.
The number of arrangements of 15 things is 15!
We then divide by the repetitions of N's and E's, which are 8! and 7! respectively.
The number of walking routes is 15!/(8!*7!).
The answer is D. |
AQUA-RAT | AQUA-RAT-39512 | fact to find the root. 16 is 4 be multiplied ( or ) divided so that the sum the. Is difficult to find the square root of a number is a number ensure you the. Table below 112−7=105 105−9=96 96−11=85 85−13=72 72−15=57 57−17=40 40−19=21 21−21=0 we have already learnt the square of is... Contribute @ geeksforgeeks.org to report any issue with the above content obtained 0 at th! Find out the square root of 121 using repeated subtraction even number is odd expression. Find square root of a number ends in an odd number is multiplied by itself gives the number a! Of repeated subtraction, repetitive subtraction of odd numbers starting from 1, find whether given... Starting from 1, find whether the following numbers are perfect squares or not have subtract odd numbers starting 1... Itself is said to be followed while calculating the square root of a square. Be multiplied ( or ) divided so that the sum of the given.! Using this property to find the square root of 2, then it is to. We have to find the square of 100 first how can one become good at Data structures Algorithms... Squaring a number ] 99 – … repeated subtraction learnt the square of... Root number set of real numbers subtract odd numbers from the given number doubts, problems we... That of an even number is a perfect square since it can be obtained by the method of repeated method... Real numbers to be performed finding the square root and cube root of a number through repeated.. A number of the number is a perfect square then find its square root… repeated.. And 8 in the table below guess and check method can also be used to find out square... When multiplied by itself gives the number or not is 16 and square root of a number example square 4... Find out the square of a number is a perfect square by which 250 is to be or... Of 100 is 10 and 169 hy the method of repeated subtraction.!
The following is multiple choice question (with options) to answer.
If the square root of 1,600 is 40, then what is 40 squared? | [
"1,600",
"16",
"4",
"440"
] | A | A number squared is a number multiplied by itself
Ex) 4 squared is 16 because 4*4=16
The square root of a number is a number, that if squared, would equal the number you're trying to find the square root of.
Ex) What is the square root of 16? The square root of 16=4, so 4 squared equals 16
So to solve this equation you would do:
The square root of 1,600=40, so 40 squared equals 1,600
(A) |
AQUA-RAT | AQUA-RAT-39513 | # Simple and Compound Interest Problem
• January 14th 2011, 01:41 AM
dumluck
Simple and Compound Interest Problem
Hi All,
Q:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received$605 as interest. What was the value of his total savings before investing in these two bonds?
1. $5500 2.$ 11000
3. $22000 4.$ 2750
5. $44000 Answer Explanation... 1. Interest for the first year of the simple compound bond is 275/2 -$275.
2. So we need to determine the rate of interest based on this so...
605 - 550 = 55. That's the difference between the interest earned on the simple vs compound interest bonds.
55/275 * 100/1 = 11/55 * 100/1 = 20% Interest
3. 275 represents 20% interest of a number
275/20 * 100/1 = 55/4 * 100/1 = $1375. 4. This represents half the money so 1375*2 =$2750. (D).
My questions is: Why are we using 55. I.E. The difference between the two interest to determine the interest in 2. What does this 55 represent (besides the difference between the two?)
• January 14th 2011, 09:20 AM
Soroban
Hello, dumluck!
I'm not impressed with their explanation.
Quote:
Q: Shawn invested one half of his savings in a bond
that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, compounded annually, for the same 2 years at the same rate of interest and received$605 as interest.
What was the value of his total savings before investing in these two bonds?
. . $1.\;\5500 \qquad 2.\;\11000 \qquad 3.\;\22000 \qquad 4.\;\2750 \qquad 5.\;\44000$
Let $\,r$ be the annual interest rate for both accounts.
Let $\,P$ be the amount invested in each account.
The following is multiple choice question (with options) to answer.
There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of $ 12,000 after 3 years at the same rate? | [
"2160",
"3120",
"3972",
"6240"
] | C | Let P = $ 100. Then, S.I. $. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = $ 12000. T = 3 years and R = 10% p.a.
CI = 3972
ANSWER C |
AQUA-RAT | AQUA-RAT-39514 | 4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?
(C) 6 - rains for 5 days from day 56-60. So 10 guys worked for 55 days and accomplished half of the work. If 6 more guys are added to the job then the rate is 16/1100. (since one man's rate is 1/1100). Half the job left means 550/1100 is left. Therefore 550/16 = 34.375 days of more work. Since there were 40 days between day 60 and job completion, it must've rained for 40-34.375 = 5.625 or ~6 days. (I'm not sure if this is correct)
5. If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is divided by t?
(E) 45 - 64.12 = 6412/100 or 1603/25. 1603/25 gives a remainder of 3, 3206/50 gives remainder of 6 and so on ..pattern = factors of 3. so to get remainder of 45, we multiply everything by 15: 1603*15/(25*15) = 24045/375.
The following is multiple choice question (with options) to answer.
A can complete a project in 20 days and B can complete the same project in 40 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed? | [
"18 days",
"20 days",
"26.67 days",
"16 days"
] | B | Let X = the number of days taken to complete the project.
The amount of work done by A is (x-10) * (1/20).
The amount of work done by B is (x) * (1/40).
(1/20)*(x-10) + (1/40)*(x) = 1
(x/20) + (x/40) - (10/20) = 1
3x/40 = 3/2
x = 20
Therefore, the answer is B: 20. |
AQUA-RAT | AQUA-RAT-39515 | # Given an Alphabet, how many words can you make with these restrictions.
I'm trying to understand from a combinatoric point of view why a particular answer is wrong. I'm given the alphabet $\Sigma = \{ 0,1,2 \}$ and the set of 8 letter words made from that alphabet, $\Sigma_8$ . There are $3^8 =6561$ such 8 letter words.
How many words have exactly three 1's?
How many words have at least one each of 0,1 and 2?
In the first question I reasoned that first I choose $\binom{8}{3}$ places for the three 1's. Then I have 5 place left where I can put 0's and 2's which is $2^5$. Since I can combine each choice of 1 positions with every one of the $2^5$ arrangements of 0's and 2's then I get $\binom{8}{3}\cdot 2^5 = 1792$ which is correct.
I tried applying the same reasoning to the second question and got $\binom{8}{3}\cdot 3^5 = 13608$ which is obviously wrong.
Was my reasoning sound in the first question or did I just happen to get the correct answer by chance? If it is sound, why doesn't it work with the second question?
-
Why was this question marked down, especially more than two years after it was asked? – Robert S. Barnes Mar 15 '14 at 17:43
The following is multiple choice question (with options) to answer.
How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? | [
"5040",
"2548",
"300",
"547"
] | A | LOGARITHMS' contains 10 different letters.
Required number of words = Number of arrangements of 10 letters, taking 4 at a time.
= 10P4
= (10 x 9 x 8 x 7)
= 5040.
ANSWER A |
AQUA-RAT | AQUA-RAT-39516 | MHF Helper
Problem : A bike manufacturer has a plant in Minneapolis and another in Philly. The Minneapolis plant produces 70% of the bikes, of which 1% are defective. The Philly plant produces the other 30%, of which 0.5% are defective.
1: What percentage of bikes made by this company are defective? a) 1% b) 0.85% c) 0.5% d) 1.5%
I figured that 1% of 70% of production is 0.7% of total production. 0.5% of 30 is 30/100 = 0.3/2 = 0.15. 0.15+0.7= 0.85 so B
2. A bike made by this company is found to be defective. What is the probability that it was produced by the Minneapolis plant? a) .824 b) .176 c) .699 d) .301
3. non defective. What is the probability that is it made by the Minneapolis plant? a) .824 b) .176 c) .699 d) .301
4. A bike made by this company is found to be defective. Probability it was produced by the philly plant? a) .824 b) .176 c) .699 d) .301
5. Non defective. Probability made by Philly plant? a) .824 b) .176 c) .699 d) .301
Frankly I cannot follow what you posted.
Lets do #2. If a bike is found to be defective, then what is the probability that the bike was produced by the Minneapolis plant?
The bike was produced at one of two plants: $$\displaystyle \mathcal{P}(D)=\mathcal{P}(D\cap M)+\mathcal{P}(D\cap P)$$
Now let us work on the question, if a bike is defective what is the probability it came from Minneapolis?
The following is multiple choice question (with options) to answer.
Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.65%, what fraction of the products was checked by worker y? | [
"1/5",
"1/2",
"2/3",
"1/4"
] | B | x: 0.5% is 0.15%-points from 0.65%.
y: 0.8% is 0.15%-points from 0.65%.
Therefore the ratio of products checked by y:x is 1:1.
Thus, worker y checked 1/2 of the products.
The answer is B. |
AQUA-RAT | AQUA-RAT-39517 | fluid-dynamics, newtonian-gravity
and so, when we put these values into $d=\frac{m}{\rho_W\,C_D\,A}\,\log\left(1+\frac{h_{eff}\,C_D\,A}{m\,\left(\frac{1}{\rho_B}-\frac{1}{\rho_W}\right)}\right)$ we get:
$$\begin{array}{ll}h=1{\rm m}&d = 1.13073{\rm m}\\h=3{\rm m}&d = 1.33494{\rm m}\\h=5{\rm m}&d = 1.48701{\rm m}\\h=7.5{\rm m}&d = 1.63506{\rm m}\\h=10{\rm m}&d = 1.75372{\rm m}\end{array}$$
giving the total depths of penetration of your feet (the above values plus $1.9{\rm m})$:
$$\begin{array}{ll}h=1{\rm m}&d = 3.03{\rm m}\\h=3{\rm m}&d = 3.23{\rm m}\\h=5{\rm m}&d = 3.39{\rm m}\\h=7.5{\rm m}&d = 3.54{\rm m}\\h=10{\rm m}&d = 3.65{\rm m}\end{array}$$
as you can see, a reasonable accounting for the transition epoch adds quite a bit of depth for shallow dives (a whole metre for a 1m dive) but only 20cm for the 10m dive.
On entering the water, the acceleration throughout the transition epoch is:
$$a(y)=e^{-\frac{A\, C_D\, \rho_W\, y}{m}} \left(-\frac{A\, C_D \, g\, h
The following is multiple choice question (with options) to answer.
50 men took a dip in a water tank 30 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4m3 , then the rise in the water level in the tank will be: | [
"20 cm",
"25 cm",
"33.3 cm",
"50 cm"
] | C | Explanation:
Total volume of water displaced =(4 x 50) m3 = 200 m3
Rise in water level = 200/30×20= 0.333m = 33.3cm
Answer: C |
AQUA-RAT | AQUA-RAT-39518 | Hence, if we eliminate at most $13$ sets of $2$ numbers, then each difference of the $2$ numbers from the remaining $105-13=92$ is distinct. However, the difference of $2$ numbers is either $1,2,\cdots, 88,89(=99-10)$, which is a contradiction. QED
Added : Byron Schmuland and Ross Millikan independently show eleven 2-digit numbers so that every pair has a different sum. So, we now know that the minimum $n_{\text{min}}$ of $n$ has to satisfy $\color{red}{12\le n_{\text{min}}\le 15}$.
The following is multiple choice question (with options) to answer.
The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers? | [
"29",
"70",
"92",
"Cannot be determined"
] | D | Explanation:
Let the ten's digit be x and units digit by y.
Then,
(10x + y) - (10y + x) = 63
9(x - y) = 63
x - y = 7
Thus, none of the numbers can be determined.
ANSWER IS D |
AQUA-RAT | AQUA-RAT-39519 | Back
## A Test Question
Today, Pearl’s $9$ grandchildren are coming to visit! She loves to spoil them, so she opens her purse and finds $13$ dollar bills.
In how many different ways can Pearl distribute those dollars amongst her grandchildren? Keep reading to find out, or skip to today’s challenge for a similar problem.
As we’ll see, there are a lot of ways for Pearl to distribute her dollars! So, let’s start with a smaller example. Last week, Pearl’s $3$ favorite grandchildren visited, and at that time, she had $4$ dollar bills to give them. To visualize how they could be distributed, she laid them out in a row, along with some pencils to divide them into $3$ groups.
We’ll represent the dollars with stars $\large \star$ and divisions between groups with bars $\large{|}.$ One arrangement that Pearl found was $\large \star \; | \, \star \star \; | \; \star$ which represents $1$ dollar for the first grandchild, $2$ dollars for the second, and $1$ dollar for the third. Another arrangement was $\large \star \; | \: | \, \star \star \, \star$ which represents $1$ dollar for the first grandchild, $0$ dollars for the second, and $3$ dollars for the third.
To create $3$ groups, we need $2$ bars to separate the stars. So, to count the total number of arrangements into groups, we can count where in the line of stars and bars we can place those bars to define the groups.
The following is multiple choice question (with options) to answer.
Mrs. Napier has 26 stickers to give to 4 students for a reward. How many
stickers will each student get? Will there be any stickers left over? | [
"6-5",
"5-4",
"3-6",
"2-3"
] | A | 26/4 = 2 R 5 Mrs. Napier will give each student 6 stickers and there
will be 5 left over.
correct answer A |
AQUA-RAT | AQUA-RAT-39520 | MHF Helper
Problem : A bike manufacturer has a plant in Minneapolis and another in Philly. The Minneapolis plant produces 70% of the bikes, of which 1% are defective. The Philly plant produces the other 30%, of which 0.5% are defective.
1: What percentage of bikes made by this company are defective? a) 1% b) 0.85% c) 0.5% d) 1.5%
I figured that 1% of 70% of production is 0.7% of total production. 0.5% of 30 is 30/100 = 0.3/2 = 0.15. 0.15+0.7= 0.85 so B
2. A bike made by this company is found to be defective. What is the probability that it was produced by the Minneapolis plant? a) .824 b) .176 c) .699 d) .301
3. non defective. What is the probability that is it made by the Minneapolis plant? a) .824 b) .176 c) .699 d) .301
4. A bike made by this company is found to be defective. Probability it was produced by the philly plant? a) .824 b) .176 c) .699 d) .301
5. Non defective. Probability made by Philly plant? a) .824 b) .176 c) .699 d) .301
Frankly I cannot follow what you posted.
Lets do #2. If a bike is found to be defective, then what is the probability that the bike was produced by the Minneapolis plant?
The bike was produced at one of two plants: $$\displaystyle \mathcal{P}(D)=\mathcal{P}(D\cap M)+\mathcal{P}(D\cap P)$$
Now let us work on the question, if a bike is defective what is the probability it came from Minneapolis?
The following is multiple choice question (with options) to answer.
A motor pool has 300 vehicles of which 30 percent are trucks. 15 percent of all the vehicles in the motor pool are diesel, including 15 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel? | [
"165%",
"90%",
"60%",
"55%"
] | C | Trucks = 30% of 300 = 90
Other Vehicles (Excluding Trucks) = 300-90 = 210
Diesel Vehicle = 15% of 300 = 45 (Including 15 Trucks)
Other Diesel Vehicles (Excluding Trucks) = 45-15 = 30
Trucks that are NOT diesel = 90 - 15 = 75
Other Vehicles that are NOT diesel Vehicles = 210-30 = 180
Required % = (180/300)*100 = 60%
Answer: option C |
AQUA-RAT | AQUA-RAT-39521 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters shouldn't the profit be calculated as a percentage of cost price, which would turn out to 22 meters. Below is what I think
(11/22) * 100
The cost price should be 22 because the profit of 11 meters is subtraccted from the selling price of 33 meters.
The question might be wrong and that is why I am seeking help.
• Profit is calculated on the cost price. The shopkeeper paid $x$ amount to buy 33 meters of cloth. When he sold the cloth, he got $x + x/3$ amount of money. Why would you subtract anything? Aug 17 '16 at 18:10
• There is often ambiguity in translating from ordinary language to math, but here I'd interpret the thing the way your book does. That is, I understand the problem to say "the shopkeeper sells $33$ units for the same amount that it would cost him to buy $44$ units." Thus, if we imagine it costs him $1$ to buy a unit, he buys the stuff for $33$ and sells it for $44$...thus a gain of $11$, or $33\frac 13\%$ of his outlay.
– lulu
Aug 17 '16 at 18:12
• Okay I get it. @shardulc it is not the selling price of 33 meters but the 33 meters of cloth. Aug 17 '16 at 18:15
The following is multiple choice question (with options) to answer.
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit? | [
"2000",
"2098",
"2028",
"2218"
] | A | Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.Answer: A |
AQUA-RAT | AQUA-RAT-39522 | (1) Kevin spent a total of $18.00 on beer. (2) Kevin bought 3 more cans of beer than bottles of beer. Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that Kevin bought Let B = the NUMBER of Bottles that Kevin bought So, we can write: C + B = 15 Statement 1: Kevin spent a total of$18.00 on beer
The COST of C cans = ($1.00)C = 1C The COST of B bottles = ($1.50)B = 1.5B
So, we can write: 1C + 1.5B = 18.00
When we combine this equation with the equation we created from the given information, we have:
C + B = 15
1C + 1.5B = 18.00
Since we COULD solve this system for C and B, we COULD determine the number of bottles of beer that Kevin bought.
(of course, we won't solve the system, since that would be a waste of our valuable time!)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: Kevin bought 3 more cans of beer than bottles of beer
We can write: C = B + 3
When we combine this equation with the equation we created from the given information, we have:
C + B = 15
C = B + 3
Since we COULD solve this system for C and B, we COULD determine the number of bottles of beer that Kevin bought.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
The following is multiple choice question (with options) to answer.
As a bicycle salesperson, David earns a fixed salary of $40 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>3 | [
"I only",
"III only",
"II,III only",
"I,III only"
] | C | II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);
III. y>3 --> if David sold 3 bicycles this week then this week he earned 40+3*6=$58, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $40. So y must be more than 3;
I. y<3x --> is not always true.
Answer: C |
AQUA-RAT | AQUA-RAT-39523 | Alternate
10% of journey's = 40 km
Then, total journey = 400 kms
\eqalign{ & {\text{And,}}\,{\text{Average speed}} \cr & = \frac{{{\text{Total distance }}}}{{{\text{Total time}}}} \cr & 30\% {\text{ of journey}} \cr & = 400 \times \frac{{30}}{{100}} \cr & = 120{\text{ km}} \cr & \cr & 60\% {\text{ of journey}} \cr & = 400 \times \frac{{60}}{{100}} \cr & = 240{\text{ km}} \cr & \cr & 10\% {\text{ of journey}} \cr & = 400 \times \frac{{10}}{{100}} \cr & = 40{\text{ km}} \cr & {\text{Average speed}} \cr & = \frac{{400}}{{\frac{{120}}{{20}} + \frac{{240}}{{40}} + \frac{{40}}{{10}}}} \cr & = \frac{{400}}{{ {6 + 6 + 4} }} \cr & = \frac{{400}}{{16}} \cr & \therefore {\text{Average speed}} = 25{\text{ km/hr}} \cr}
The following is multiple choice question (with options) to answer.
In a group of 100 people, 55 have visited Iceland and 43 have visited Norway. If 61 people have visited both Iceland and Norway, how many people have visited neither country? | [
"60",
"61",
"62",
"63"
] | D | This is an example of a standard Overlapping Sets question. It has no 'twists' to it, so you'll likely find using the Overlapping Sets Formula to be a fairly easy approach. If you're not familiar with it, then here is the Formula:
100= 55 + 43 - 61 + (# in Neither Group)
=63
The prompt gives you all of the numbers you need to get to the correct answer. Just plug in and solve.
D |
AQUA-RAT | AQUA-RAT-39524 | per hour. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. What is its speed? 4) A car goes 250 km in 4 hours. The total time is 5 seconds, so t = 5. 4. Aptitude Questions and Answers. Learn how teachers can make BrainPOP-style assessments by using the Quiz Mixer with a My BrainPOP account. Marco drove from home to work at an average speed of 50 miles per hour and returned home along the same route at an average speed of 46 miles per hour. ⇒ Distance traveled = Speed × Time = 200/29 × 29/5 = 40 Km ⇒ Distance between city and town = 40/2 = 20 km. Refer how to solve speed problems to …Feb 28, 2016 · Hi Friends This Video will helps you to Understand the concept on the Time and Distance(Quantitative Aptitude). Distance, Speed and Time Problems This Math quiz is called 'Distance, Speed and Time Problems' and it has been written by teachers to help you if you are studying the subject at middle school. Speed Distance and Time. When the train is crossing a moving object, the speed has to be taken as the relative speed of the train with respect to the object. 42 minutes on DVD. In this speed, distance and time worksheet, students read statements and then mentally determine the speed, distance or time in a given problem. GMAT Time, Speed, Distance and Work, GRE Time, Speed, Distance and Work, SAT Time Speed Distance and Work, SSC - CGL Time Speed Distance and Work, Tags gmat gre cat sat act time speed distance formula time speed distance concepts time speed distance problems with solutions Rate This Lesson Velocity word problems The following velocity word problems will strengthen your knowledge of speed, velocity, In the end, the difference between speed and velocity should be clear. 5, and we get an average speed of 10 miles per hour. You will have 4 minutes to complete this challenge. The distance for the second leg is 200, and the rate is v+25, so the time of the second leg is. 5 miles traveled. A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. As for your brand-new red sports car, your friend was …Now just plug in your values for speed and time to solve for distance: d = 40 miles/hour x
The following is multiple choice question (with options) to answer.
In a race of 4Kms A beats B by 100m or 25 seconds, then time taken by A is | [
"15 min 8 sec",
"16 min 15 sec.",
"8 min 15 sec.",
"10 min 17 sec."
] | B | s=d/t
where t=d/s
therefore 4000*25/100=1000sec
convert 1000sec into min
we get 16min 15sec
ANSWER:B |
AQUA-RAT | AQUA-RAT-39525 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours. P is opened at 10 am and Q is opened at 11 am, while R is kept open throughout. If the tank was initially empty, approximately at what earliest time it will be full if P or Q cannot be opened together and each of them needs to be kept closed for at least 15 minutes after they have been opened for 1 hour?
A. $$4:30 PM$$
B. $$6:00 PM$$
C. $$6: 30 PM$$
D. $$8:30 PM$$
E. $$9:30 PM$$
To access all the questions: Question of the Week: Consolidated List
_________________
Number Properties | Algebra |Quant Workshop
Success Stories
Guillermo's Success Story | Carrie's Success Story
Ace GMAT quant
Articles and Question to reach Q51 | Question of the week
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities
Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets
| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com
The following is multiple choice question (with options) to answer.
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in? | [
"3 9/87 hrs",
"3 9/27 hrs",
"3 9/17 hrs",
"3 2/17 hrs"
] | C | Net part filled in 1 hour = 1/5 + 1/6 - 1/12 = 17/60
The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.
Answer: C |
AQUA-RAT | AQUA-RAT-39526 | 5%------------------20%
so ratio is 1:4 in final mixture
Earlier type 1 alcohol was 1
Now it is 1/5 ----> so loss of 4/5 = 80%...
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 56303
Re: Mixture problem-Can someone explain this [#permalink]
### Show Tags
02 Sep 2010, 08:52
11
14
zest4mba wrote:
If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?
a 3%
b 20%
c 66%
d 75%
e 80%
Question can be solved algebraically or using allegation method.
Algebraic approach:
Initial solution is "half water/half alcohol mix" means it's 50% (0.5) alcohol solution.
Let the portion replaced be $$x$$ and the volume of initial solution be 1 unit.
Then the amount of alcohol after removal of a portion will be $$0.5(1-x)$$ and the amount of alcohol added will be $$0.25x$$, so total amount of alcohol will be $$0.5(1-x)+0.25x$$. On the other hand as in the end 30% alcohol solution was obtained then the amount of alcohol in the end was $$0.3*1$$.
So $$0.5(1-x)+0.25x=0.3$$ --> $$x=0.8$$, or 80%.
_________________
Intern
Joined: 06 Jul 2010
Posts: 6
Re: Mixture problem-Can someone explain this [#permalink]
### Show Tags
02 Sep 2010, 10:11
zest4mba wrote:
If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?
a 3%
b 20%
c 66%
d 75%
e 80%
The following is multiple choice question (with options) to answer.
The ratio, by volume, of soap to alcohol to water in a certain solution is 6:30:90. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 150 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? | [
"1200",
"1300",
"1500",
"1800"
] | D | soap:alcohol
Initial ratio soap:alcohol: water --> 6:30:90
Initial soap:alcohol = 6/30 =6:30
after doubled soap:alcohol =2* 6/30 = 12/30=12:30
Initial soap:water = 6/90=6:90
after halved soap:water: 1/2 * 6/90 = 3/90 = 3:90= 12:360
After soap: alcohol:water --> 12:30:360
given alcohol 150 cubic centimeter.
ratio is 60:150:1800 (12:30:360)
For 150 cubic centimeter of Alcohol ---1800 cu cm water is required.
Answer-D |
AQUA-RAT | AQUA-RAT-39527 | Let us take another mixture problem:
Question 2:
Two types of rice costing $60 per kg and$40 per kg are mixed in a ratio 2: 3. What will be the cost per kg of mixed rice?
Solution:
• Can we apply alligation to this question?
• Can we assume the price of the mixed rice to be $x per kg and make this diagram? • Now does it mean that $$x – 40 = 2$$ and $$60 – x = 3$$? • We can see that we are getting 2 different values of x above • Thus, we cannot use alligation in this way here • Well, we can still use these numbers by using proportions here as follows, • $$\frac{x-40}{60-x}=\frac{2}{3}$$ $$\Rightarrow 3x-120=120-2x$$ $$\Rightarrow 5x=240$$ $$\Rightarrow x=48$$ However, as you can see that we still need to do some calculations, and hence alligation does not help us a lot here. • Hence, we always recommend, for questions such as this where we are asked to find the resultant concentration upon mixing\combining direct parameters of two entities, it is always preferred to use a weighted average. So, let us apply that. • Since the two rice are mixed in the ratio 2 : 3, let us assume the quantities mixed be 2a and 3a • Thus, after which we can write $$x=\frac{60\times 2a+40\times 3a}{2a+3a}$$ $$\Rightarrow x=\frac{120a+120a}{5a}$$ $$\Rightarrow x=\frac{240a}{5a}$$ $$\Rightarrow x=48$$ • So, the final concentration or the price of the mix will be$48 per kg
• The point to be noted here is that all mixture questions need not be tackled with the alligation method
Alligation in other topics?
Alligation is generally associated with mixtures of questions
The following is multiple choice question (with options) to answer.
Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction? | [
"337",
"278",
"189",
"271"
] | C | CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100] = Rs. 189.
Answer:C |
AQUA-RAT | AQUA-RAT-39528 | Then, if we keep doing this, we are going to approach to a vertical line with zero area. If we keep increasing its width while decreasing its height, we will approach to a horizontal line with zero area. So, both of these extreme endpoints give us an area of $$0$$. Therefore, it makes sense to have a rectangle with equal sides in order to make the area size as large as possible. b) Now, we imagine that $$w$$ and $$h$$ cannot be equal to each other. However, we still want to maximize the area size while keeping the perimeter at $$36$$ cm. Then, given that the sides have to be integer-valued, we can decrease either one of the optimal $$w$$ or $$h$$ values by $$1$$ while increasing the other one by $$1$$, e.g., $$w=10$$ cm and $$h=8$$ cm ($$A = 10 \cdot 8 = 80$$).
The following is multiple choice question (with options) to answer.
The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area? | [
"15%",
"20%",
"25%",
"30%"
] | C | Sol. Required change = (20*100)/(100-20)=25%
C |
AQUA-RAT | AQUA-RAT-39529 | Decide the seating order of the people, starting from one of the brothers, say Ivan. Then position the other brother, Alexei, in one of the two slots (fourth and fifth) that fulfill the "separated by two others" condition - $2$ options. Then with Ivan and Alexei resolved, order the remaining five people in one of $5!=120$ ways. Finally add the empty chair to the right of someone, $7$ options, giving $2\cdot 120\cdot 7 = 1680$ options.
$\underline{Get\;the\;bothersome\;empty\;chair\;out\;of\;the\;way\;\;as\;a\;marker\;at\;the\;12\;o'clock\;position}$
• Brother $A$ has $7$ choices of seats
• Brother $B$ now has only $2$ choices (one clockwise and one anticlockwise of $A$ )
• the rest can be permuted in $5!$ ways
• Thus $7\cdot2\cdot5!\;$ways
The following is multiple choice question (with options) to answer.
In a camp, there is a meal for 120 men or 200 children. If 100 children have taken the meal, how many men will be catered to with remaining meal? | [
"41",
"30",
"35",
"60"
] | D | D
60
There is a meal for 200 children.
100 children have taken the meal.
Remaining meal is to be catered to 100 children.
Now, 200 children 120 men.
100 children = (120/200)x 100 = 60 men. |
AQUA-RAT | AQUA-RAT-39530 | You want to end up with exactly 6 gallons in the unmarked container.
(YES: the unmarked container > 6 gallons!)
Your mission is to do it in exactly 9 moves, and using the MINIMUM number of gallons of water
from the water supply.
A "move" is any pouring, filling or emptying.
For example, filling the 9-gal from the water supply,
then pouring it to fill the 4-gal container,
then emptying it is 3 moves: fill - pour - empty.
How do you do it?
Spoiler:
(1) Fill the "9".
Code:
* *
|/////|
|/////| * *
|/////| | |
|/////| | |
* * |//9//| | 0 |
| | |/////| | |
| 0 | |/////| | |
*-----* *-----* *-----*
4 9 U
(2) Pour "9" into "4".
Code:
* *
| |
| | * *
| | | |
|/////| | |
* * |/////| | 0 |
|/////| |//5//| | |
|//4//| |/////| | |
*-----* *-----* *-----*
4 9 U
(3) Empty "4",
Code:
* *
| |
| | * *
| | | |
|/////| | |
* * |/////| | 0 |
| | |//5//| | |
| 0 | |/////| | |
*-----* *-----* *-----*
4 9 U
(4) Pour "9" into "4".
Code:
* *
| |
| | * *
| | | |
| | | |
* * | | | 0 |
|/////| | | | |
|//4//| |//1//| | |
* - - * * - - * * - - *
4 9 U
(5) Pour "9" into "U".
The following is multiple choice question (with options) to answer.
If Henry were to add 5 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full? | [
"25",
"40",
"64",
"80"
] | B | 7/8x-3/4x=5 galls
1/8*x=5gallons
x=40 gallons
ANSWER:B |
AQUA-RAT | AQUA-RAT-39531 | Now find the time Rick spends running.
$\displaystyle t_{r,R}=\frac{D}{2v_r}$
Now just add the two times up and you’re done.
$\displaystyle t_R=\frac{D}{2v_w}+\frac{D}{2v_r}=\frac{D}{2v_wv_r}\left(v_w+v_r\right)$
#### PART B. Find Rick’s average speed for covering the distance D.
You were given the total distance and have calculated the total time. Recall that average speed is equal to the total distance traveled divided by the amount of time it took to travel this distance.
$\displaystyle v_{ave,\:R}=\frac{2v_rv_w}{v_w+v_r}$
#### PART C. How long does it take Tim to cover the distance?
Tim walks at speed $\displaystyle v_w$ half the time and runs at speed $\displaystyle v_r$ for the other half.
$\displaystyle v_{ave,\:T}=\frac{v_w+v_r}{2}$
The time is just the distance divided by the average speed.
$\displaystyle t_T=\frac{D}{\frac{v_w+v_r}{2}}=\frac{2D}{v_r+v_w}$
#### PART D. Who covers the distance D more quickly?
Imagine that both Rick and Tim do all of their walking before they start to run. Rick will start running when he has covered half of the total distance. When Tim reaches half of the total distance, will he already have started running?
#### PART E. In terms of given quantities, by what amount of time, Δt, does Tim beat Rick?
$\displaystyle \Delta t=\frac{D\left(v_w-v_r\right)^2}{2v_rv_w\left(v_r-v_w\right)}$
This is just simple subtraction between the two computed times.
The following is multiple choice question (with options) to answer.
During a recent track meet, Peter ran x meters of the 100 meter dash in 4 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash? | [
"4zx",
"4z/x",
"4x/z",
"4/xz"
] | B | Speed of Peter = x/4 meters per second
Time needed to run z meters = DISTANCE/SPEED = z / (x/4) = 4z/x
Option B
The values 100m and 200m have no role to play here and are just given to confuse you. |
AQUA-RAT | AQUA-RAT-39532 | ### Exercise 20
Mr. Halsey has a choice of three investments: Investment A, Investment B, and Investment C. If the economy booms, then Investment A yields 14% return, Investment B returns 8%, and Investment C 11%. If the economy grows moderately, then Investment A yields 12% return, Investment B returns 11%, and Investment C 11%. If the economy experiences a recession, then Investment A yields a 6% return, Investment B returns 9%, and Investment C 10%.
1. Write a payoff matrix for Mr. Halsey.
2. What would you advise him?
#### Solution
1. .14.08.11.12.11.11.06.09.10.14.08.11.12.11.11.06.09.10 size 12{ left [ matrix { "." "14" {} # "." "08" {} # "." "11" {} ## "." "12" {} # "." "11" {} # "." "11" {} ## "." "06" {} # "." "09" {} # "." "10"{} } right ]} {}
2. 010010 size 12{ left [ matrix { 0 {} # 1 {} # 0{} } right ]} {}, 010010 size 12{ left [ matrix { 0 {} ## 1 {} ## 0 } right ]} {} or 010010 size 12{ left [ matrix { 0 {} # 1 {} # 0{} } right ]} {}, 001001 size 12{ left [ matrix { 0 {} ## 0 {} ## 1 } right ]} {}, value=.11value=.11 size 12{"value"= "." "11"} {}
### Exercise 21
Mr. Thaggert is trying to decide whether to invest in stocks or in CD's(Certificate of deposit). If he invests in stocks and the interest rates go up, his stock investments go down by 2%, but he gains 1% in his CD's. On the other hand if the interest rates go down, he gains 3% in his stock investments, but he loses 1% in his CD's.
The following is multiple choice question (with options) to answer.
A person want to give his money of $3600 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share? | [
"$2000",
"$1200",
"$2500",
"$1800"
] | B | B's share = 3600*3/9 = $1200
Answer is B |
AQUA-RAT | AQUA-RAT-39533 | ### Show Tags
16 Jun 2018, 09:16
agdimple333 wrote:
During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of$25.00 Did the store sell more sweaters than shirts during the sale?
1) The average of the prices of all of the shirts and sweaters that the store sold during the sale was $21.00 2) The total of the prices of all of the shirts and sweaters that the store sold during the sale was$420.00
The average of the prices of all of the shirts and sweaters that the store sold during the sale was $21.00. Since the average price of$21 is closer to $25 than it is to$15, there must be more sweaters sold than shirts. Statement one alone is sufficient.
Statement Two Alone:
The total of the prices of all of the shirts and sweaters that the store sold during the sale was $420.00. It’s possible that 12 sweaters and 8 shirts are sold since 12 x 25 + 8 x 15 = 300 + 120 =$420. It’s also possible that 6 sweaters and 18 shirts are sold since 6 x 25 + 18 x 15 = 150 + 270 = $420. In the former example, more sweaters were sold; however, in the latter example, more shirts were sold. Statement two alone is not sufficient. Answer: A _________________ # Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com 181 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Intern Joined: 11 Mar 2018 Posts: 1 Re: During a sale, a clothing store sold each shirt at a price of$15 and [#permalink]
### Show Tags
24 Jan 2020, 02:24
1
Bunuel wrote:
dchow23 wrote:
from statement 2,
shirts x
sweaters y
15x +20y = 420
Can we say that since 60 is a common multiple between the 15 and 20, there will be more than one answer that can satisfy the equation?
If there is a common multiple for
The following is multiple choice question (with options) to answer.
On decreasing the price of a cooler by 25 %, its sale is increased by 50%. The effect on the revenue is? | [
"4 % decrease",
"12.5 % increase",
"16% decrease",
"16% increase"
] | B | Net% change in revenue
= ( x + y + xy/100) %
= [-25 + 50+ ( -25 x 50)/100]% or 12.5%
ANSWER:B |
AQUA-RAT | AQUA-RAT-39534 | ### Show Tags
12 Nov 2013, 20:38
I solved by thinking about how you find the sum of a series of numbers; average of that set multiplied by how many numbers are in the set. Noting that it was only even numbers in the set A-C could be eliminated since their sums would be FAR too small. From there I thought about how many even numbers would be in the set if k was 157; in this case 78, with 156 being the final number in the set. Since 2 was the first, and 156 the last, the average would be 79. So this makes no sense for an answer.
Next I looked at 159. I see that there are 79 even integers between 0 and 159, ranging from 2-158. The average would be 80, leading to a sum of 80*79, thus E must be the answer
Kudos [?]: 190 [0], given: 40
Manager
Joined: 23 May 2013
Posts: 189
Kudos [?]: 125 [0], given: 42
Location: United States
Concentration: Technology, Healthcare
Schools: Stanford '19 (M)
GMAT 1: 760 Q49 V45
GPA: 3.5
Re: The sum of the even numbers between 1 and n is 79*80, where [#permalink]
### Show Tags
06 Jun 2014, 11:35
Notice that $$\frac{79*80}{2} = \sum_{i=1}^{\79}i,$$ or is 1+2+3+....+78+79.
Therefore $$79*80 = 2\sum_{i=1}^{\79}i$$, or that 79*80 = 2+4+6+...+156+158.
Since 159 includes the even numbers until 158, the answer is E.
Kudos [?]: 125 [0], given: 42
Senior Manager
Joined: 07 Apr 2012
Posts: 442
Kudos [?]: 85 [0], given: 58
Re: The sum of the even numbers between 1 and n is 79*80, where [#permalink]
### Show Tags
The following is multiple choice question (with options) to answer.
The average (arithmetic mean) of eight numbers is 47.1. If the sum of half of these numbers is 158.4, what is the average of the other half? | [
"12.8",
"24.2",
"54.6",
"72.1"
] | C | arithmetic mean = sum / total numbers
sum = 47.1 * 8 = 376.8
sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 376.8-158.4 = 218.4
Arithmetic mean of the 4 nos = 218.4/4 = 54.6
Hence, C is the answer. |
AQUA-RAT | AQUA-RAT-39535 | # Permutations of the word $\text{TRIANGLE}$ with no vowels together.
First of all, $$\text{TRIANGLE}$$ has $$8$$ distinct letters, $$3$$ of which are vowels($$\text{I, A, E}$$) and rest are consonants($$\text{T, R, N, G, L}$$).
While attempting this, I came up with the idea of putting alternate vowels and consonants not to group same types together.
So, I decided to form two 'batteries'. [$$\text{V}$$ stands for Vowels and $$\text{C}$$ stands for consonants.]
$$\text{V} \text{ C}\text{ V} \text{ C}\text{ V}$$
And,
$$\text{C} \text{ V}\text{ C} \text{ V}\text{ C}$$
If we count all the permutations and then add them up (Mutually Exclusive Events), we can get total number of permutations.
Now, For the first case,
$$3$$ vowels can be arranged in the $$3$$ spaces required in $$3! = 6$$ ways
From $$5$$ consonants, $$2$$ spaces can be filled with consonants in $$^5P_2 = 20$$ ways
One battery, $$(8 - 3- 2) = 3$$ letters to arrange.
Total number of permutations : $$6 * 20 * 4! = 2880$$.
In Second case,
From $$3$$ vowels, $$2$$ spaces can be filled with vowels in $$^3P_2 = 6$$ ways
From $$5$$ consonants, $$3$$ spaces can be filled with consonants in $$^5P_3 = 60$$ ways.
One battery, $$(8 - 2- 3) = 3$$ letters to arrange.
Total number of permutations : $$6 * 60 * 4! = 8640$$
So, Total number of permutations for the word $$\text{TRIANGLE} = 2880 + 8640 = 11520$$
The following is multiple choice question (with options) to answer.
In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions? | [
"None of these",
"64",
"120",
"36"
] | D | Explanation :
The word 'DETAIL' has 6 letters which has 3 vowels (EAI) and 3 consonants(DTL)
The 3 vowels(EAI) must occupy only the odd positions.
Let's mark the positions as (1) (2) (3) (4) (5) (6).
Now, the 3 vowels should only occupy the 3 positions marked as (1),(3) and (5) in any order.
Hence, number of ways to arrange these vowels = 3P3
= 3! = 3 x 2 x 1 = 6
Now we have 3 consonants(DTL) which can be arranged in the remaining 3 positions in any order
Hence, number of ways to arrange these consonants = 3P3
= 3! = 3 x 2 x 1 = 6
Total number of ways
= number of ways to arrange the vowels x number of ways to arrange the consonants
= 6 x 6 = 36. Answer : Option D |
AQUA-RAT | AQUA-RAT-39536 | ## anonymous 5 years ago 100 people are present in a party. If each of them must do a handshake with all the other people, how many handshakes should be done? Please explain how to get the answer, thanks!
1. anonymous
you need 2 people for an hand shake and u have 100 people so i think that its C(100,2) but i am not sue of it..
2. anonymous
$\sum_{n=1}^{99}n=\frac{1}{2}\times99\times100=4950$
3. anonymous
Could you solve it using factorials, please?
4. anonymous
hmm i found the answer as 9900
5. amistre64
if there are 3 people: 1,2 ; 1,3 ; 2,3 .... is that right?
6. anonymous
Think about it like this: the first person has 99 people to shake hands with, the second person has 98 because they've already shaken hands with the first, the third has 97...
7. anonymous
yea but its harder to calculate this like that... so i think C(100,2) better way of solve
8. amistre64
5054 if we do that ..... add all the numbers from 1 to 100 :)
9. anonymous
No, all the numbers from 1 to 99.
10. amistre64
n(n+1) ------ :) 2
11. amistre64
ack .... 99 then lol
12. amistre64
wouldnt the last guy have noone to shake hands with?
13. anonymous
mhmh yea but there is 100 people and they and we need 2 people to shake hands so that it should be 100 x 99 /2,
14. anonymous
Yeah, the last guy has no-one to shake hands with, that's why it's sum of the first 99 integers, not the first 100.
15. anonymous
yea you right
16. amistre64
The following is multiple choice question (with options) to answer.
3 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place? | [
"10",
"15",
"3",
"9"
] | C | the formula to count handshakes is n(n−1)2n(n−1)2
Where n is the number of people
=> 3(3-1)/2 = 3*2/2 = 6/2 = 3
=> the answer is C(3) |
AQUA-RAT | AQUA-RAT-39537 | # probability of the 3rd pick is a boy
10 students are in a class,
4 of these students are boys and 6 are girls
the teacher wanted to randomly select 3 students to represent the class in an event
what is the probability that the 3rd student is a boy?
Here is what I have tried
the probability of that 1st student is a boy = 4/10 the probability of that 1st student is a girl = 6/10
the probability of that 3rd student is a boy means one of these scenarios
1- previously 2 boys were selected
2- previously 2 girls were selected
3- previously a boy and a girl were selected
in case (1) the probability of having the 3rd is a boy would be 2/8
in case (2) the probability of having the 3rd is a boy would be 4/8
in case (3) the probability of having the 3rd is a boy would be 3/8
So which one of these is the right answer?!
• You can do it that way but there's no need to, each choice is like any other so the answer is $\frac 4{10}$. To do it the way you started, you need to weight each case by the probability of being in that scenario. – lulu Apr 28 at 22:50
• @lulu but when we select the 1st and 2nd student, number of students change and the distribution changed as well.. how come it is the same as the 1st pick? – asmgx Apr 28 at 22:53
• If you specify the first two choices then of course the answer changes, but if you don't specify them then there is no information from them, – lulu Apr 28 at 22:56
• – JMoravitz Apr 28 at 22:59
• If you were to simplify that god-awful expression however... it very simply results in $\frac{4}{10}$... which as many of the answers and comments in the linked question as well as other answers and comments here already will tell you makes sense as being "the third" person to be selected is not different enough from being "the first" person selected, so naturally the probability the third is a boy is going to be the same as the probability the first is a boy which is obviously $\frac{4}{10}$ with no tedious calculations required. – JMoravitz Apr 28 at 23:50
The following is multiple choice question (with options) to answer.
Out of a classroom of 7 boys and 4 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions? | [
"2/165",
"4/165",
"7/165",
"2/33"
] | B | The number of ways to choose three people is 11C3=165.
The number of ways to choose three girls is 4C3=4.
P(only girls are chosen)=4/165
The answer is B. |
AQUA-RAT | AQUA-RAT-39538 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters shouldn't the profit be calculated as a percentage of cost price, which would turn out to 22 meters. Below is what I think
(11/22) * 100
The cost price should be 22 because the profit of 11 meters is subtraccted from the selling price of 33 meters.
The question might be wrong and that is why I am seeking help.
• Profit is calculated on the cost price. The shopkeeper paid $x$ amount to buy 33 meters of cloth. When he sold the cloth, he got $x + x/3$ amount of money. Why would you subtract anything? Aug 17 '16 at 18:10
• There is often ambiguity in translating from ordinary language to math, but here I'd interpret the thing the way your book does. That is, I understand the problem to say "the shopkeeper sells $33$ units for the same amount that it would cost him to buy $44$ units." Thus, if we imagine it costs him $1$ to buy a unit, he buys the stuff for $33$ and sells it for $44$...thus a gain of $11$, or $33\frac 13\%$ of his outlay.
– lulu
Aug 17 '16 at 18:12
• Okay I get it. @shardulc it is not the selling price of 33 meters but the 33 meters of cloth. Aug 17 '16 at 18:15
The following is multiple choice question (with options) to answer.
Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? | [
"2000",
"2978",
"2682",
"2688"
] | A | (10*10)/100 = 1%loss
100 --- 99
? --- 1980 =>
Rs.2000
Answer:A |
AQUA-RAT | AQUA-RAT-39539 | # If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
Let $f(x)$ be a function such that $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$. Then for what value of $k$ is the relation $f(x + k) = f(x)$ necessarily true for every real $x$?
The answer/solution suggested in my module is like this: "this is a bit involved but can be proved that $k=6$". Could anybody explain me this?
-
Just add two consecutive relations: $$f(x+2)+f(x)=f(x+1)$$ $$f(x+3)+f(x+1)=f(x+2)$$ Then you'll get $$f(x+3)+f(x)=0$$ vor every real $x$. You have also $f(x+6)+f(x+3)=0$ for every real $x$, and therefore $f(x)=f(x+6)$ for every real $x$.
The following is multiple choice question (with options) to answer.
. Star question:
If f(1)=4 and f(x+y)=f(x)+f(y)+7xy+4,then f(2)+f(5)=? | [
"125",
"977",
"289",
"1077"
] | A | Let x =1 and y = 1
f(1 + 1) = f(1) + f(1) + 7 x 1 x 1 + 4 ⇒⇒ f(2) = 19
Let x =2 and y = 2
f(2 + 2) = 19 + 19 + 7 x 2 x 2 + 4 ⇒⇒ f(4) = 70
Let x = 1 and y = 4
f( 1 + 4) = 4 + 70 + 28 + 4 = 106
f(2) + f(5) = 125
Answer:A |
AQUA-RAT | AQUA-RAT-39540 | (A) 1
(B) 2
(C) 4
(D) 6
(E) 8
11. What is the area of the shaded region of the given 8 X 5 rectangle?
The following is multiple choice question (with options) to answer.
The perimeter of a square is 52 m. Find the area of the square. | [
"132 m².",
"169 m².",
"146 m².",
"189 m²."
] | B | Perimeter of square = 52 m
But perimeter of square = 4 × side
Therefore, 4 × side = 52 m
Therefore, side= 52/4 m = 13m
Now, the area of the square = (side × side)
Therefore, area of the square = 13 × 13 m² = 169 m².
ANSWER :B |
AQUA-RAT | AQUA-RAT-39541 | => 18x/4=154
x=308/9
TOTAL WAGES PAID WILL BE
(12/11 + 18/7)*309/9
PLEASE TELL ME WHERE I AM WRONG
Lets try -
SW4 wrote:
Elana was working to code protocols for computer processing. She did 11/18 of the job and allowed Andy to finish it. They both work at the same rate and receive the same hourly pay. If the difference between the amounts they were paid was $154, what was the total amount the two were paid for the entire coding job? Let total work be 1 Elana did 11/18 Andy did 7/18 Thus share of wages will be in the ratio of work done by them.... Ratio of their work is as follows - Elana : Andy = 11 : 7 and the total work is 18 Proportion of difference in work = Proportion of Difference in pay So, 4 =$ 154
Or, 1 = $154/4 And Total pay = 154/4*18 =>$ 693
The following is multiple choice question (with options) to answer.
A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent should the number of hours worked be increased? | [
"12.5%",
"20%",
"25%",
"50%"
] | C | Assume
Hours Worked: 10 hours
Hourly Wage: 10 $
Weekly Wage: 100 $
After decrease of 20 % in Hourly Wage would become 8 $
Hours Worked would have to be 12.5 hours in order to maintain Weekly Wage of 100 $
% increase in number of hours worked = (12.5 - 10 ) / 10
= 0.25 * 100
= 25%
Answer is C |
AQUA-RAT | AQUA-RAT-39542 | --------------
Back to your question, after finding the 2 breakpoints, namely 0, and 1. We then, split it into 3 different parts:
1. x < 0:
When x < 0, x is negative, right? So |x| = -x
When x < 0, x - 1 is also negative, right? So |x - 1| = -(x - 1) = -x + 1
So, when x < 0, your function will be (without absolute signs) f(x) = |x| + |x - 1| = -x + (-x + 1) = -2x + 1
2. 0 <= x < 1: (pay attention to the <= sign, it should be less than or equal, not just less than, since you should consider x = 0 as well)
This can be worked out in almost the same manner.
3. x >= 1:
This part should be simple too, just follow my example. :)
Last edited: Sep 2, 2009
The following is multiple choice question (with options) to answer.
If xy > 0, which of the following must be negative? | [
"-x/-y",
"x/y",
"-x/y",
"2xy"
] | C | - / + = -
Answer : C |
AQUA-RAT | AQUA-RAT-39543 | Since the the percentage of tagged fish in the second catch approximates the percentage of tagged fish in the pond, the approximate number of fish in the pond is:
0.04(total fish) = 50
This equation assumes that there are 50 fish tagged in the total population. We do not know that. The only thing we know is that that the percentage of tagged fish in the second catch is 4%. The question says that 4% approximates the number of tagged fish in the pond. So this is the true equation we have:
Quote:
.04 (total) = tagged fish
We are missing two variables. We don't know the total fish and we don't know the tagged fish.
If there are 16 tagged fish, then choice A is correct.
If there are 26 tagged fish, then choice B is correct, and etc.
If we assume that the number of fish in the second catch (50) is the number of fish tagged, then yes the total fish would be 1250. However, that's not what the question provides. I think this question is written poorly.
So the question states that "In a certain pond, 50 fish were caught, tagged, and returned to the pond."
From this sentence, we can deduce that there are indeed a total of 50 tagged fish in the pond. The only way to have some other number of tagged fish in the pond is if there were already some number of tagged fish in the pond (in which case, the question would have told us so) or if either more fish were tagged afterward or some of the tagged fish were removed from the pond (again, we would have been told). Since we have no such information, we cannot assume that there might be some other number of tagged fish in the pond.
Perhaps you are missing the fact that 50 fish are caught TWICE: first all of them are tagged, and the second time, the tagged fish are counted.
_________________
Scott Woodbury-Stewart
Founder and CEO
GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions
CEO
Joined: 12 Sep 2015
Posts: 2705
Re: In a certain pond, 50 fish were caught, tagged, and returned [#permalink]
### Show Tags
The following is multiple choice question (with options) to answer.
Of the goose eggs laid at a certain pond, 1/4 hatched and 4/5 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond? | [
"1200",
"1300",
"1400",
"1500"
] | D | Let x be the number of eggs that were laid.
(2/5)(4/5)(1/4)x = 120
(8/100)x = 120
x = 1500
The answer is D. |
AQUA-RAT | AQUA-RAT-39544 | Veritas Prep Reviews
Math Expert
Joined: 02 Sep 2009
Posts: 37109
Followers: 7252
Kudos [?]: 96499 [0], given: 10752
### Show Tags
05 Jun 2013, 23:44
PKPKay wrote:
Sarang wrote:
For 1 hour-
Machine A rate- 2000 envelopes
Machine B+C rate- 2400 envelopes
Since A + C = 3000 envelopes A's rate is 2000 envelopes as above, C has a rate of 1000 envelopes per hour.
Which makes machine B's rate as 1400 envelopes per hour.
Thus, it will take 8 hours to manufacture 12000 envelopes.
I did this but shouldn't the work take 9 hours instead?
In 8 hours machine B would have made 1400 * 8 = 11200 envelopes.
In order to make 12000 it would require a fraction of an hour to create 200 more envelopes.
Am I mistaken?
Edited the options.
Check for a solution here: machine-a-can-process-6000-envelopes-in-3-hours-machines-b-105362.html#p823509 or here: machine-a-can-process-6000-envelopes-in-3-hours-machines-b-105362.html#p823655
_________________
Intern
Joined: 18 Mar 2013
Posts: 5
Followers: 0
Kudos [?]: 2 [0], given: 45
Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
### Show Tags
07 Jun 2013, 04:35
How much time should one take in solving these kind of questions which involves though simple yet a lot of calculations?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7187
Location: Pune, India
Followers: 2168
Kudos [?]: 14022 [0], given: 222
Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
### Show Tags
09 Jun 2013, 19:52
samheeta wrote:
How much time should one take in solving these kind of questions which involves though simple yet a lot of calculations?
This can be easily done in under 2 mins. If you look at the explanation provided above:
The following is multiple choice question (with options) to answer.
It takes 40 identical printing presses 12 hours to print 500,000 papers. How many hours would it take 30 of these printing presses to print 500,000 papers? | [
"14",
"15",
"16",
"18"
] | C | 40 printing presses can do 1/12 of the job each hour.
30 printing presses can do 3/4*1/12 = 1/16 of the job each hour.
The answer is C. |
AQUA-RAT | AQUA-RAT-39545 | 98% Female, simple interpolation. First premise 90% female, leaves 10%, second premise only leaves 2% of the existing 10%, hence 98% female
-
The following is multiple choice question (with options) to answer.
10 % of 2 is equal to | [
"0.2",
"0.4",
"0.6",
"0.7"
] | A | 10 % of 2 = (10 / 100) * 2 = 0.2
Answer: Option A |
AQUA-RAT | AQUA-RAT-39546 | evolution, population-dynamics
Title: How many humans have been in my lineage? Is it almost the same for every human currently living? If I were to count my father, my grandfather, my great-grandfather, and so on up till, say chimps, or the most common ancestor, or whatever that suits the more accurate answer, how many humans would there have been in my direct lineage?
And would it be almost the same for every human being currently living? A quick back-of-the-envelope answer to the number of generations that have passed since the estimated human-chimp split would be to divide the the split, approximately 7 million years ago (Langergraber et al. 2012), by the human generation time. The human generation time can be tricky to estimate, but 20 years is often used. However, the average number is likely to be higher. Research has shown that the great apes (chimps, gorilla, orangutan) have generation times comparatble to humans, in the range of 18-29 years (Langergraber et al. 2012).
Using 7 million years and 20 years yields an estimated 350000 ancestral generations for each living human. A more conservative estimate, using an average generation time of 28, would result in 250000 generations. However, some have argued that the human-chimp split is closer to 13 million years old, which would mean that approximately 650000 generations have passed (using a generation time of 20 years).
The exact number of ancestral generations for each human will naturally differ a bit, and some populations might have higher or lower numbers on average due to chance events or historical reasons (colonizations patterns etc). However, due to the law of large numbers my guess would be that discrepancies are likely to have averaged out. In any case, the current estimates of the human-chimp split and average historical generation times are so uncertain, so that they will swamp any other effects when trying to calculate the number of ancestoral generations.
However, this is only answering the number of ancestral generations. The number of ancestors in your full pedigree is something completely different. Since every ancestor has 2 parents, the number of ancestors will grow exponentially. Theoretically, the full pedigree of ancestors can be calculated using:
The following is multiple choice question (with options) to answer.
3 years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is | [
"1 years",
"2 years",
"3 years",
"4 years"
] | B | Sol.
Total age of 5 members, 3 years ago = (17 x 5)years = 85 years.
Total age of 5 members now = (85 + 3 x 5)years = 100 years.
Total age of 6 members now = (17 x 6)years = 102 years.
∴ Age of the baby = (102 - 100)years = 2 years
Answer B |
AQUA-RAT | AQUA-RAT-39547 | Let us take another mixture problem:
Question 2:
Two types of rice costing $60 per kg and$40 per kg are mixed in a ratio 2: 3. What will be the cost per kg of mixed rice?
Solution:
• Can we apply alligation to this question?
• Can we assume the price of the mixed rice to be $x per kg and make this diagram? • Now does it mean that $$x – 40 = 2$$ and $$60 – x = 3$$? • We can see that we are getting 2 different values of x above • Thus, we cannot use alligation in this way here • Well, we can still use these numbers by using proportions here as follows, • $$\frac{x-40}{60-x}=\frac{2}{3}$$ $$\Rightarrow 3x-120=120-2x$$ $$\Rightarrow 5x=240$$ $$\Rightarrow x=48$$ However, as you can see that we still need to do some calculations, and hence alligation does not help us a lot here. • Hence, we always recommend, for questions such as this where we are asked to find the resultant concentration upon mixing\combining direct parameters of two entities, it is always preferred to use a weighted average. So, let us apply that. • Since the two rice are mixed in the ratio 2 : 3, let us assume the quantities mixed be 2a and 3a • Thus, after which we can write $$x=\frac{60\times 2a+40\times 3a}{2a+3a}$$ $$\Rightarrow x=\frac{120a+120a}{5a}$$ $$\Rightarrow x=\frac{240a}{5a}$$ $$\Rightarrow x=48$$ • So, the final concentration or the price of the mix will be$48 per kg
• The point to be noted here is that all mixture questions need not be tackled with the alligation method
Alligation in other topics?
Alligation is generally associated with mixtures of questions
The following is multiple choice question (with options) to answer.
If a quarter kg of onions costs 50 paise, how many paise will 100 gm cost? | [
"20 paise",
"65 paise",
"56 paise",
"87 paise"
] | A | Explanation:
Let the required cost be x paise.
Less weight, Less cost (Direct proportion)
250 : 100 : : 50 : x
250 * x = (100 * 50)
x = (100 * 50) / 250
x = 20
ANSWER: A |
AQUA-RAT | AQUA-RAT-39548 | 5. Hello, James!
Another approach . . .
12 Students are in a class.
Five can go to room A, Four to room B, and Three to room C.
How many ways can this happen?
Assign 5 students to room A.
. . There are: . $_{12}C_5 \:=\:\frac{12!}{5!7!} \:=\:792$ ways.
From the remaining 7 students, assign 4 students to room B.
. . There are: . $_7C_4 \:=\:\frac{7!}{4!3!} \:=\:35$ ways.
From the remaining 3 students, assign 3 students to room C.
. . Of course, there is: . $_3C_3 \:=\:1$ way.
Therefore, there are: . $792 \times 35 \times 1 \:=\:27,\!720$ ways.
The following is multiple choice question (with options) to answer.
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 5 employees to 2 different offices? | [
"30",
"32",
"31",
"33"
] | B | Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2*2*2=2^5=32.
Answer: B. |
AQUA-RAT | AQUA-RAT-39549 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 900m covered). So, distance from origin $$= 900 + 1350m = 2250m$$.Physics
The following is multiple choice question (with options) to answer.
A 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? | [
"227",
"266",
"230",
"500"
] | D | Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 48 = 50/3
3(x + 300) = 2400 è x = 500m.
Answer: D |
AQUA-RAT | AQUA-RAT-39550 | c#, beginner, io
Example run:
Welcome to Buzzway Subs!
May I take your order?
Catering Menu:
Sandwich Platter: $39.99
Cookie Platter: $19.99
Purchase how many of Sandwich Platter for $39.99 each?
1
Purchase how many of Cookie Platter for $19.99 each?
2
Subtotal: 79.97
Tax: 4.80
Total: 84.77
Your total due is $84.77.
Pay how much?
85
Your change is $0.23.
--- Receipt ---
1 Sandwich Platter $39.99 ea. $39.99
2 Cookie Platter $19.99 ea. $39.98
Subtotal: $79.97
Tax: $4.80
Total: $84.77
Payment: $85.00
Your change is $0.23.
Thank you for shopping at Buzzway! First, keep track of your instances of a class:
new BuzzwaySubs();
BuzzwaySubs.processCustomer();
That should be:
BuzzwaySubs restaurant = new BuzzwaySubs(); // or `var restaurant`
restaurant.processCustomer();
As it is, the first line is utterly useless. Additionally, this only works because your methods are all static.
Keeping track of your instances is important because what happens when you have two restaurants? You need to know which restaurant is controlled by which class instance so you can manage them appropriately.
Second, declare your variables in the tightest scope possible:
int itemQty = 0;
foreach (var item in order)
{
itemQty = item.Value;
decimal costOfItems = itemQty * cateringMenu[item.Key];
subTotal += costOfItems;
}
That variable should be declared in the foreach loop. You have this probably in a great many places.
foreach (var item in order)
{
int itemQty = item.Value;
decimal costOfItems = itemQty * cateringMenu[item.Key];
subTotal += costOfItems;
}
This is important for many reasons, including keeping your variables from leaking information to other sections of the program, releasing memory when you aren't using it, and more.
Third, your naming does not follow standard C# naming practices:
public static void printCateringMenu()
The following is multiple choice question (with options) to answer.
A restaurant meal cost $35.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between: | [
"$40 and $42",
"$39 and $41",
"$38 and 40",
"$37 and $39"
] | B | let tip=t
meal cost=35.50
range of tip = from 10% of 35.5 to 15% of 35.5 = 3.55 to 5.325
hence range of amount paid= 35.5+T= 39.05 to 40.825
ANSWER:B |
AQUA-RAT | AQUA-RAT-39551 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters shouldn't the profit be calculated as a percentage of cost price, which would turn out to 22 meters. Below is what I think
(11/22) * 100
The cost price should be 22 because the profit of 11 meters is subtraccted from the selling price of 33 meters.
The question might be wrong and that is why I am seeking help.
• Profit is calculated on the cost price. The shopkeeper paid $x$ amount to buy 33 meters of cloth. When he sold the cloth, he got $x + x/3$ amount of money. Why would you subtract anything? Aug 17 '16 at 18:10
• There is often ambiguity in translating from ordinary language to math, but here I'd interpret the thing the way your book does. That is, I understand the problem to say "the shopkeeper sells $33$ units for the same amount that it would cost him to buy $44$ units." Thus, if we imagine it costs him $1$ to buy a unit, he buys the stuff for $33$ and sells it for $44$...thus a gain of $11$, or $33\frac 13\%$ of his outlay.
– lulu
Aug 17 '16 at 18:12
• Okay I get it. @shardulc it is not the selling price of 33 meters but the 33 meters of cloth. Aug 17 '16 at 18:15
The following is multiple choice question (with options) to answer.
An article is bought for Rs.675 and sold for Rs.900, find the gain percent? | [
"16 2/3%",
"30%",
"33 1/3%",
"33 1/6%"
] | C | Explanation:
675 ---- 225
100 ---- ? => 33 1/3%
ANSWER IS C |
AQUA-RAT | AQUA-RAT-39552 | javascript
Title: More efficient version of an ID calculator in JavaScript The following function takes two numbers that are linked with a "user" and calculates an ID number based on that. I have been trying to make this as clean as possible, and would like some advice on how to make this more efficient. an example of the input would be "12195491" for the num and "3120" for the ts, which would output "8511"
function getidnumber(num, ts) {
num = num.substr(4, 4);
ts = ((ts == undefined) ? "3452" : (ts));
var _local5 = "";
var _local1 = 0;
while (_local1 < num.length) {
var _local4 = Number(num.substr(_local1, 1));
var _local3 = Number(ts.substr(_local1, 1));
var _local2 = String(_local4 + _local3);
_local5 = _local5 + _local2.substr(_local2.length - 1);
_local1++;
}
return("@user" + _local5);
}; Here's a better implementation.
Used the unary + operator for number conversion.
Used null instead of undefined since it's shorter and produces the same result because of type coersion.
Avoid performing a substring operation by starting to iterate from index 4.
Cached num.length into len so that we save on property lookups when the condition is evaluated for every loop iteration.
Removed uneeded parenthesis.
Took advantage of the += operator.
Made sure that every variables were locally scoped. The _local1 variable in the selected answer isin't properly scoped.
Used a single var statement; it's a better practice to declare variables at the top of the function for readability.
Stole the % 10 idea from the other answer since I thought it was great ;)
function getidnumber (num, ts) {
var i = 4,
len = num.length,
res = '@user';
ts = ts == null? '3452' : ts;
The following is multiple choice question (with options) to answer.
The difference between the local value and the face value of 7 in the numeral 32675149 is? | [
"75142",
"64851",
"5149",
"69993"
] | D | (Local value of 7) - (Face value of 7) = (70000 - 7) = 69993
D) |
AQUA-RAT | AQUA-RAT-39553 | or two consecutive tails ($TT$) are observed. What is the probability that three of those selected are women? Two standard dice with 6 sides are thrown and the faces are recorded. $$P(A \cup B\cup C)=a+b+c-ac-bc=\frac{11}{12}.$$ two previous problems. $GG$ from $\frac{1}{3}$ to about $\frac{1}{2}$. Compare your Example 1 a) A fair die is rolled, what is the probability that a face with "1", "2" or "3" dots is rolled? Let’s get to it! Compound probability is when the problem statement asks for the likelihood of the occurrence of more than one outcome. $$E_1$$= event did not complete college education; $$E_2$$= event of completion of bachelor's degree; $$E_3$$= event of completion of graduate or professional degree program. (ii) What is the probability that exactly one of them will solve it? Let $$B_k$$ be the event of a black ball on the $$k$$th draw and $$R_k$$ be the event of a red ball on the $$k$$th draw. visualize the events in this problem. Let $$T$$ = event test indicates defective, $$D$$ = event initially defective, and $$G =$$ event unit purchased is good. The probability that it's not raining and there is heavy traffic and I am not late can Here you can assume that if a child is a girl, her name will be Lilia with probability $\alpha \ll 1$ Hence $$P(A_6|S_k) = 1/6, 1/5. the probability that both children are girls, given that the family has at least one daughter named Lilia. What is the (conditional) probability that he or she will make 25,000 or more? Find the total probability that a person's income category is at least as high as his or her educational level. Previous experience indicates that 20 percent of those who do not favor the policy say that they do, out of fear of reprisal. We can calculate the probabilities of each outcome in the sample space by
The following is multiple choice question (with options) to answer.
Lola rolls a die 3 times. What is the probability that she gets a 4 on the last one of the 3 rolls? | [
"215/216",
"216",
"1/216",
"none"
] | A | the die has 6 sides and it was rolle 3 times, then 6*6*6=216
the number of ways to get 4 is 1
then 1/216
the probability would be
1-1/216=215/216
Answer A |
AQUA-RAT | AQUA-RAT-39554 | 4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?
(C) 6 - rains for 5 days from day 56-60. So 10 guys worked for 55 days and accomplished half of the work. If 6 more guys are added to the job then the rate is 16/1100. (since one man's rate is 1/1100). Half the job left means 550/1100 is left. Therefore 550/16 = 34.375 days of more work. Since there were 40 days between day 60 and job completion, it must've rained for 40-34.375 = 5.625 or ~6 days. (I'm not sure if this is correct)
5. If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is divided by t?
(E) 45 - 64.12 = 6412/100 or 1603/25. 1603/25 gives a remainder of 3, 3206/50 gives remainder of 6 and so on ..pattern = factors of 3. so to get remainder of 45, we multiply everything by 15: 1603*15/(25*15) = 24045/375.
The following is multiple choice question (with options) to answer.
A can complete a project in 20 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed? | [
"18",
"19",
"20",
"21"
] | A | A's 1day work=1/20;
B's 1day work=1/30;
(A+B) 1day work=(1/20+1/30)=1/12;
It is given that A leaves the work 10 days before completion of the project..
Thus,B alone does the remaining job in 10 days.
So,In 10 days ,B can do 1/3 w ..
Thus,(A+B) have worked (1-1/3)=2/3 w..
(A+B)can do 1/12 work in 1 day...
They did 2/3 w in 8 days.
Total days=(8+10) = 18
ANSWER:A |
AQUA-RAT | AQUA-RAT-39555 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters shouldn't the profit be calculated as a percentage of cost price, which would turn out to 22 meters. Below is what I think
(11/22) * 100
The cost price should be 22 because the profit of 11 meters is subtraccted from the selling price of 33 meters.
The question might be wrong and that is why I am seeking help.
• Profit is calculated on the cost price. The shopkeeper paid $x$ amount to buy 33 meters of cloth. When he sold the cloth, he got $x + x/3$ amount of money. Why would you subtract anything? Aug 17 '16 at 18:10
• There is often ambiguity in translating from ordinary language to math, but here I'd interpret the thing the way your book does. That is, I understand the problem to say "the shopkeeper sells $33$ units for the same amount that it would cost him to buy $44$ units." Thus, if we imagine it costs him $1$ to buy a unit, he buys the stuff for $33$ and sells it for $44$...thus a gain of $11$, or $33\frac 13\%$ of his outlay.
– lulu
Aug 17 '16 at 18:12
• Okay I get it. @shardulc it is not the selling price of 33 meters but the 33 meters of cloth. Aug 17 '16 at 18:15
The following is multiple choice question (with options) to answer.
Calculate the share of profit that belongs to Mark in a partnership business he invested Rs 31,000. His partner Abel invested RS.36,800 and the business made a profit of Rs 18,400. | [
"8499.98",
"8489.98",
"8412.98",
"8732.98"
] | C | Explanation:
Ratio of their shares = 31,000 : 36,800 = 155 : 184.
Mark's share = Rs. (18400 * 155/339) = Rs. 8412.98.
Answer: C) 8412.98 |
AQUA-RAT | AQUA-RAT-39556 | 12:14 AM
@MatheinBoulomenos nice
12:25 AM
quick question... IF we have eight people showing up for free concert tickets and we want to figure out how many ways can exactly 3 of them get tickets, isn't that just 8 choose 3 or $\binom{8}{3}$?
yes
ok so if we wanted to find out how many subsets of size k are there from a set of size n isn't it just $\binom{n}{k}$ or am I missing something here since we need different subsets of size k ... maybe it's $\binom{n}{k_{1}}\binom{n-k_{1}}{k_{2}}$ and so forth?
12:48 AM
it is just $\binom n k$
ah got it. I've been typing a lot and staying up late these past couple of days X_X
so my thinking is like weeeeee
oh oh ... it's Demonark
3 hours later…
whooaaa
2 hours later…
5:57 AM
do you know tensor product?
In above argument, we can conclude that $K_1K_2$ is spanned by $\alpha_i\beta_j$ over F, because, closed set under addition and multiplication of $\sum\alpha_i\beta_j$ is a field, right?
@LeakyNun no!
there's no need to shout that
ok :)
@Silent yes
6:02 AM
they span K_1 K_2 because they include the generators $\alpha_i$, $\beta_j$
so the ring they generate contains $F[\alpha_i, \beta_j]$
which is $K_1 K_2$
@Silent Yeah
Well, $\sum a_{ij}\alpha_i\beta_j$
sorry
It's a field, it contains $\alpha$ and $\beta$, and anything that contains $\alpha$ and $\beta$ contains $\sum a_{ij}\alpha_i\beta_j$
Therefore it's the field generated by $\alpha$ and $\beta$
The following is multiple choice question (with options) to answer.
At a certain amateur bands rock show the ratio of freaks to nerds to geeks( G) is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yelling rock on!, what are the chances that the next person who yells rock on!will be a geek? | [
"1/8",
"1/3",
"1/2",
"1/4"
] | C | Another approach is toassign some nice valuesfor the number of freaks, nerds and geeks.
Given: the ratio of freaks to nerds to geeks is 1:2:3
So, let's say there is: 1 freak, 2 nerds and3geeks for a TOTAL of6people.
P(next person who yellsrock on!is a geek) = (# of geeks in the crowd)/(TOTAL # of people in the crowd)
=3/6
= 1/2
Answer:
C |
AQUA-RAT | AQUA-RAT-39557 | They're compounding this much every day, so if I were to write this as a decimal ... Let me just write that as a decimal. 0.06274%. As a decimal this is the same thing as 0.0006274. These are the same thing, right? 1% is .01, so .06% is .0006 as a decimal. This is how much they're charging every day. If you watch the compounding interest video, you know that if you wanted to figure out how much total interest you would be paying over a total year, you would take this number, add it to 1, so we have 1., this thing over here, .0006274. Instead of just taking this and multiplying it by 365, you take this number and you take it to the 365th power. You multiply it by itself 365 times. That's because if I have$1 in my balance, on day 2, I'm going to have to pay this much x $1. 1.0006274 x$1. On day 2, I'm going to have to pay this much x this number again x $1. Let me write that down. On day 1, maybe I have$1 that I owe them. On day 2, it'll be $1 x this thing, 1.0006274. On day 3, I'm going to have to pay 1.00 - Actually I forgot a 0. 06274 x this whole thing. On day 3, it'll be$1, which is the initial amount I borrowed, x 1.000, this number, 6274, that's just that there and then I'm going to have to pay that much interest on this whole thing again. I'm compounding 1.0006274. As you can see, we've kept the balance for two days. I'm raising this to the second power, by multiplying it by itself. I'm squaring it. If I keep that balance for 365 days, I have to raise it to the 365th power and this is counting any kind of extra penalties or fees, so let's figure out - This right here, this number, whatever it is, this is - Once I get this and I subtract 1 from it, that is the mathematically
The following is multiple choice question (with options) to answer.
A town in California fines residents who do not pay their property taxes on time. All residents must pay their taxes before July 1st for that calendar year or face the following fine structure: For the first month the taxes are overdue (that would be any payment made on July 1st through July 31st), the total fine is 1% of the original tax bill; for each additional month that the taxes are overdue, the total fine is increased by $1000 or doubled, whichever results in the lesser amount. What is the total fine for a resident of that town who originally owed $50,000 in property taxes, but did not pay until October 15th? | [
"$1,400",
"$1,800",
"$4,000",
"$21,400"
] | C | Original amount = 50,000
Fine for July = 50,000 * 1% = 500
Fine for August = lesser of the 2 , 500+1000= 1500 or 500*2=1000 . Pick 1000
Fine for September = 1000+1000=2000 or 1000*2 = 2000. Pick 2000
Fine for October = 2000+1000=3000 or 2000*2 = 4000. Pick 4000.
The wording of the question should be have been clearer as total fines should be = 4000+2000+1000+500 = 7500 and NOT 4000.
4000 is the fine ONLY for the month of October!
C |
AQUA-RAT | AQUA-RAT-39558 | earth
Well, lets look at the values returned compared to days in a non-leap year:
Month N1 Day Diff
1. 30 31 -1
2. 61 59 +2
3. 91 90 +1
4. 122 120 +2
5. 152 151 +1
6. 183 181 +2
7. 213 212 +1
8. 244 243 +1
9. 275 273 +2
10. 305 304 +1
11. 336 334 +2
12. 366 365 +1
A bit messy, right? Now, remember that you're subtracting 30 from the total at the end to get N, and we're adding in the current date. This means that although we multiply our current month to get N1, we're actually using this to calculate the dates from the months prior to our current month! Thus if we take the value of N1, subtract it by 30, and compare it to the preceding month, the chart will come out like this:
Month N1 Day Diff
1. 31 31 0
2. 61 59 +2
3. 92 90 +2
4. 122 120 +2
5. 153 151 +2
6. 183 181 +2
7. 214 212 +2
8. 245 243 +2
9. 275 273 +2
10. 306 304 +2
11. 336 334 +2
12. --- 365 ---
From this, you can see that the value of N1 will equal 2 greater than the actual date for any day in which it is March or later. This is perfect, as N2 is already a formula determining this for catching leap days. Note, these would all equal +1 on a leap year, as in another day would have been added in February. Thus coming back to the final calculation:
N = N1 - (N2 * N3) + day - 30
The following is multiple choice question (with options) to answer.
The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8900. If his salary for the month of May is Rs.6500, find his salary for the month of January? | [
"s.2900",
"s.3570",
"s.4500",
"s.4550"
] | A | Sum of the salaries of the person for the months of January, February, March and April
= 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May
= 4 * 8900
= 35600 ----(2)
(2)-(1) i.e. May - Jan =3600
Salary of May is Rs.6500
Salary of January = Rs.2900
Answer:A |
AQUA-RAT | AQUA-RAT-39559 | # What is the largest integer value of $n$ for which $8^n$ evenly divides $(100!)$?
I know that this may be an unnecessary question, but I am a bit confused. The problem asks for the highest integer $$n$$ such that $$8$$ to the power of $$n$$ is divisible, evenly of course, by $$100$$. Now, I searched the site, and, in general, it seems that one can use floor function for a problem like this, but this seems to only work for prime numbers possibly. My process, which I realized was incorrect:
The floor function of $$100/8 = 12$$, and then doing it for the second power would lead to one, and, by adding those up, I acquired thirteen. Of course, after seeing the answer, $$32$$, I went back to see what was wrong and did the problem slower. I got $$12$$ numbers from the numbers in $$100!$$, and then got another $$8$$ from $$2 \times 4$$, but, that can be applied for all the multiples of $$2$$ and $$4$$ that aren't of $$8$$. So, essentially, I am wondering if there is a quicker method for calculating this number without specifically counting out the numbers. Thanks in advance!
• are you talking about (100!) or (100) ?
– Seth
Feb 13 '19 at 22:59
• I intended for it to be meant as (100!) with a question mark at the end. Feb 13 '19 at 23:00
• Edited title for easier reading. Thanks for the concern. Feb 13 '19 at 23:01
• Is it $8^n$ is divisible by $100$ or $8^n$ divides $100!\,$? Feb 13 '19 at 23:07
• It is the second one ( 8^n divides (100!) ) Feb 13 '19 at 23:09
The following is multiple choice question (with options) to answer.
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer W that must divide n is? | [
"6",
"12",
"24",
"36"
] | B | Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer W that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B |
AQUA-RAT | AQUA-RAT-39560 | ### Show Tags
16 Jun 2018, 09:16
agdimple333 wrote:
During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of$25.00 Did the store sell more sweaters than shirts during the sale?
1) The average of the prices of all of the shirts and sweaters that the store sold during the sale was $21.00 2) The total of the prices of all of the shirts and sweaters that the store sold during the sale was$420.00
The average of the prices of all of the shirts and sweaters that the store sold during the sale was $21.00. Since the average price of$21 is closer to $25 than it is to$15, there must be more sweaters sold than shirts. Statement one alone is sufficient.
Statement Two Alone:
The total of the prices of all of the shirts and sweaters that the store sold during the sale was $420.00. It’s possible that 12 sweaters and 8 shirts are sold since 12 x 25 + 8 x 15 = 300 + 120 =$420. It’s also possible that 6 sweaters and 18 shirts are sold since 6 x 25 + 18 x 15 = 150 + 270 = $420. In the former example, more sweaters were sold; however, in the latter example, more shirts were sold. Statement two alone is not sufficient. Answer: A _________________ # Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com 181 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Intern Joined: 11 Mar 2018 Posts: 1 Re: During a sale, a clothing store sold each shirt at a price of$15 and [#permalink]
### Show Tags
24 Jan 2020, 02:24
1
Bunuel wrote:
dchow23 wrote:
from statement 2,
shirts x
sweaters y
15x +20y = 420
Can we say that since 60 is a common multiple between the 15 and 20, there will be more than one answer that can satisfy the equation?
If there is a common multiple for
The following is multiple choice question (with options) to answer.
Sanoop bought 8 t-shirts at an average price (arithmetic mean) of Rs.530. If Sanoop returned 3 t-shirts to the retailer, and the average price of the remaining t-shirts was Rs.505, then what is the average price, of the three returned t-shirts? | [
"560",
"561",
"562",
"571.6"
] | D | Total price of 8 t-shirts= 8*530=4240
Total price of 5 t-shirts=5*505=2525
Total price of 3 t-shirts=4240-2525=1715
Average price of 3 t-shirts=1715/3=571.6
Correct option Answer:D |
AQUA-RAT | AQUA-RAT-39561 | # Linear Algebra Money Question
bleedblue1234
## Homework Statement
I have 32 bills in my wallet in the denominations $1,$5, and $10, worth$100 in total. How many of each denomination do I have?
## Homework Equations
A= # $1 bills B= #$5 bills
C= # $10 bills A+B+C = 32 1A+5B+10C = 100 ## The Attempt at a Solution So I attempted to solve for C in terms of A and B in terms of A but I'm getting nowhere. ## Answers and Replies E_M_C Hi bleedblue1234, You can only solve for n variables when you have n linearly independent equations. In this case, you have 3 variables and 2 linearly independent equations, so you're one equation short. But if you choose a value of zero for A, B or C then you reduce the problem to 2 variables and 2 linearly independent equations. What do you get when you try out the different combinations? Be careful: There is more than one solution. azizlwl You can narrow the selection.$1 can only be in a group of 5.
Homework Helper
This not, strictly speaking, a "linear algebra" problem, but a "Diophantine equation" because the "number of bills" of each denomination must be integer. Letting "O", "F", and "T" be, respectively, the number of "ones", "fives" and "tens", we must have O+ F+ T= 32 and O+ 5F+ 10T= 100. Subtracting the first equation from the second, 4F+ 9T= 68.
Now you can use the standard "Eucidean algorithm" to find all possible integer values for F and T and then find O.
Last edited by a moderator:
Homework Helper
Dearly Missed
## Homework Statement
I have 32 bills in my wallet in the denominations $1,$5, and $10, worth$100 in total. How many of each denomination do I have?
## Homework Equations
A= # $1 bills B= #$5 bills
C= # \$10 bills
A+B+C = 32
1A+5B+10C = 100
## The Attempt at a Solution
The following is multiple choice question (with options) to answer.
A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? | [
"90",
"94",
"96",
"97"
] | A | Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
A |
AQUA-RAT | AQUA-RAT-39562 | Examveda
# In an institute, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession?
A. 360
B. 280
C. 320
D. 330
E. 350
### Solution(By Examveda Team)
Let us assume there are 100 students in the institute.
Then, number of boys = 60
And, number of girls = 40
Further, 15% of boys get fee waiver = 9 boys
7.5% of girls get fee waiver = 3 girls
Total = 12 students who gets fee waiver
But, here given 90 students are getting fee waiver. So we compare
12 = 90
So, 1 = $$\frac{{90}}{{12}}$$ = 7.5
Now number of students who are not getting fee waiver = 51 boys and 37 girls
50% concession = 25.5 boys and 18.5 girls (i.e. total 44)
Hence, required students = 44 × 7.5 = 330
1. 60%*15%+40%*7.5%=12%
12%=90
1=750
750-90=660
50%= 330
2. let total students = x
then
(15/100*60/100*x)+(7.5/100*40/100*x)=90
900x+300x=90,0000
x=750
number of students who are not getting fee waiver=750-90=660
50% of those not getting a fee waiver are eligible=660/2=330
required students=330
Related Questions on Percentage
The following is multiple choice question (with options) to answer.
The ration of the number of boys and girls in a college is 2:3. If the percentage is increase in the number of boys and girls be 10% and 20% respectively. What will be the new ration? | [
"21:22",
"13:17",
"15:43",
"11:18"
] | D | Let the number of boys and girls be 2x and 3x
their increased number is 110% of 2x and 120% of 3x
2x*110/100 and 3x*120/100
11x/5 and 18x/5
Required ratio = 11x/5 : 18x/5 = 11:18
Answer is D |
AQUA-RAT | AQUA-RAT-39563 | Let one woman complete the job in $$w$$ days and one man in $$m$$ days.
First equation:
It takes 6 days for 3 women and 2 men working together to complete a work:
As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day, then the rate of 2 men will be $$\frac{2}{m}$$ job/day. Combined rate of 3 women and 2 men in one day will be: $$\frac{3}{w}+\frac{2}{m}$$ job/day.
As they do all the job in 6 days then in 1 day they do 1/6 of the job, which is combined rate of 3 women and 2 men --> $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.
Second equation:
3 men would do the same work 5 days sooner than 9 women:
As 1 man needs $$m$$ days to do the job 3 men will need $$\frac{m}{3}$$ days to do the job. As 1 woman needs $$w$$ days to do the job 9 women will need $$\frac{w}{9}$$ days to do the job. 3 men would do the same work 5 days sooner means that 3 men will need 5 less days to do the job, hence $$\frac{m}{3}$$ is 5 less than $$\frac{w}{9}$$ --> $$\frac{m}{3}+5=\frac{w}{9}$$.
Hope it's clear.
The following is multiple choice question (with options) to answer.
A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work? | [
"56",
"48",
"30",
"40"
] | B | B = 1/16 – 1/24 = 1/48 => 48 days
ANSWER B |
AQUA-RAT | AQUA-RAT-39564 | in n yrs and A 2 in (n+1) yrs, then Rate of compound interest =(A 2 - A 1)/A 1 *100% Sum = A 1 (A 1 /A 2) n. 596 APPENDIXC:COMPOUNDINTERESTTABLES 1/2% CompoundInterestFactors 1/2% SinglePayment UniformPaymentSeries ArithmeticGradient Compound Present Sinking Capital Compound Present Gradient Gradient Amount Worth Fund Recovery Amount Worth Uniform Present Factor Factor Factor Factor Factor Factor Series Worth Find F Find P Find A Find A Find F Find P. Compound Interest CBSE TEST PAPER: Maths for Class VIII (8th) 1. Compound interest − a phenomenon that you want to get cozy with − can be a difficult thing for your child to get. 2 : Nov 20, 2013, 9:14 AM: Pete Esser: Ċ: 04 Interest Bearing Bank Accounts and Applications. To make it plain for students to understand, I explain that it is an amount that is accrued over a certain amount of time. , compounded monthly. A savings account compounds its interest quarterly at a rate of 8%. SSC CGL & CHSL Previous Year Complete Paper with Solution Provide Only at Our Website. 747302 periods is 15. 5% interest compounded annually when you were born. To register Maths Tuitions on Vedantu. How much will the gift be wirth in 17 years, if it in invested at 7% compounded quarterly? 2) A bank is offering a CD that. 5 3 Growth of 1. How long would it take for an investment of$3,500 to become $4,200 if it is invested in an account that earns 6% compounded monthly? Since, in this problem, the variable is in the exponent, logarithms will be used to solve it. If$3000 is borrowed at a rate of 12% interest per year, flnd the amount due at the end of 5 years if the interest is compounded continuously. Straightforward amounts of money and interest rates for 2 to 4 years. It is basically earning “ interest on interest “. This addition of interest to the principal is called compounding. This calculator demonstrates how compounding can affect your savings, and how interest on your interest really adds up!. In Coordinate Algebra, you worked with the Compound Interest Formula nt n r A P(1 ) where A = the amount of money
The following is multiple choice question (with options) to answer.
A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum? | [
"2999",
"2770",
"2708",
"2000"
] | D | P(11/10)4 - P(6/5)2 = 482
P = 2000
Answer: D |
AQUA-RAT | AQUA-RAT-39565 | Question
# Three natural numbers are taken at random from a set of numbers $$\left \{ 1, 2, .... 50 \right \}$$.The probability that their average value taken as $$30$$ is equals
A
30C289C2
B
89C250C47
C
89C8750C3
D
None of these
Solution
The following is multiple choice question (with options) to answer.
Find the average of the first 19 natural numbers? | [
"8",
"9",
"10",
"11"
] | C | Average of the first 'n' natural numbers = (n + 1)/2
We get (19 + 1)/2 = 10
ANSWER:C |
AQUA-RAT | AQUA-RAT-39566 | # Minimum tickets required for specified probability of winning lottery
In a lottery, 1/10 of the 50 000 000 tickets give a prize.
What is the minimum amount of tickets one should buy to have at least a 50% chance to win?
Would be very glad if you could explain your methodology when resolving this. Please consider this as homework if you will.
## 1 Answer
I should really ask what your thoughts are so far on this. This problem is very closely related to the "birthday problem". The easiest way to do these problems is to count the possible ways of either winning or losing. Usually one is much easier to do than the other, so the key is to find the right one. Before we get into the actual calculation, let's start with some heuristics.
Heuristics: Let $n$ be the total number of tickets and $m$ be the number of winning tickets. In this case $n = 50\,000\,000$ and $m = 5\,000\,000$. When $n$ is very large then purchasing multiple distinguishable tickets is almost the same as sampling with replacement from the population of tickets.
Let's suppose that, instead of having to purchase $k$ separate tickets, we purchased a ticket, looked to see if it was a winner and then returned it to the lottery. We then repeat this procedure where each such draw is independent from all of the previous ones. Then the probability of winning after purchasing $k$ tickets is just $$\Pr( \text{we won} \mid \text{purchased k tickets} ) = 1 - \left(\frac{n-m}{n}\right)^k .$$
For our case then, the right-hand side is $1 - (9/10)^k$ and so we set this equal to $1/2$ and solve for $k$ in order to get the number of tickets.
But, we're actually sampling without replacement. Below, we'll go through the development, with the point being that the heuristics above are more than good enough for the present problem and many similar ones.
There are $50\,000\,000$ tickets. Of these $5\,000\,000$ are winning ones and $45\,000\,000$ are losing ones. We seek
The following is multiple choice question (with options) to answer.
Alice and Bob contributed $8 and $4 respectively to the price of a $12 lottery ticket. The ticket won fourth prize, worth $24,000. How much money should they each receive from the prize? | [
"Alice should get $13,000; Bob should get $11,000",
"Alice should get $16,000; Bob should get $8,000",
"Alice should get $17,000; Bob should get $7,000",
"Alice should get $17,500; Bob should get $6,500"
] | B | A = $8
B = $4
A share 8 parts & B share 4 parts
Total 12 parts -----> $24000
----> 1 part -------> $2000
A share = 8 parts -----> $12000
B |
AQUA-RAT | AQUA-RAT-39567 | solution: solution to get the median: the mean compared to sets a mean questions with solutions b Question! To new CBSE exam Pattern, MCQ questions for Class 10to help you are presented 6 ICSE.. A- a ; each being equal to the common difference we will help you sum must 12! Step 3: the given mean of a set of numbers deep understanding of maths.... Mean μ ' and the new standard deviation σ MCQ questions for Class 10to help.... To get the mean compared to sets a, a, b and C. a given data set you. Is 8 of all 5 numbers about Harmonic progression formula for nth term, sum of 5! Multiply all data values by a constant k and Calculate the mean been designed to test for understanding! Μ ' and the new standard deviation σ understanding of maths concepts b – =. Averages problem is a vey easy Question so the sequence is 2, 3 8... Mean is also called average of 56, 41, 59, 52, 42 and.... ' and the new standard deviation σ exercises on calculating the mean of given sets and word problems on mean. Set, you may need to determine the possible values of the 3 numbers in. Aggarwal Solutions Class 10 Chapter 9 - Benefits the workers earn a salary of Rs 6 to get the for. Set has a mean μ ' and the new standard deviation of the page 7 +11 ) /5 5.6! Using the average of the given classes will give the sum is 18 Divide by! Their sum must be 12, so you have x+y+z=12 ⇒ a = A- a ; each being equal the. To sets a, b are in A.P x in the middle solution: Question 21 properties... One of the 5 numbers using the average of 56, 41, 59, 52, and..., a, b and C. a given data set a = 3 if r1, r2 r3... B are in A.P a ) Calculate the mean example 2: Compute sum of set! So you have x+y+z=12 a complete solution 2 # the mean questions with solutions mean (... Lower part of the 20 people and Harmonic mean the minimum number 1! Between the first and second must be equal to the difference second and third, giving the x-y=y-z! =
The following is multiple choice question (with options) to answer.
The sum of the mean, the median, and the range of the set {1, 2, 9} equals which one of the following values? | [
"12",
"14",
"16",
"8"
] | B | set {1, 2, 9}
Mean = (1+2+9)/3 = 4
Meadian = Middle term = 2
Range = Highest - Lowest = 9-1 = 8
Mean+Median+Range = 4+2+8 = 14
Answer: Option B |
AQUA-RAT | AQUA-RAT-39568 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 900m covered). So, distance from origin $$= 900 + 1350m = 2250m$$.Physics
The following is multiple choice question (with options) to answer.
Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 16 seconds, the speed of each train (in km/hr) is | [
"42",
"27",
"28",
"20"
] | B | Explanation:
Distance covered = 120+120 = 240 m
Time = 16 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/16 = 15 m/s
Speed of each train = v = 15/2 = 7.5 m/s
= 7.5×36/10 km/hr = 27 km/hr
Answer: Option B |
AQUA-RAT | AQUA-RAT-39569 | distance from a given point called centre. You can use the formula for the volume of a cylinder to find that amount! In this tutorial, see how to use that formula and the radius and height of the cylinder to find the volume. As you can imagine, as the discs become thinner, the volume of the sphere gets more accurate. (Assume ≈ 3. Diameter - a line going through the circle from edge to edge, dividing circle in half. The cubic volume of a cylinder is found by multiplying the radius times the radius times pi times the height. Cylinder, hollow Calculate the volume, height, inner or outer radius of hollow cylinder. Cylinder Volume Formula Calculator - How to Calculate the volume of a cylinder. Net of a Cone. Find the area of a circle when you know the diameter. When the piston has moved up to the top of its stroke inside the cylinder, and the remaining volume inside the head or combustion chamber has been reduced to 100 cc, then the compression ratio would be proportionally described as 1000:100, or with fractional reduction, a 10:1 compression ratio. Show that the rectangle of maximum area that can be inscribed in a circle is a square. The Volume of a Cylinder is. The volume of each cone is equal to ⅓Bh = ⅓(28. Volume calculator will determine the volume of the most common geometric solids. The base of the cylinder is large circle and the top portion is smaller circle. Volume of a cylinder : V = πr 2 h where r is the radius and h is the height of the cylinder. It is the same measurement for circles of any size. 25 × 6 Inches Height = 37. cm, the base ring area is 115. What is the value of pi, rounded to the nearest hundredth? 3. However (a) the statements are in the incorrect order; (b) the function calls are incorrect: (c) the logical expression in the while loop is incorrect; and (d) function definitions are incorrect. Their radius (r) is therefore 3 m. Usually the pipe line would be in the shape of cylinder. Now you see that the ratio of the volume of a sphere to the volume of a cylinder is 2/3. 14 x 9 2 x 7. Therefore, the volume of a cylinder = πr2h cubic units. Also, this is important to know that the radius of a circle is always the half of its. Calculate the volume of a
The following is multiple choice question (with options) to answer.
Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes? | [
"24.",
"28.",
"36.",
"42."
] | A | Diameter of tube= 5 inches
Height of wooden tube= 15 inches
Two tubes can stand in 31 inches height
Two tubes can fit in 11 inches length
Two tubes can fit in 10 inches width
So, one box can hold 8 tubes
Three boxes can hold= 8*3= 24 tubes
A is the answer |
AQUA-RAT | AQUA-RAT-39570 | # Math
How do you divide fractions???
Cross multiply:
For example, 4/5 divided by 6/7 would be 28/30 or 14/15.
3/4 divided by 2/3 would be 9/8 or 1 and 1/8
Actually, the word cross multiply is a misnomer. What is being done is multiplying by the reciprocal
for instance 4/5 divide by 6/7 is the same as 4/5 multiplied by 7/6
3/4 divided by 2/3 is the same as 3/4 multiplied by 3/2
Both 14/15 and 9/8 are correct for the examples given; however, I don't call that cross multiplying.To divide fractions, invert the deonimator and multiply.
(4/5)/(6/7) = (4/5)*(7/6)=28/30=14/15
(3/4)/(2/3) = (3/4)*(3/2)= 9/8.
1. 👍
2. 👎
3. 👁
1. (3/4 : 4/5)x 4/6
1. 👍
2. 👎
2. .06 divided by 7.1
1. 👍
2. 👎
3. 15/4:5/3
1. 👍
2. 👎
4. 2/5 × 3/9
1. 👍
2. 👎
## Similar Questions
1. ### Math
1/4 divided by 3/8 (write in simplest form) -------------------------------------- 1/3 divided by 5/6 (simplest form) --------------------------------------- 1 3/4 divided by 3 (simplest form)
2. ### Algebra
The following is multiple choice question (with options) to answer.
What is 2 2/3 - 1 1/4 divided by 1/4 - 1/6 ? | [
"17/36",
"36/17",
"17/6",
"17/1"
] | D | 2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12
1/4 - 1/6 = (6-4)/24 = 2/24 = 1/12
So 17/12/1/12 = 17/12 * 12 = 17/1
Answer - D |
AQUA-RAT | AQUA-RAT-39571 | If stock price is $$X = (0,30)$$; we use the 7 puts (A) for profit = 7(40 - X); 9 (B) puts are used giving a loss = 9(30 - X). Total earning = 7(40-X) -9(30-X) + 2$= 2X + 12$ > 0
- 3 years, 2 months ago
Assume that the $40 put is still priced at$10.
What would be the price of the $30 put option, where there will be no arbitrage opportunity? Staff - 3 years, 2 months ago Log in to reply Let the price at which the 30$ put options is priced be $$M$$.
Now suppose that an arbitrage opportunity does exist. It is easily proved that the arbitrage opportunity(AO) must consist of buying 40$(A) put options and selling 30$ (B) put options. Let x (A) puts be bought and y (B) puts be sold for the AO.
So we spend $$10x$$ for the (A) puts and gain $$My$$ for the (B) puts. Total gain =$$My - 10x$$
If the stock price is above 40; both puts remain unused. Therefore net earnings = $$My - 10x.$$ Since earning is greater than 0 in an AO, $$My - 10x \geq 0 \implies My > 10x \implies (30-M)My > 10(30-M)x$$. Also, since $$M < 10$$, we have $$y > x$$
If the stock price is $$= P = (0,30)$$; both puts are used. Earning on (A) puts = $$x(40 - P)$$. Loss on B puts$$= y(30 - P).$$ Total earning = $$x(40 - P) - y(30-P) + My - 10x = 30x - (30 - M)y + (y-x)P$$
Since $$y - x > 0$$. Total earning is minimum when $$P = 0$$.
The following is multiple choice question (with options) to answer.
X and Y started a business in partnership investing Rs. 8,000 and Rs. 12,000 respectively. After nine months, Z joined them with Rs. 20,000. What will be Z's share in total profit of Rs. 20,000 earned at the end of 3 years from the starting of the business? | [
"Rs. 8,751",
"Rs. 8,571",
"Rs. 9,751",
"Rs. 9,571"
] | B | Solution: X : Y : Z = (8,000 * 36) : (12,000 * 36) : (20,000 * 27) = 8 : 12 : 15.
So B's share = Rs. (20000 * 15/35) = Rs. 8,571.
Answer: Option B |
AQUA-RAT | AQUA-RAT-39572 | 5. Hello, James!
Another approach . . .
12 Students are in a class.
Five can go to room A, Four to room B, and Three to room C.
How many ways can this happen?
Assign 5 students to room A.
. . There are: . $_{12}C_5 \:=\:\frac{12!}{5!7!} \:=\:792$ ways.
From the remaining 7 students, assign 4 students to room B.
. . There are: . $_7C_4 \:=\:\frac{7!}{4!3!} \:=\:35$ ways.
From the remaining 3 students, assign 3 students to room C.
. . Of course, there is: . $_3C_3 \:=\:1$ way.
Therefore, there are: . $792 \times 35 \times 1 \:=\:27,\!720$ ways.
The following is multiple choice question (with options) to answer.
In Kaya's teacher's desk there are 24 pink highlighters, 28 yellow highlighters, and 25 blue highlighters. How many highlighters are there in all? | [
"11",
"22",
"77",
"33"
] | C | Add the numbers of highlighters.
24 + 28 + 25 =77.
Answer is C. |
AQUA-RAT | AQUA-RAT-39573 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 900m covered). So, distance from origin $$= 900 + 1350m = 2250m$$.Physics
The following is multiple choice question (with options) to answer.
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? | [
"48",
"9",
"7",
"67"
] | A | :
Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125
= 48 sec.
Answer: A |
AQUA-RAT | AQUA-RAT-39574 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 900m covered). So, distance from origin $$= 900 + 1350m = 2250m$$.Physics
The following is multiple choice question (with options) to answer.
A train running at the speed of 54 km/hr crosses a pole in 9 seconds. What is the length of the train? | [
"140",
"135",
"150",
"170"
] | B | Speed=(54x5/18)m/sec = 15 m/sec.
Length of the train = (Speed x Time).
Length of the train = (15 x 9)m = 135 m.
Answer is B. |
AQUA-RAT | AQUA-RAT-39575 | # Simple and Compound Interest Problem
• January 14th 2011, 01:41 AM
dumluck
Simple and Compound Interest Problem
Hi All,
Q:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received$605 as interest. What was the value of his total savings before investing in these two bonds?
1. $5500 2.$ 11000
3. $22000 4.$ 2750
5. $44000 Answer Explanation... 1. Interest for the first year of the simple compound bond is 275/2 -$275.
2. So we need to determine the rate of interest based on this so...
605 - 550 = 55. That's the difference between the interest earned on the simple vs compound interest bonds.
55/275 * 100/1 = 11/55 * 100/1 = 20% Interest
3. 275 represents 20% interest of a number
275/20 * 100/1 = 55/4 * 100/1 = $1375. 4. This represents half the money so 1375*2 =$2750. (D).
My questions is: Why are we using 55. I.E. The difference between the two interest to determine the interest in 2. What does this 55 represent (besides the difference between the two?)
• January 14th 2011, 09:20 AM
Soroban
Hello, dumluck!
I'm not impressed with their explanation.
Quote:
Q: Shawn invested one half of his savings in a bond
that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, compounded annually, for the same 2 years at the same rate of interest and received$605 as interest.
What was the value of his total savings before investing in these two bonds?
. . $1.\;\5500 \qquad 2.\;\11000 \qquad 3.\;\22000 \qquad 4.\;\2750 \qquad 5.\;\44000$
Let $\,r$ be the annual interest rate for both accounts.
Let $\,P$ be the amount invested in each account.
The following is multiple choice question (with options) to answer.
The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places? | [
"Rs.20043.94",
"Rs.20043.99",
"Rs.20043.91",
"Rs.20043.92"
] | A | Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
Answer:A |
AQUA-RAT | AQUA-RAT-39576 | Again, for the new set of {2,3,4,5} the average is 3.5 . Now, if the last integer is removed, the new average will again be = 3.5-0.5 = 3.
Similarly, for the same set {2,3,4,5,6}, if we remove the first integer from the given set, the average increases by 0.5 and so on and so forth.
Back to the problem:
From F.S 1, we know that the average of the first 9 integers is 7. Thus, the average with the original 11 integers must have been 7+0.5+0.5 = 8. Sufficient.
From F.S 2, we know that the average of the last 9 integers is 9, thus the average with the initial 11 integers must have been 9-0.5-0.5 = 8. Sufficient.
D.
_________________
Intern
Joined: 26 May 2010
Posts: 10
Followers: 0
Kudos [?]: 33 [5] , given: 4
Re: What is the average (arithmetic mean ) of eleven consecutive [#permalink]
### Show Tags
12 Aug 2013, 23:15
5
KUDOS
3
This post was
BOOKMARKED
zz0vlb wrote:
What is the average (arithmetic mean ) of eleven consecutive integers?
(1) The avg of first nine integers is 7
(2) The avg of the last nine integers is 9
As a general rule whenever there is a AP the average of the series is always the median of the series. Here it is a AP with difference 1
1. First 9 integers average is 7 . So the median that is the 5th digit is 7. Hence we can easily find the series and the average of the 11 consecutive digit series. Sufficient
2. Average of last 9 integers is 9 hence we know that for this subset of 9 integers the 5th integer would be 9 and we can find the series on the basis of this and the average. Sufficient
And is D
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12145
Followers: 538
Kudos [?]: 151 [0], given: 0
Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]
### Show Tags
28 Aug 2014, 09:43
Hello from the GMAT Club BumpBot!
The following is multiple choice question (with options) to answer.
The average of five integers is 60, and none of these integers is greater than 100. If the average of three of the integers is 65, what is the least possible value of one of the other two integers? | [
"5",
"15",
"20",
"21"
] | A | When it comes to averages, we know thataverage value = (sum of n values)/n
We can rewrite this into a useful formula:sum of n values = (average value)(n)
The average of five integers is 60
So, the sum of ALL 5 integers = (60)(5) =300
The average of three of the integers is 65
So, the sum of the 3 integers = (65)(3) =195
So, the sum of the 2 REMAINING integers =300-195=105
If the sum of the 2 REMAINING integers =105, and we want to minimize one value, we must MAXIMIZE the other value.
100 is the maximum value so let 1 integer = 100, which means the other must equal 5
Answer: A |
AQUA-RAT | AQUA-RAT-39577 | Or, 1 = $154/4 And Total pay = 154/4*18 =>$ 693
Hence answer will be (E) $693 The wage difference is not with respect to time , correct approach will be with respect to work done.. ( Errorr is highlighted in red ) Further explanation as provide to you via PM Wages/Salary can be of 2 types ( Something You will certainly admit ) - 1. Hourly Wage payment System ( Most White collar Jobs ) 2. Unit of Work Done ( Most Blue collar Jobs ) Here it is given the part of job completed by A and B , both have diff efficiency.. Suppose total Work is 18 units Efficiency of A = 11 and Efficiency of B = 7 Now, tell me , whom will you give more money A or B ( According to the amount of work completed ) Certainly A !!! Continuing with the same example - Time Taken by A = 18/11 = 1.63 Hours Time Taken by B = 18/7 = 2.57 Hours Now, tell me , whom will you give more money A or B ??? B is inefficient , straightay, he takes more time to complete less amount of work than A... Hence Hourly wage approach is not suited here, hope this helps.. _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Current Student Joined: 26 Jan 2016 Posts: 110 Location: United States GPA: 3.37 Re: Elana was working to code protocols for computer processing. She did [#permalink] ### Show Tags 02 Nov 2016, 11:44 Elena did 11/18 which means that Andrew did 7/18. They both earn the same hourly rate. The difference between the work they did is 4/18. We know that 4/18 equals$154 because that is the difference in pay. Divide $154 by 4 so we can see how much 1/11th of the job is worth.$154/4=\$38.5
The following is multiple choice question (with options) to answer.
At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $8.50 per hour, how much less than a manager does a chef earn each hour? | [
"$1.40",
"$2.40",
"$3.40",
"$4.40"
] | C | Manager wages per hour = $8.50
Dishwasher wages per hour = half of manager's wages. = 1/2($8.50) ==> $4.25
Chef wages per hour = 20% greater than Dishwasher wages
--> 20% of $4.25 = (20*($4.25)) /100
--> ($85)/100
--> $0.85
Therefore,
Chef wages per hour = $4.25 + $0.85 ==> $5.10
Difference of wages between manager and chef = $8.50 - $5.10 ==> $3.40
ANSWER:C |
AQUA-RAT | AQUA-RAT-39578 | Hint: You may suppose, w.l.o.g. that $$|x-2|<\frac12$$, in which case $$|x-1|>\frac12$$, so that $$\left|\frac{x-2}{x - 1}\right| <2|x-2|.$$
$$\delta<\min(1,\varepsilon)/2$$ should do the job.
The following is multiple choice question (with options) to answer.
If y exceeds x by 25%, then x is less than y by? | [
"21%",
"29%",
"20%",
"80%"
] | C | X=100 y=125
125--------25
100--------? => 20%
Answer:C |
AQUA-RAT | AQUA-RAT-39579 | human-biology, cancer, medicine
Title: Why are only few cigarette smokers prone to cancer? It's tacit that only a few populace of smokers get cancer. What spares the others from it or what specifically cause cancer in those populace? See this Washington Post Article Cigarette smokers are most certainly prone to cancer. See Cecil Medicine, Chapter 183, on the epidemiology of cancer, exposure to tobacco is the most important environmental risk factor for cancer development, at least in the US:
Exposure to tobacco is the single largest cause of cancer in the United States... All forms of tobacco can cause cancer. Cigarette smoking causes cancer of the lip, oral cavity, nasal cavity, paranasal sinuses, pharynx (nasal, oral, and hypopharnyx), larynx, lung, esophagus (squamous cell and adenocarcinoma), stomach, colorectum, pancreas, liver, kidney (adenocarcinoma and renal pelvis), urinary bladder, uterine cervix, and myeloid leukemia.
Cancer may be identified or the cause of death in fewer smokers than might be expected, though, because smoking is an even greater risk factor for cardiovascular disease, and death due to cardiovascular disease.
Cancer is an unlikely phenomenon in an individual cell, but becomes more likely at the organism level, and even more likely over time. Though tobacco may be the most important environmental risk factor for cancer, age is actually a stronger predictor of cancer (see again, Cecil Chapter 183. Autopsy studies give us a quite remarkable example, this one shows incidental prostate cancer in nearly 60% of men over 80 who died from other causes. That figure is not out of the ordinary. Live long enough and you are likely to develop cancer.
Death due to heart disease may account for the lower than expected rates of cancer diagnoses and deaths in smokers. Nothing prevents cancer as well as dying from something else. And as discussed in the blog in the Washington Post you linked to, up to 2/3 of smokers die from smoking related causes
The following is multiple choice question (with options) to answer.
In a survey, 60 percent of the people surveyed admitted to being smokers, while 25 percent of the people surveyed who were smokers declined to include that information in the survey. What percent of the people surveyed were actually smokers? | [
"20%",
"80%",
"90%",
"75%"
] | B | Statement: 60% of People Surveyed (PS) Admitted to being Smokers (AS). Of the people who took the survey who were Smokers (S), 25% declined to admit to being smokers (notAS). [Note: A Venn Diagram is useful to visualize the problem.]
Solution: Sample space is 100%.
PS = 100%
AS/PS = 60%
notAS/S = 25% => 100% - 25% => AS/S = 75%
S/PS = (60)/(75)% = 80%
Answer: B |
AQUA-RAT | AQUA-RAT-39580 | homework-and-exercises, pressure, fluid-statics
Title: Which tank fills up first? Which tank would fill first. My first guess was 3 and 4 simultaneously due to Pascal's Law of pressure distribution. Then tank 2 and then 1. Could you please help? This is my first question ever on Stack Exchange. Tank 1 will to the level of the pipe. Then water will flow into 2.
If the pipe is blocked, 2 will fill. When the water in 2 reaches the level of the upper pipe, tanks 1 and 2 will stay even with each other. When tank 2 reaches the top, water will spill out. It ends there.
If the pipe to 2 is open, tank 2 will fill to the level of the lower pipe. Then water will flow into 3. Water in tank 3 will stay even with the level in the pipe to 4.
It looks like the level of the upper part of both pipes from 3 are the same. When the level in 3 rises to the pipes, water will begin to spill into 4. When 4 is full up to the pipe, the level will rise in 2, 3, and 4 until it spills over the top of 3 and 4.
The following is multiple choice question (with options) to answer.
Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank? | [
"65 hrs",
"16 hrs",
"88 hrs",
"55 hrs"
] | B | 1/20 + 1/30 = 1/12
1 + 1/3 = 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs
Answer:B |
AQUA-RAT | AQUA-RAT-39581 | for full-screen mode. TRIG WHEEL 1. A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. Interested in seeing how well you grasp a specific area of trigonometry? Take Study. 11 mm into kilometers and divided. They are going to start the chapter on graphing trigonometric functions on Monday, so this is an introductory activity to help students develop some of the vocabulary and background knowledge that. Trigonometry problems dealing with the height of two people on a ferris wheen. All we ask is that you link back to this site. For angles greater than 2π or less than −2π, simply continue to rotate around the circle, just like the ferris wheel. To the nearest inch per minute, what is the linear velocity of a point on the rim? asked by helo on July 3, 2013; trigonometry. Trig TX56 Stack NAV/COM Trig's TX56 and TX57 Nav/Com units provide the ideal platform to update legacy avionics or equip your new aircraft. Before beginning this activity, students should have been introduced to sine and cosine. WHEEL TRIG FUNCTIONS. Applications of trigonometry to waves Two-dimensional motion Suppose that a wheel of radius R is rotating anticlockwise as shown in Figure 38. This means that f(45) = 4(1) and 200. You will see that the values for sin and cos all lie on a circle of diameter ONE UNIT, centre (0. The field emerged during the 3rd century BC, from applications of geometry to astronomical studies. What is the linear speed of a point on its rim in feet per minute? Solution: Equation: 2. Chapter 13 : Trigonometric Ratios and Functions Bicycle Gears. Book title: Algebra and Trigonometry Publication date: Feb 13, 2015 Location: Houston, Texas Book. Trigonometry simply means calculations with triangles (that's where the tri comes from). Ferris Wheel Trig Problem. Trigonometry. including basic Ferris Wheel problems considering a person's position over time. The 0° angle is to the right in the "X" axis and aligned with the center of the bolt circle in the "Y" axis. It's really hard to find models and contexts for Unit Circle Trigonometry. The Trigonometry of Circles - Cool Math has free online cool
The following is multiple choice question (with options) to answer.
Ben is driving on the highway at y miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of z feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? | [
"5,280(x/y)",
"5,280(y/z)",
"5,280(xy)",
"5,280/(xy)"
] | B | In one hour, at the rate of y miles per hour, Ben covers y miles, so 5,280y feet.
The number of revolutions = distance/circumference = 5,280y/z.
Answer: B. |
AQUA-RAT | AQUA-RAT-39582 | In $2x^3- 3x^2+ a+ 1= 0$, there are either one or two sign changes depending upon whether a+ 1 is positive or negative. If a< 1, so that a+ 1 is negative, the signs are "+, -, -" so there is one sign change and exactly one positive root. If a> 1, so that a+ 1 is positive, the signs are "+, -, +" so there are two sign changes and two positive roots or none.
For negative roots, replace x with -x and do the same. $2(-x)^3- 3(-x)^2+ a+ 1= -2x^3- 3x^2+ a+ 1= 0$. Now, if a+ 1> 0, there is one sign change so the original equation has exactly one negative root. If a+1< 0, there are no sign changes so the original equation has no negative roots.
Thus, we can say that if a> -1, there is one negative root and either 0 or 2 positive roots. If a<-1, there is one positive root and no negative roots.
Of course, if a= 1, the equation is $2x^3- 3x^2= x^2(2x- 3)= 0$ which has x= 0 as a double root and x= 3/2 as a positve root.
The following is multiple choice question (with options) to answer.
If there is exactly one root of the equation x^2 + 2ax + b, where a and b are positive constants, what is b in terms of a? | [
"a/2",
"a",
"3a/2",
"a^2"
] | D | one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1
Here b = 2a
c= b
a = 1
substituting these values in 1, we have
2^2*a^2 = 4b => b =a^2
Answer is D. |
AQUA-RAT | AQUA-RAT-39583 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters shouldn't the profit be calculated as a percentage of cost price, which would turn out to 22 meters. Below is what I think
(11/22) * 100
The cost price should be 22 because the profit of 11 meters is subtraccted from the selling price of 33 meters.
The question might be wrong and that is why I am seeking help.
• Profit is calculated on the cost price. The shopkeeper paid $x$ amount to buy 33 meters of cloth. When he sold the cloth, he got $x + x/3$ amount of money. Why would you subtract anything? Aug 17 '16 at 18:10
• There is often ambiguity in translating from ordinary language to math, but here I'd interpret the thing the way your book does. That is, I understand the problem to say "the shopkeeper sells $33$ units for the same amount that it would cost him to buy $44$ units." Thus, if we imagine it costs him $1$ to buy a unit, he buys the stuff for $33$ and sells it for $44$...thus a gain of $11$, or $33\frac 13\%$ of his outlay.
– lulu
Aug 17 '16 at 18:12
• Okay I get it. @shardulc it is not the selling price of 33 meters but the 33 meters of cloth. Aug 17 '16 at 18:15
The following is multiple choice question (with options) to answer.
A man sells a horse for Rs.620 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse? | [
"587",
"679",
"740",
"860"
] | C | CP = SP + 1CP = SP - g
620 + x = 980 - 2x
3x = 360 => x
= 120
CP = 620 + 120
= 740
Answer:C |
AQUA-RAT | AQUA-RAT-39584 | • so $x=12$ or $x=-14$
Let $$\mathbb S$$ be a set of all even integers, i.e:
$$\mathbb S = \{x | x = 2k, k\in \mathbb Z \}$$
Suppose we have two consecutive elements $$x_1$$ and $$x_2$$ in the set $$\mathbb S$$, i.e:
$$x_1 = 2k$$ ...(1)
$$x_2=2k+2$$ ...(2)
...such that their product is 168, i.e:
$$(2k)(2k+2)=168$$
Solving for k:
$$4k^2 + 4k -168 = 0$$
$$k^2 + k - 42 = 0$$
$$(k-6)(k+7) = 0$$
$$k= 6$$ or $$k = -7$$
Substituting the above into (1) and (2) gives us two solutions:
$$x_1 =12$$ and $$x_2 = 14$$, or,
$$x_1 =-14$$ or $$x_2 = -12$$
The following is multiple choice question (with options) to answer.
A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 13 multiples of 14, how many multiples of 7 are there in Q? | [
"23",
"24",
"25",
"26"
] | C | Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 13+12 = 25.
The answer is C. |
AQUA-RAT | AQUA-RAT-39585 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 900m covered). So, distance from origin $$= 900 + 1350m = 2250m$$.Physics
The following is multiple choice question (with options) to answer.
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? | [
"27 seconds",
"29 seconds",
"40 seconds",
"11 seconds"
] | C | Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer:C |
AQUA-RAT | AQUA-RAT-39586 | (1) $$a^2+b^2>16$$
Doesn't tell us about the value of a. a could be 2 or 10 or many other values.
(2) a=|b|+5
a is 5 or greater since |b| is at least 0. This tells us that 'a' does not lie between -4 and 4. Hence this statement is sufficient to answer the question.
_________________
Karishma
Veritas Prep | GMAT Instructor
My Blog
The following is multiple choice question (with options) to answer.
If A^4 + B^4 = 100, then the greatest possible value of B is between | [
"0 and 1",
"1 and 2",
"2 and 3",
"3 and 4"
] | D | for the greatest possible value of B^4, we must minimize the value of B^4 i.e. lets say A^4 = 0
then we need to find a number B such that B^4 < 100. 3^4 = 81 and 4^4 = 256 so we can say that the maximum possible value of B can be a little more than 3 hence answer = between 3 and 4
hence D |
AQUA-RAT | AQUA-RAT-39587 | Another answer that use almost the same idea: the sum or subtraction of two even or odd number is an even number. How many odd number we have?
Replacing 100 with $n$ and using Brian M. Scott's solution, we want a partition of $\{1, 2, ..., n+1\}$ into two sets with equal sums.
The sum is $\frac{(n+1)(n+2)}{2}$, and if $n=4k$, this is $(4k+1)(2k+1)$ which is odd and therefore impossible.
If $n = 4k+1$, this is $(2k+1)(4k+3)$ which is also odd, and therefore impossible.
If $n = 4k+2$, this is $(4k+3)(2k+2)$, so it is not ruled out, and each sum must be $(4k+3)(k+1)$.
if $n = 4k+3$, this is $(2k+2)(4k+5)$ which is also not ruled out, and each sum must be $(k+1)(4k+5)$.
Now I'll try to find a solution for the not impossible cases. (I am working these out as I enter them.)
The following is multiple choice question (with options) to answer.
Set A contains all the even numbers between 4 and 50 inclusive. Set B contains all the even numbers between 104 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A? | [
"2400",
"2550",
"5050",
"6275"
] | A | Set A contains 4 , 6 ... 50
Set B contains 104 , 106 ... 150
Number of terms in each set = 24
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*24 = 2400
Answer A |
AQUA-RAT | AQUA-RAT-39588 | Less rigorous and mathematical, but perhaps more intuitive approach:
(a) note that for each girl,
there is no relationship at all between the number whispered and the number said; they are parts of different cycles.
(b)
in the group of girls we care about, the thought-of numbers averaged to $[1, 3, 5, 7, 9]$.
(c)
Note that this is symmetrical, so the number that was a component of both 1 and 9 must be 5. From there, the rest follows:
$5 + a = 9\times2 \therefore a = 13$
$13 + b = 7\times2 \therefore b = 1$
(d) to check the work, go the other way around the circle:
$5 + d = 1\times2 \therefore d = -3$
$-3 + c = 3\times2 \therefore c = 9$
$9 + b = 5\times2 \therefore b = 1.$
(The other 5 girls each thought of the number 1 higher than the girl sitting to one side of her).
The following is multiple choice question (with options) to answer.
The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation? | [
"9",
"8",
"7",
"6"
] | A | 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81 = 9
Answer: A |
AQUA-RAT | AQUA-RAT-39589 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters shouldn't the profit be calculated as a percentage of cost price, which would turn out to 22 meters. Below is what I think
(11/22) * 100
The cost price should be 22 because the profit of 11 meters is subtraccted from the selling price of 33 meters.
The question might be wrong and that is why I am seeking help.
• Profit is calculated on the cost price. The shopkeeper paid $x$ amount to buy 33 meters of cloth. When he sold the cloth, he got $x + x/3$ amount of money. Why would you subtract anything? Aug 17 '16 at 18:10
• There is often ambiguity in translating from ordinary language to math, but here I'd interpret the thing the way your book does. That is, I understand the problem to say "the shopkeeper sells $33$ units for the same amount that it would cost him to buy $44$ units." Thus, if we imagine it costs him $1$ to buy a unit, he buys the stuff for $33$ and sells it for $44$...thus a gain of $11$, or $33\frac 13\%$ of his outlay.
– lulu
Aug 17 '16 at 18:12
• Okay I get it. @shardulc it is not the selling price of 33 meters but the 33 meters of cloth. Aug 17 '16 at 18:15
The following is multiple choice question (with options) to answer.
A shopkeeper sells sugar in such a way that the selling price of 950g of sugar is the same s the cost price of 1 kg of sugar. What is his gain percent? | [
"5(5/19)",
"5(1/5)",
"5",
"4(1/19)"
] | A | Solution: Sell sugar = 950g instead of 1000g.
Profit in Sugar = 1000 - 950 = 50g.
Now, % profit = (50*100)/950 = 5(5/19)%.
Short-Cut
% profit = (Goods left/Goods sold)*100.
= (50/950)*100 = 5(5/19)%.
Answer: Option A |
AQUA-RAT | AQUA-RAT-39590 | (1) Kevin spent a total of $18.00 on beer. (2) Kevin bought 3 more cans of beer than bottles of beer. Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that Kevin bought Let B = the NUMBER of Bottles that Kevin bought So, we can write: C + B = 15 Statement 1: Kevin spent a total of$18.00 on beer
The COST of C cans = ($1.00)C = 1C The COST of B bottles = ($1.50)B = 1.5B
So, we can write: 1C + 1.5B = 18.00
When we combine this equation with the equation we created from the given information, we have:
C + B = 15
1C + 1.5B = 18.00
Since we COULD solve this system for C and B, we COULD determine the number of bottles of beer that Kevin bought.
(of course, we won't solve the system, since that would be a waste of our valuable time!)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: Kevin bought 3 more cans of beer than bottles of beer
We can write: C = B + 3
When we combine this equation with the equation we created from the given information, we have:
C + B = 15
C = B + 3
Since we COULD solve this system for C and B, we COULD determine the number of bottles of beer that Kevin bought.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
The following is multiple choice question (with options) to answer.
A collector collects stamps from foreign countries. In June, she gave 20 percent of her stamps to her friend. In July, she gave 15 percent of her remaining stamps to another friend. If these were the only changes in the number of stamps in the stamp collection during those two months, what percent of her collection at the beginning of June did she give to away in June and July? | [
"28%",
"32%",
"36%",
"40%"
] | B | Let x be the number of stamps in the original collection.
The percentage of the collection given away is:
0.2x + 0.15(0.8x) = 0.2x + 0.12x = 0.32x = 32%
The answer is B. |
AQUA-RAT | AQUA-RAT-39591 | Since the sum of the ages of all 48 people must be equal to the sum of the ages of the 22 men plus the sum of the ages of the 26 women, we have
48(35) = 22(38) + 26x
1680 = 836 + 26x
26x = 844
x = 844/26
x = 32 12/26 ≈ 32.5
_________________
Scott Woodbury-Stewart
Founder and CEO
GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4342
Location: India
GPA: 3.5
A total of 22 men and 26 women were at a party, and the average [#permalink]
### Show Tags
04 May 2016, 09:23
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33
Kudos for a correct solution.
Total age of men and women = 48*35 => 1,680
Total age of men is = 22*38 => 836
So, total age of women in = 1680 - 836 => 844
Average age of women is 844/26 => 32.46
Hence answer will be (D) 32.5
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager
Joined: 18 Aug 2013
Posts: 128
Location: India
Concentration: Operations, Entrepreneurship
GMAT 1: 640 Q48 V28
GPA: 3.92
WE: Operations (Transportation)
Re: A total of 22 men and 26 women were at a party, and the average [#permalink]
The following is multiple choice question (with options) to answer.
The average age of a family of 6 members is 40 years.If the age of the youngest member is 7 years,what was the average age of the family at the birth of the youngest member? | [
"33",
"18",
"21",
"12"
] | A | Present age of total members = 6 X 40 = 240
7 yrs back their ages were = 6 x 7 = 42
Ages at the birth of youngest member = 240 - 42 = 198
Therefore, avg age at the birth of youngest member = 198/6 = 33.
ANSWER:A |
AQUA-RAT | AQUA-RAT-39592 | If $\displaystyle H(x)=\frac{2x\sin\alpha}{[x^2-2x\sin\alpha+1][x^2+2x\sin\alpha+1]},$
$$H(-x)=\frac{2(-x)\sin\alpha}{[(-x)^2-2(-x)\sin\alpha+1][(-x)^2+2(-x)\sin\alpha+1]}$$
$$=\frac{-2x\sin\alpha}{[x^2+2x\sin\alpha+1][x^2-2x\sin\alpha+1]}=-H(x)$$
The following is multiple choice question (with options) to answer.
If x is an integer, which of the following is a possible value of H=(x^2 +2x – 7)/9? | [
"-2.4",
"0.268",
"1.166 repeating",
"4.555 repeating"
] | D | x is an integer, which of the following is a possible value of H=(x^2 +2x – 7)/9?
Used process of elimination
A. -2.4
when this is multiplied by 9, x is not an integer
B. 0.268
when this is multiplied by 9, x is not an integer
C. 1.166 repeating
when this is multiplied by 9, x is not an integer
D. 4.555 repeating
E. 8.125
when this is multiplied by 9, x is not an integer
Answer choice D seems to fit |
AQUA-RAT | AQUA-RAT-39593 | (A) 9
(B) 12
(C) 18
(D) 24
(E) 27
Weight of 2nd piece = 4 pound
Since the weight is directly proportional to the square of its length., we may write
$$\frac{16}{36^2}$$ = $$\frac{4}{x^2}$$
Solving above, we get x = 18
_________________
If you like the post, show appreciation by pressing Kudos button
Director
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: A wire that weighs 20 pounds is cut into two pieces so that one of the [#permalink]
### Show Tags
30 Jun 2017, 04:02
Bunuel wrote:
A wire that weighs 20 pounds is cut into two pieces so that one of the pieces weighs 16 pounds and is 36 feet long. If the weight of each piece is directly proportional to the square of its length, how many feet long is the other piece of wire?
(A) 9
(B) 12
(C) 18
(D) 24
(E) 27
$$20$$ pounds wire is cut into two pieces = $$16$$ pounds $$+$$ $$4$$ pounds
The piece weighs $$16$$ pounds is $$36$$ feet long.
Ratio of weight and length of $$16$$ pounds piece $$= \frac{16}{36^2} = \frac{4 * 4}{36 * 36} = \frac{1}{81}$$
Therefore required ratio of other part would also be $$\frac{1}{81}$$
Ratio $$= \frac{4}{x^2} =$$ $$\frac{1}{81}$$
$$x^2 = 81*4$$ $$=> x = \sqrt{81*4}$$
$$x = 9 * 2 = 18$$
Hence length of $$4$$ pounds wire $$= 18$$
The following is multiple choice question (with options) to answer.
A 35 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? | [
"10",
"20",
"88",
"77"
] | A | 1: 2/5 = 5: 2
2/7 * 35 = 10
Answer: A |
AQUA-RAT | AQUA-RAT-39594 | # Clock losing time puzzle
The question goes as:
A wall clock and a Table clock are set to correct time today on 10 pm. The wall clock loses 3 minute in 1st hour, 6 minutes in the second hour and 9 minutes in the third hour and so on. The table clock loses 5 minutes in the 1st hour, 10 minutes in the second hour and 15 minutes in the third hour and so on. When will they show the same time?
My approach:
In the first hour, the difference between the two clocks would be $2$ (obtained from $5-3$) minutes.
In the second hour, it'll be four minutes and so on. This would form an arithmetic progression with $a$ = 2 and $d = 2$. I, then, formulated the problem as:
$$2 + 4 + 6+ 8 + \dots + n = 720$$
The RHS is $720$ because I assumed they'll meet after 12 hours.
With this, I got the root as $23.337$ hours, so I arrived at the answer as $10 \, \text{PM} + 23.337$ hours i.e $9:20 \, \text{PM}$.
Is this correct?
EDIT: I realised this equation won't give an integral answer, and we need one as $n$ on the LHS represents the number of terms. So instead of that, I wrote it as:
$$2 + 4 + 6 + \dots + n = 720 \times k$$ where $k \in (1,2,3,4, \dots)$.
Using this method, for $k = 9$, I get the value of $n$ $\text{as}$ $80 \, \text{hours}$.
Does this seem correct?
The following is multiple choice question (with options) to answer.
A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Friday at 12 AM, what will be the time at the end of 10 days? | [
"12:54:40 AM",
"12:56:24 AM",
"01:16:40 PM",
"12:54:24 AM"
] | D | Loses 8 minutes each day.
so total loss = 4×8 = 32min
subsequent 6 days = 6×24×60 minutes
1% gain = ( 6×24×60)/100 = 86.4 minutes
so, total gain = 86.4 - 32 = 54.4 min = 54 + 0.4 min = 54 minutes + 0.4 × 60 seconds = 54min + 24seconds
10 days later the clock should be 54 min and 24seconds fast.
so time , 12:54:24 am (Answer D) |
AQUA-RAT | AQUA-RAT-39595 | 0.00698 acre1 acre = 43560 square feet304 sq ft * 1 acre/43560 sq ft = 0.00698 acre
### Number of sq ft per acre?
1 sq mi=5280ft x 5280ft = 27878400 sq ft/sq mi/ 27,878,400 sq ft/sq mi divided by 640acres/sq mi = 43,560 sq ft /acre 1 acre = 43,560 sq ft
### How many square feet are in 1.8 acre?
1 acre = 43,560 sq ft → 1.8 acre = 1.8 × 43,560 sq ft = 78,408 sq ft
### What does 0.2 acres equals sq feet?
1 acre = 43,560 sq ft .2 acre * 43560 sq ft = 8712 sq ft
### What percentage of acres in 160 feet x 180 feet?
160 ft * 180 ft = 28800 sq ft = 66.1% of an acre.160 ft * 180 ft = 28800 sq ft = 66.1% of an acre.160 ft * 180 ft = 28800 sq ft = 66.1% of an acre.160 ft * 180 ft = 28800 sq ft = 66.1% of an acre.
### How many ft are in a acre?
There are 43559.66 sq ft in an acre.
### What is a fifth of an acre?
an acre is 43,560 sq ft 1/5th of that is 8,712 sq ft
### How many acres is 11026 sq ft?
43,560 sq ft = 1 acre11,026 sq ft = 0.2531 acre (rounded)
### Figure how many acres in 60000 sq ft?
(60,000 sq ft) / (43,560 sq ft / acre) = 1.3774 acre (rounded)
### What is the convertion of 435 acre to square feet?
1 acre = 43,560 sq ft → 435 acre = 435 x 43,560 sq ft = 18,948,600 sq ft
### How many sq ft for one acre 14 guntas in India?
The following is multiple choice question (with options) to answer.
A certain farmer pays $30 per acre per month to rent farmland. How much does the farmer pay per month to rent a rectangular plot of farmland that is 1080 feet by 605 feet? (43,560 square feet = 1 acre) | [
"$5,330",
"$3,360",
"$450",
"$360"
] | C | Basically the question an error. 1 acre = 43,560 square feet and if it is then the answer is 450(C) |
AQUA-RAT | AQUA-RAT-39596 | 1111121, 1111202, 1111211, 1112002, 1120002, 1120012, 1120102, 1121002, 1121102, 1122002, 1200002, 1200012, 1200102, 1200112, 1200202, 1201002, 1201012, 1202002, 1210002, 1210102, 1210202, 1211002, 1212002, 1220002, 1220102, 2000002, 2000012, 2000022, 2000102, 2000112, 2000122, 2000202, 2000212, 2001002, 2001012, 2001022, 2001102, 2001112, 2001122, 2001202, 2001212, 2010012, 2010022, 2011012, 2020012, 2020022,$ and their inverses.
The following is multiple choice question (with options) to answer.
1,11,21,_ what comes in the next series. | [
"1",
"11",
"21",
"31"
] | D | 1+10=11
11+10=21
21+10=31
ANSWER:D |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.