question stringlengths 10 716 | options listlengths 4 4 | answer stringclasses 4 values | correct_option stringlengths 1 63 | explanation stringlengths 0 2.6k | dataset stringclasses 3 values |
|---|---|---|---|---|---|
If x and y are positive integers and 5 + x + y + xy = 19, what is the value of x + y? | [
"3",
"5",
"6",
"8"
] | C | 6 | Try each answer choices.
For A: 5 + 3 + xy = 19; xy = 11 (impossible, 11 prime number. 1 + 11 doesn't equal 3)
For B: 5 + 5 + xy = 19; xy = 9 (no combination of xy = 9 and x + y = 5)
For C: 5 + 6 + xy = 19; xy = 8 (x + y = 6; x = 2, y = 4 or x = 4, y = 2)
For D: 5 + 8 + xy = 19; xy = 6 (no combination of xy = 6 and x + y = 8)
For E: 5 + 9 + xy = 19; xy = 5 (impossible, 5 prime number. 1 + 5 doesn't equal 9)
Therefore, answer C. | aqua_rat |
Which of the following is true? | [
"lemonade can be heated to form water",
"lemonade can be cooled to form steam",
"lemonade can be heated to form steam",
"water can be cooled to form steam"
] | C | lemonade can be heated to form steam | science | |
The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be English teachers? | [
"2/3",
"1/3",
"2/9",
"1/12"
] | D | 1/12 | Probability of first member an English teacher = 3/9
Probability of second member an English teacher = 2/8
Probability of both being english teacher = 3/9 x 2/8 =1/12 (D)
ANSWER:D | aqua_rat |
The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year? | [
"12300",
"12350",
"12000",
"12500"
] | C | 12000 | Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100 = 12000
C | aqua_rat |
What forms the pathway of water and nutrients from roots to leaves and flower? | [
"the pistil",
"the stem",
"the stamen",
"the stigma"
] | B | the stem | science | |
The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher | [
"45 Years",
"46 Years",
"49 Years",
"52 Years"
] | C | 49 Years | Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years
C | aqua_rat |
If x =- |x| , then which one of the following statements could be true?
I. x = 1
II. x < 0
III. x > 0 | [
"None",
"I only",
"II only",
"I and II"
] | C | II only | Answer copied from NOVA guide
Statement I could be true because + 1 = −(+1) = −(1) = -1 .
Statement II could be true because the right side of the equation is always negative [ ± x = –(a positive number) = a negative number].
Now, if one side of an equation is always negative, then the other side must always be negative,
otherwise the opposite sides of the equation would not be equal.
Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly:
Suppose x were positive. Then x = x, and the equation x = ± x becomes x = –x. Dividing both sides of this equation by x yields 1 = –1. This is contradiction.
Hence, x cannot be positive. The answer is (C). | aqua_rat |
The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 25% more than the price of the other, what is the price of each of these two oranges? | [
"Rs 11.5, Rs 14.5",
"Rs 8, Rs 12",
"Rs 10, Rs 16",
"Rs 12, Rs 14"
] | A | Rs 11.5, Rs 14.5 | Explanation :
Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
Let the price of one orange be Rs. x.
Then, the price of other orange = Rs. (x + 25% of x) = Rs. x + 1/4x = Rs. 5x/4
So, x + 5x/4 = 26
9x = 104
x = 11.5
The prices of the two oranges are Rs. 11.5 and Rs. 14.5
Answer : A | aqua_rat |
The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 400 per sq. metre. | [
"Rs. 15000",
"Rs. 8250",
"Rs. 15600",
"Rs. 16500"
] | B | Rs. 8250 | Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (400 × 20.625) = 8250. Answer B | aqua_rat |
An institute organised a fete and 1/5 of the girls and 1/8 of the boys participated in the same. What fraction of the total number of students took part in the fete ? | [
"2/13",
"13/40",
"Data inadequate",
"14/50"
] | C | Data inadequate | Explanation:
Data insufficient to solve the question
Answer is C | aqua_rat |
If 50% of (x-y) = 20% of (x+y), then what percent of x is y? | [
"50.5%",
"42.8%",
"22.2%",
"33.3%"
] | B | 42.8% | 50% of (x-y) = 20% of (x+y)
50/100 (x-y) = 20/100 (x+y)
3x = 7y
Required percentage = y/x *100 = 3y/7y * 100 = 42.85%
Answer is B | aqua_rat |
Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is? | [
"2400 m^2",
"2500 m^2",
"2520 m^2",
"2560 m^2"
] | C | 2520 m^2 | Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C | aqua_rat |
12*18*6 is the volume of some material. How many cubes of edge 3 can be insert into it? | [
"48",
"49",
"50",
"51"
] | A | 48 | no. of such cubes = volume of material / volume of one cube
(12*18*6)/(3*3*3)= 48
ANSWER:A | aqua_rat |
How many integers between 1000 and 10000 have
no digits other than 4, 5 or 6? | [
"91",
"51",
"81",
"71"
] | C | 81 | Any number between 1,000 and 10,000 is of 4 digits. The unit’s place can be filled up by 4,5 or 6, that is, in 3 ways.
Similarly, the ten’s place can be filled up by 4 or 5 or 6, that is in 3 ways. The hundred’s place can be filled up by 4, 5 or 6, that is in 3 ways and the thousand’s place can.be filled up by 4 or 5 or 6, that is, in 3 ways.
Hence the required numbers = 3 x 3 x 3 x 3 = 81
ANSWER:C | aqua_rat |
Three archers each have an equal chance of hitting a target, and if only two of the three shoot the likelihood of the two hitting the target is 4/9 . What is the likelihood of all three men missing the target? | [
"probability is 1/27",
"16/81",
"8/27",
"19/27"
] | A | probability is 1/27 | Let the probability of an archer hitting a target be xx. Then the probability of two hitting the target will be P=x∗x=49P=x∗x=49 - -> x=23x=23, so the probability of an archer missing the target will be P=1−23=13P=1−23=13.
The probability of all three men missing the target will be P=(13)3=127P=(13)3=127.
Answer: A. | aqua_rat |
In the coordinate plane, one of the vertices of a square is the point (-4, -4). If the diagonals of that square intersect at point (3, 2), what is the area of that square? | [
"180",
"196",
"160",
"164"
] | B | 196 | One point (-4-4), Intersection (3,2) so the distance from the first point -4-3=-7 is the midpoint of the square --> whole side 14, 14*14=196
B | aqua_rat |
Covalent compounds form individual molecules rather than what? | [
"atoms",
"carbon",
"crystals",
"chemicals"
] | C | crystals | Covalent compounds form individual molecules rather than crystals. Compared with ionic compounds, they have low melting and boiling points. They are also poor conductors of electricity. In polar covalent compounds, oppositely charged ends of different molecules attract each other. This affects the properties of polar compounds. | science |
Find the percentage gain if a shop owner sells 40 mtr of fabric and gains Cost Price of 15 meters? | [
"38.50%",
"39.50%",
"27.50%",
"37.50%"
] | D | 37.50% | Let cost of each metre be Rs. 100.
Therefore, cost price of 15m cloth = 15*100 =1500
cost price of 40m cloth = 40*100 = 4000
Since the trader made the CP of 15m from the sale of 40m therefore
Profit on sale of 40m = cost price of 15 m cloth = 1500
Selling price of 40m = 4000+1500 = 5500
Profit % = 37.50%
D | aqua_rat |
If X boxes of mango juice cost 250 cents, how much will Y boxes cost in dollars? | [
"Y*2/x",
"Y*2.6/x",
"2Y*2.5/x",
"Y*2.5/x"
] | D | Y*2.5/x | X boxes of mango juice cost 250 cents or 2.5 dollars.
cost of mango juice = 2.5/x
Cost of Y mango juices = Y*2.5/x
Hence Answer : D | aqua_rat |
In one hour, a boat goes 15 km/hr along the stream and 9 km/hr against the stream. The speed of the boat in still water (in km/hr) is: | [
"12 kmph",
"13 kmph",
"14 kmph",
"15 kmph"
] | A | 12 kmph | Explanation:
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water =1/2(a+b) km/hr
Rate of stream = 1/2(a−b) km/hr
Speed in still water = 1/2(15+9) kmph = 12 kmph.
Answer: Option A | aqua_rat |
What is the simplest form of matter that has a unique set of properties? | [
"atom",
"element",
"quark",
"molecule"
] | B | element | An element is the simplest form of matter that has a unique set of properties. | science |
A given positive integer is divided by 9 with a remainder of 5. The same integer when divided by 12 has a remainder of 3. What is the remainder if the it integer is divided by 35. | [
"Between 1 and 4, inclusive",
"Between 5 and 7, inclusive",
"Between 8 and 10, inclusive",
"5"
] | B | Between 5 and 7, inclusive | Put in real numbers.
Let the integer be x
9x+5= 12x+3
Start 9x+5 -->14, 23, 32,....41...
Of these only 41 fit the description 12x+3. The remainder when divided by 35 is 6. So answer is B).
Answer = B) | aqua_rat |
If p/5 = r/2 and r = 0.75s, what is the ratio of p to r to s? | [
"2 : 3 : 4",
"8 : 12 : 9",
"15 : 6 : 8",
"6 : 4 : 3"
] | C | 15 : 6 : 8 | p/5=r/2, r=0.75s, what is p:r:s?
we get p/r=5/2 and r/s=3/4, so
5/3*3/2 and 2/2*3/4
15/6 and 6/8
C | aqua_rat |
If n = 4^11 – 4, what is the units digit of n? | [
"0",
"1",
"4",
"6"
] | A | 0 | Always divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 4^3 - 4. Now 4^3 has last digit 4. , we subtract 4 from 4 = 0 is the answer. Option A | aqua_rat |
Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually. | [
"Rs 309",
"Rs 319",
"Rs 3109",
"Rs 109"
] | C | Rs 3109 | Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = Rs'. [8000 X (1+¬(15/100))2 X (1+((1/3)*15)/100)]
=Rs. [8000 * (23/20) * (23/20) * (21/20)]
= Rs. 11109. .
:. C.I. = Rs. (11109 - 8000) = Rs. 3109.
ANSWER C 3109 | aqua_rat |
What produces hormones that directly regulate body processes? | [
"hypothalamus",
"hippocampus",
"pancreas",
"lymph glands"
] | A | hypothalamus | The hypothalamus also produces hormones that directly regulate body processes. For example, it produces antidiuretic hormone. This hormone travels to the kidneys and stimulates them to conserve water by producing more concentrated urine. | science |
The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 60 percent of the pollutant? | [
"$300,000",
"$100,000",
"$50,000",
"$10,000"
] | A | $300,000 | To remove 90% of pollutant
C= 100,000(90)/(100-90) = 900,000
To remove 60% of pollutant
C' = 100,000(60)/(100-60) = 600,000
Difference = C - C' = 300,000
Answer - A | aqua_rat |
The tailor has a 10 meter long piece of fabric for which to sew a ball room dress.
She has to cuts this fabric into strips of 200 centimeters each.
How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ? | [
"150",
"200",
"188",
"245"
] | D | 245 | The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D | aqua_rat |
A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is? | [
"3.34 sq m",
"98.8 sq m",
"67.8 sq m",
"27.9 sq m"
] | A | 3.34 sq m | Area of the path = Area of the outer circle - Area of the inner circle
= ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16
= 3.34 sq m
Answer: A | aqua_rat |
What does a hairy organism have under its skin to help insulate the body? | [
"fat",
"hair",
"food",
"cell"
] | A | fat | An organism with hair has a layer of fat under the skin to help insulate the body. | qasc |
A seismometer can note how earthquakes are | [
"small",
"fast",
"strong",
"long"
] | C | strong | science | |
The anodes in each cell of a rechargeable battery are plates or grids of lead containing spongy lead metal, while the cathodes are similar grids containing powdered what? | [
"coal",
"lead dioxide",
"straight dioxide",
"carbon dioxide"
] | B | lead dioxide | The anodes in each cell of a rechargeable battery are plates or grids of lead containing spongy lead metal, while the cathodes are similar grids containing powdered lead dioxide (PbO2). The electrolyte is an aqueous solution of sulfuric acid. The value of E° for such a cell is about 2 V. Connecting three such cells in series produces a 6 V battery, whereas a typical 12 V car battery contains six cells in series. When treated properly, this type of high-capacity battery can be discharged and recharged many times over. As the cell is discharged, a powder of PbSO4 forms on the electrodes. Moreover, sulfuric acid is consumed and water is produced, decreasing the density of the electrolyte and providing a convenient way of monitoring the status of a battery by simply measuring the density of the electrolyte. | science |
pollutants have a negative impact on animals if what? | [
"kill them",
"ignored",
"ingested",
"Cars"
] | C | ingested | eating something that contains pollutants has a negative impact on an animal's survival | qasc |
The average of first 6 prime numbers is? | [
"10.11",
"11.11",
"12.11",
"6.83"
] | D | 6.83 | Sum of 6 prime no. = 41
Average = 41/6 = 6.83
ANSWER: D | aqua_rat |
If the product of two positive integers is 40, which of the following could be the LCM and HCF of the two numbers? a. LCM 20 : HCF 2 b. LCM 40 : HCF 5 c. LCM 20 : HCF 4 | [
"b only",
"c only",
"a only",
"a, c only"
] | C | a only | a is the correct answer.
Answer : C | aqua_rat |
The ratio of 4 seconds to 8 hours | [
"1:80",
"1:6000",
"1:600",
"1:7200"
] | D | 1:7200 | 1 hour =3600 sec
then 8 hours =8*3600=28800
so ,4:28800=1:7200
ANSWER:D | aqua_rat |
log base 10 root of 10 root of 10 root of 10..........infinity? | [
"0",
"1",
"2",
"3"
] | B | 1 | root 10 of 10 of 10 ............infinity=10
so log base 10 of 10=1
ANSWER:B | aqua_rat |
Mike and his friend are going on a road trip and hoping to miss traffic. If they are driving at a rate of 6 miles per minute, what is their speed in kilometers per hour? [1km = 0.6 miles] | [
"60",
"30",
"300",
"600"
] | D | 600 | To calculate the equivalent of kilometres in a mile
6 miles = 6*(0.6)^-1 = 10 kilometres
In 1 hour there are 60 minutes
Speed in kmph = 10 * 60 = 600
Correct answer - D | aqua_rat |
If C and D are non-zero integers, and C/D > 1, then which of the following must be true? | [
"CD > D",
"2C > D",
"C^2< D^2",
"C > D"
] | A | CD > D | MULTIPLICATION OF TWO INTEGER IS OBIVIOUSLY GREATER THAN EACH ONE OF THEM.
A | aqua_rat |
Most diseases caused by bacteria can be cured by which medicines? | [
"antibiotics",
"antioxidants",
"hydroxides",
"inhibitors"
] | A | antibiotics | Living things that cause human diseases include bacteria, fungi, and protozoa. Most infectious diseases caused by these organisms can be cured with medicines. For example, medicines called antibiotics can cure most diseases caused by bacteria. Bacteria are one-celled organisms without a nucleus. Although most bacteria are harmless, some cause diseases. | science |
A boy has seven trousers and 8 shirts. In how many different ways can he select a trouser and a shirt? | [
"56 ways",
"57 ways",
"58 ways",
"108 ways"
] | A | 56 ways | The boy can select one trouser in seven ways.
The boy can select one shirt in 8 ways.
The number of ways in which he can select one trouser and one shirt is 7 * 8 = 56 ways.
Answer:A | aqua_rat |
The fetus is connected to what by a tube called the umbilical cord? | [
"Fallopian tube",
"placenta",
"Stomach",
"Intestines"
] | B | placenta | The placenta is a spongy mass of blood vessels. Some of the vessels come from the mother. Some come from the fetus. The placenta is attached to the inside of the mother’s uterus. The fetus is connected to the placenta by a tube called the umbilical cord . The cord contains two arteries and a vein. Substances pass back and forth between the mother’s and fetus’s blood through the placenta and cord. Oxygen and nutrients pass from the mother to the fetus. Carbon dioxide passes from the fetus to the mother. | science |
The Average of 100, 200, 300, 400, ... , 1000 is 550. If each number is divided by 5, then the new average will be equal to | [
"450",
"45",
"55",
"None of these"
] | D | None of these | Answer
Actual average
=( 100 + 220 + 300 + ... + 1000 ) / 10
=550
New Average = 550 / 5
=110
Correct Option: D | aqua_rat |
At 1:00 pm, there were 10.0 grams of bacteria. The bacteria increased to x grams at 4:00 pm, and 16.9 grams at 7:00 pm. If the amount of bacteria present increased by the same fraction during each of the 3-hour periods, how many grams of bacteria were present at 4:00 pm? | [
"13.0",
"13.3",
"13.6",
"13.9"
] | A | 13.0 | Let x be the factor by which the bacteria increases every three hours.
At 4:00 pm, the amount of bacteria was 10x and at 7:00 pm it was 10x^2.
10x^2 = 16.9
x^2=1.69
x=1.3
At 4:00 pm, the amount of bacteria was 10(1.3)=13 grams.
The answer is A. | aqua_rat |
Sunil invested $ 2200 fir 2 years and $ 2100 for 3 years at the same rate of Simple Interest. If the total interest from these investments is $ 1400, what is the rate of interest? | [
"12 3/4%",
"12 %",
"13 %",
"16%"
] | C | 13 % | (2200x2xR)/100+(2100x3xR)/100=1400
107R=1400
R= 13 %
Answer is C | aqua_rat |
When positive integer k is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer? | [
"k + 1",
"k -11",
"4k + 2",
"(k-3)/3 +2"
] | C | 4k + 2 | First, because k/6 leaves a remainder of 3, we know k must be odd.
(k=6x+3 = 3(2x+1) = odd*odd = odd)
Knowing k is odd we can examine the answer choices:
a. k + 1 --> odd + 1 --> must be even
b. k -11 --> odd - odd --> must be even
c. 4k + 1 --> 4*odd + 1 = even + 1 --> must be odd
d. (k-3)/3 +2 --> (6x+3-3)/3 + 2 = 2x + 2 --> must be even
e. k/3 --> (6x+3)/3 = 2x+1 = Must be odd
ANSWER:C | aqua_rat |
From the set of numbers {p, t, u, v, w, x, y, z}, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc... and note that (x,y)=(y,x) | [
"32",
"63",
"64",
"127"
] | D | 127 | Any letter (p, u, v, w, x, y, z) can be included or not.
Thus there are 2^7 combinations - 1 empty combination = 127 combinations
The answer is D. | aqua_rat |
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long? | [
"288",
"190",
"188",
"188"
] | B | 190 | L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B | aqua_rat |
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 16%? | [
"26%",
"28%",
"27%",
"40%"
] | A | 26% | SP2 = 2/3 SP1
CP = 100
SP2 = 84
2/3 SP1 = 84
SP1 = 126
100 --- 26 => 26%
Answer:A | aqua_rat |
Which is better investment: 11% stock at 143 or 9 3/4% stock at 117? | [
"11% stock at 143",
"9 3/4% stock at 117",
"Both are equally good",
"Cannot be compared, as the total amount of investment is not given"
] | B | 9 3/4% stock at 117 | Let investment in each case be Rs. (143 x 117).
Income in 1st case = Rs.11 x 143 x 117/143 = Rs. 1287.
Income in 2nd case = Rs.39 x 143 x 117/(4*117) = Rs. 1394.25
Clearly, 9 3/4% stock at 117 is better.
ANSWER:B | aqua_rat |
Which setup likely refracts light? | [
"a banjo and a flute",
"two mirrors in unison",
"a cat in a hat",
"gems and glowlights arranged precisely"
] | D | gems and glowlights arranged precisely | science | |
What could occur should a person scrape themselves? | [
"Loss of gravity",
"looseness of dirt or compost",
"Contaminated wounds",
"Development of super powers"
] | C | Contaminated wounds | Scraping oneself may lead to contaminated wounds. | qasc |
What affect does high pressure have on the boiling point | [
"heat",
"Rise",
"Increase",
"forces"
] | C | Increase | Pressure can increase or decrease the boiling point. | qasc |
Sum of two numbers is 80. Greater number exceeds by 5 from four times of the smaller. Find the numbers? | [
"015",
"28",
"17",
"19"
] | A | 015 | Explanation:
x + y = 80
x – 4y = 5
x = 65 y = 15
Answer:A | aqua_rat |
A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth? | [
"$69",
"$78",
"$90",
"$86"
] | C | $90 | C
$90
SP of 1m of cloth = 8925/85 = $105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= $105 - $15 = $90. | aqua_rat |
In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 31 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ? | [
"33 years",
"34 years",
"35 years",
"26 years"
] | D | 26 years | Explanation :
Let the age of youngest player be x.
Then, age of the captain = (x + 11).
=> 3*31 + 3*28 + 3*30 + x + x + 11 = 11*28.
=> 93+84+90+2x+11=308
so 2x = 30
so x = 15.
Age of the captain = (x+11)
= 26 years.
Answer : D | aqua_rat |
Certain loan amount was repaid in two annual installments of Rs.1331/- each. If the rate of interest be 10% per annum Compounded annually the sum borrowed was? | [
"Rs.2310/-",
"Rs.2400/-",
"Rs.2420/-",
"Rs.2430/-"
] | A | Rs.2310/- | Principal = (P.W of Rs. 1331/- due 1 year hence) + (P.W of Rs. 1331/- due 2 years hence)
= [1331/(1 + 10/100) + 1331/(1 + 10/100)2]
= [1331/(110/100) + 1331/(110/100 × 110/100)]
= 13310/11 + 133100/121 = 1210 + 1100 = Rs.2310/-
A | aqua_rat |
The square root of 636 is between which set of integers? | [
"24 and 25",
"25 and 26",
"26 and 27",
"27 and 28"
] | B | 25 and 26 | 25^2=625
26^2=676
Hence 636 lies between 25^2 & 26^2
ANSWER:B | aqua_rat |
A magician holds one six-sided die in his left hand and two in his right. What is the probability the number on the dice in his left hand is greater than the sum of the dice in his right? | [
"7/108",
"5/54",
"1/9",
"2/17"
] | B | 5/54 | The least sum of the numbers of the two dice in the right hand is 2. The maximum sum of the numbers on these two dice can be 5, for the left hand dice to be able to have a greater number.
Therefore the number on the dice in the left hand must be 3 or more.
Number of ways to get a sum of 2 with the two dice in the right hand= 1
Number of ways to get a sum of 3 with the two dice in the right hand= 2
Number of ways to get a sum of 4 with the two dice in the right hand= 3
Number of ways to get a sum of 5 with the two dice in the right hand= 4
Therefore required probability = P(two right dice have a sum of 2)*P(left dice has 3) + P(right dice have sum of 2 or 3)*P(left dice has 4) + P(two right dice have a sum of 2,3, or 4)*P(left dice has 5) + P(two right dice have a sum of 2,3,4,or 5)*P(left dice has 6)
= (1/36)*(1/6) + (3/36)*(1/6) + (6/36)*(1/6) + (10/36)*(1/6)
= (1/216) * (1+3+6+10)
= 20/216
= 5/54
Option B | aqua_rat |
Last September the sales total for a certain car dealership was 400% greater than the average monthly sales total for the other 11 months. The sales total for September was approximately what percent of the year´s sales? | [
"15 %",
"27%",
"31%",
"42%"
] | C | 31% | 11 moth avg = x
11 month total = 11x
sept = 400% of x + x = 5x
sept/total = =5x/(11x+5x) = =31%
ANSWER:C | aqua_rat |
A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 240 m long? | [
"38 sec",
"35 sec",
"44 sec",
"48 sec"
] | D | 48 sec | Explanation:
Speed = 45 km/hr = 45×(10/36) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 240 = 600 meter
Time taken to cross the platform = 600/(25/2) = 600×2/25 = 48 seconds
Answer: Option D | aqua_rat |
ABCD is a square. E and F are the midpoints of sides CD and BC, respectively. What is the ratio of the shaded region area to the unshaded region? | [
"1:1",
"2:1",
"3:1",
"5:3"
] | D | 5:3 | Let's join the midpoints as shown in the figure then we'll get four small squares...
AODX be 1 and similarly all squares..and we can split the unit 1 into half and half as per the mid points...
Then shaded will be 1+1/2+1/2+1/2 = 5/2
and unshaded is 1/2+1/2+1/2 = 3/2..
shaded : unshaded is 5:3..
ANS option D. | aqua_rat |
A student got 74% in math and 84% in history. To get an overall average of 75%, how much should the student get in the third subject? | [
"61%",
"63%",
"65%",
"67%"
] | D | 67% | 74 + 84 + x = 3*75
x = 67
The answer is D. | aqua_rat |
Solve(0.76 × 0.76 × 0.76 − 0.008)/(0.76 × 0.76 + 0.76 × 0.2 + 0.04) | [
"0.56",
"0.62",
"0.5",
"0.48"
] | A | 0.56 | 0.56
Option 'A' | aqua_rat |
If Albert’s monthly earnings rise by 14%, he would earn $678. If, instead, his earnings rise by only 15%, how much (in $) would he earn this month? | [
"643",
"689",
"683",
"690"
] | C | 683 | =678/1.14∗1.15
=683=683
Answer is C | aqua_rat |
what do animals find in hot temperatures? | [
"shelter",
"excretion",
"Roundworms",
"emissions"
] | A | shelter | animals use shelter in hot temperatures | qasc |
A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 30 days, then together ,all will finish the work in : | [
"13 1/3 days",
"12 1/3 days",
"15 days",
"12 days"
] | D | 12 days | C alone can finish the work in 30 days.
(A + B)can do it in 20 days
(A + B)s 1 days wok = 1/20.
As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.
A’s 1 day’s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30
(A+B+c)S 1 day’s work = (1/60) + (1/30) + (1/30) = 1/12
All the three together will finish it in 1/12 = 12 days.
ANSWER:D | aqua_rat |
In a weight-lifting competition, the total weight of Joe's two lifts was 600 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift? | [
"225",
"275",
"300",
"350"
] | C | 300 | This problem is a general word translation. We first define variables and then set up equations.
We can define the following variables:
F = the weight of the first lift
S = the weight of the second lift
We are given that the total weight of Joe's two lifts was 600 pounds. We sum the two variables to obtain:
F + S = 600
We are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift. We express this as:
2F = 300 + S
2F – 300 = S
We can now plug in (2F – 300) for S into the first equation, so we have:
F + 2F – 300 = 600
3F = 900
F = 300
Answer is C | aqua_rat |
The profits of QRS company rose 20% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? | [
"15%",
"32%",
"44%",
"62%"
] | C | 44% | Assume 100 in march , then 120 in April as 20% increase , Then 96 in may as 20% decrease from April , and then 144 in june which is 150% of 96 .
So overall increase is from 100 to 144 is 44%
Answer C | aqua_rat |
What are the most numerous organisms in the world? | [
"jellyfish",
"insects",
"primates",
"reptiles"
] | B | insects | Insects are arthropods in the class Hexapoda. They are the most numerous organisms in the world. | science |
Water molecules move about continuously due to what type of energy? | [
"potential",
"optical",
"seismic",
"kinetic"
] | D | kinetic | Water molecules move about continuously due to their kinetic energy. When a crystal of sodium chloride is placed into water, the water’s molecules collide with the crystal lattice. Recall that the crystal lattice is composed of alternating positive and negative ions. Water is attracted to the sodium chloride crystal because water is polar and has both a positive and a negative end. The positively charged sodium ions in the crystal attract the oxygen end of the water molecules because they are partially negative. The negatively charged chloride ions in the crystal attract the hydrogen end of the water molecules because they are partially positive. The action of the polar water molecules takes the crystal lattice apart (see image below). | science |
A project manager needs to select a group of 4 people from a total of 4 men and 4 women. How many possible group combinations exist such that no group has all men or all women? | [
"72",
"68",
"74",
"82"
] | B | 68 | First list all the possible combinations of Groups wit F = Female and M = Male:
MMMF
Total Combinations of 16 (4*3*2/3! *4)
FFFM
Total Combinations of 16 (same as above)
FFMM
Total Combinations of 36 (4*3/2! * 4*3/2!)
Altogether that makes 68.
Answer Choice B | aqua_rat |
If a boat is moving in upstream with velocity of 14 km/hr and goes downstream with a velocity of 40 km/hr, then what is the speed of the stream ? | [
"13 km/hr",
"26 km/hr",
"34 km/hr",
"44 km/hr"
] | A | 13 km/hr | if the downstream is a km/hr and upstream is b km/hr then speed of stream is 1/2(a-b)
so, 1/2(40-14)=13 km/hr ANSWER:A | aqua_rat |
A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 2 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used? | [
"3/4",
"4",
"18/19",
"9"
] | C | 18/19 | yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as:
A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 2 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used?
So for a job to be done in 2 hours R = 1/2
R_a(Rate of Machine R) = 1/36
R_s(Rate of Machine S) = 1/2
Lets say x machines are used to attain the desired rate, thus
x/36+x/2 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours)
(x+18x)/36 = 1/2
19x/36 = 1/2
x = 18/19.
QA = 18/19 (ANSWER C) | aqua_rat |
A bag contains 6 black and 7 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? | [
"3/4",
"7/13",
"1/7",
"1/8"
] | B | 7/13 | Let number of balls = (6 + 7) = 13.
Number of white balls = 7.
P (drawing a white ball) =7/13
Option B. | aqua_rat |
In the rectangular coordinate system, what is the area of triangle CDE with points
C=(5,8)
D=(4,2)
E=(8,0) | [
"13",
"12",
"12.8",
"14"
] | A | 13 | Use the formula of the distance formula
square root (x2-x1)^2+(y2-y1)^2
Do this for each of the sides and then the value is given as A. | aqua_rat |
Working simultaneously and independently at an identical constant rate, 10 machines of a certain type can produce a total of x units of product P in 4 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 6 days? | [
"14",
"15",
"18",
"20"
] | D | 20 | The rate of 10 machines is rate=job/time=x/4 units per day --> the rate of 1 machine 1/10*(x/4)=x/40 units per day;
Now, again as {time}*{combined rate}={job done}
then 6*(m*x/40)=3x --> m=20.
Answer: D. | aqua_rat |
Two numbers are such that the square of one is 224 less than 8 times the square of the other. If the numbers be in the ratio of 3 : 4, the numbers are | [
"6, 8",
"9, 12",
"12, 16",
"16, 20"
] | A | 6, 8 | Solution
Let the numbers be 3x and 4x. Then,
(4x)2 = 8 x (3x)2 - 224
‹=›16x2 = 72x2 - 224
‹=›56x2 = 224.
‹=›x2 = 4.
‹=›x = 2.
So, the numbers are 6 and 8.
Answer A | aqua_rat |
In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability Y that the worker is under 25 years old? | [
"0.30",
"0.25",
"0.45",
"0.70"
] | D | 0.70 | Percentage of male worker = 48
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total number of workers under 25 = 1000 - 296 = 704
Probability that a worker randomly selected is under 25 years old = 704/1000 = .704
Alternatively , since the answer options are not close , we can use estimation here .
Percentage of male worker 25 or older = (4/10)*48 = 20 % approx
Percentage of female worker 25 or older = (2/10)*52 = 10 % approx
Percentage of total worker 25 or older = 30 %
Percentage of total worker under 25 = 70 %
Probability that a worker randomly selected is under 25 years old Y= .7
Answer D | aqua_rat |
Find the average of all the numbers between 6 and 34 which are divisible by 5. | [
"18",
"20",
"24",
"30"
] | B | 20 | Solution
Average = (10+15+20+25+30/5)
= 100 / 5
= 20.
Answer B | aqua_rat |
3 years ago the average age of a family of 5 members was 17 years. With the birth of a new baby, the average age of six members remains the same even today. Find the age of the new baby. | [
"1 year",
"2 years",
"1 1⁄2 years",
"cannot be determined"
] | B | 2 years | Sum of present ages of the six members
= (17 × 6) years = 102 years.
Sum of present ages of the 5 members (excluding baby)
= 5 × (17 + 3) years = 100 years.
∴ Age of the baby = 102 – 100 = 2 years
Answer B | aqua_rat |
Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number? | [
"9",
"12",
"14",
"16"
] | B | 12 | Explanation:
We have, 2/3 * 2/5 * 3/4 * X = 36
X = 180
Now, 4/5 * X ===> 4/5 * 180 = 144
√144 = 12
ANSWER: B | aqua_rat |
Which of the following prolongs combustion? | [
"fire extinguishers",
"water",
"smothering",
"candle wax"
] | D | candle wax | science | |
I. a^2 + 11a + 30 = 0,
II. b^2 + 6b + 5 = 0 to solve both the equations to find the values of a and b? | [
"If a < b",
"If a ≤ b",
"If a > b",
"If the relationship between a and b cannot be established"
] | B | If a ≤ b | Explanation:
I. (a + 6)(a + 5) = 0
=> a = -6, -5
II. (b + 5)(b + 1) = 0
=> b = -5, -1 => a ≤ b
Option B | aqua_rat |
What does the triploid cell develop into during fertilization? | [
"zygote",
"tubers",
"endosperm",
"membrane"
] | C | endosperm | Double Fertilization After pollen is deposited on the stigma, it must germinate and grow through the style to reach the ovule. The microspores, or the pollen, contain two cells: the pollen tube cell and the generative cell. The pollen tube cell grows into a pollen tube through which the generative cell travels. The germination of the pollen tube requires water, oxygen, and certain chemical signals. As it travels through the style to reach the embryo sac, the pollen tube’s growth is supported by the tissues of the style. In the meantime, if the generative cell has not already split into two cells, it now divides to form two sperm cells. The pollen tube is guided by the chemicals secreted by the synergids present in the embryo sac, and it enters the ovule sac through the micropyle. Of the two sperm cells, one sperm fertilizes the egg cell, forming a diploid zygote; the other sperm fuses with the two polar nuclei, forming a triploid cell that develops into the endosperm. Together, these two fertilization. | science |
The distance between A&B is 1540km. A person is traveling from A to B at 100km/hr started at 6AM and another person is traveling from B to A at 120km/hr and started at same time. Then at what time they meet together. | [
"11AM",
"1PM",
"3PM",
"10AM"
] | B | 1PM | Let x hours be they will meet together
distance covered by 1st person+distance covered by 2nd person = 1540km
100x+120x = 1540
x= 7 hr
They will meet = 6AM +7hr = 1PM
Answer is B | aqua_rat |
Find the sum of the number of combinations possible by using 1,2,3,4 such that no number is repeated(ex:- 1223,4322 are invalid 1234,4321 are valid)more than once. | [
"66660",
"66760",
"66860",
"66960"
] | A | 66660 | total no. formed = 4!=4*3*2*1=24
each digit will be used at each positions, 6 times
sum of digits at unit place = 6*1+6*2+6*3+6*4 = 6*(1+2+3+4)= 60
this sum will be same for hundred, tens & unit places
sum of all 4 digit numbers formed using digits 1,2,3,4
= 1000*60+100*60+10*60+60
=60*(1000+100+10+1)
=60*1111
=66660
ANSWER:A | aqua_rat |
A clothing manufacturer has determined that she can sell 100 suits a week at a selling price of Rs. 200 each. For each rise of Rs. 4 in the selling price she will sell 2 less suits a week. If she sells the suits for Rs. x each, how many rupees a week will she receive from the sales of the suits? | [
"x2/2",
"200−x/2",
"50x - (x^2)/4)",
"150x - (x^2)/4)"
] | B | 200−x/2 | Explanatory Answer
Assume that she sells the suits at Rs.204; then she will sell two suits lesser or 98 suits.
Substitute x = 204 in each of the answer choices and check where the answer is 98.
For choice (2), the answer is 98 and this is the quickest way to find the answer.
Answer B | aqua_rat |
The Royal Hawaiian Hotel decorates its Rainbow Christmas Tree with non-flashing white lights and a series of colored flashing lights - red, blue, green, orange, and yellow. The red lights turn red every 20 seconds, the blue lights turn blue every 30 seconds, the green lights turn green every 45 seconds, the orange lights turn orange every 60 seconds, and yellow lights turn yellow every 1 minute and 20 seconds. The manager plugs the tree in for the first time on December 1st precisely at midnight and all lights begin their cycle at exactly the same time. If the five colored lights flash simultaneously at midnight, what is the next time W all five colored lights will all flash together at the exact same time? | [
"0:03 AM",
"0:04 AM",
"0:06 AM",
"0:12 AM"
] | D | 0:12 AM | Time taken by each light to on
Red = 20 secs
Blue = 30 secs
Green = 45 secs
Orange = 60 secs
Yellow = 80 secs
We need to take LCM to find the time all five colored lights will flash together.
LCM = 720 secs
=12 mins
=0.12 AM
Ans = D | aqua_rat |
A soccer store typically sells replica jerseys at a discount of 30 percent to 70 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price? | [
"20",
"25",
"30",
"40"
] | D | 40 | Let the list price be 2x
for min sale price, the first discount given should be 70%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 40
and 0.8x = 32
so lowest sale price is 32, which is 40% of 80
hence, D is the answer | aqua_rat |
The physical sciences can be divided into physics and what other science? | [
"phsycology",
"astrology",
"biology",
"chemistry"
] | D | chemistry | Physical science, in turn, can be divided into chemistry and physics. Chemistry is the study of matter and energy at the scale of atoms and molecules. For example, the synthetic fibers in the swimmer’s suit were created in labs by chemists. Physics is the study of matter and energy at all scales—from the tiniest particles of matter to the entire universe. Knowledge of several important physics concepts—such as motion and forces—contributed to the design of the swimmer’s suit. | science |
What is the sum of the 1st 6 prime numbers greater than 10? | [
"112",
"111",
"212",
"115"
] | A | 112 | Required numbers are= (11 + 13 + 17 + 19 + 23+ 29) = 112
Note: 1 is not a prime number
Answer A | aqua_rat |
At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 1). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 2? | [
"$0.50",
"$0.75",
"$1.25",
"$1.50"
] | B | $0.75 | Salary grade of 5 is p(5)=9.50+0.25(5–1)=9.50+0.25*4;
Salary grade of 2 is p(2)=9.50 + 0.25(2–1)=9.50+0.25;
p(5)-p(2)=9.50+0.25*4-9.50-0.25=0.75.
Answer: B. | aqua_rat |
Pipe A can fill a tank in 60 min . There is a second pipe in the bottom of the cistern to empty it. If all the two pipes are simultaneously opened, then the cistern is full in 180 min. In how much time, the second pipe alone can empty the cistern? | [
"60 min",
"45 min",
"90 min",
"70 min"
] | B | 45 min | Work done by the third pipe in 1 min = 1/180 - (1/60) = - 1/45.
[-ve sign means emptying]
The third pipe alone can empty the cistern in 45 min.
ANSWER:B | aqua_rat |
An agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 12.50 as commission, the cloth sold through him on that day is worth | [
"333",
"500",
"887",
"299"
] | B | 500 | Explanation:
Let the total sale be Rs. x.
Then, 2.5%. of x = 12.50 <=> (25/100 * 1/100 * x) = 125/10 <=> x = 500.
Answer: B) 500 | aqua_rat |
Two trains, each 100 meters long, moving in opposite directions, completely pass each other in 10 seconds. If one train is moving twice as fast the other, then what is the speed of the faster train (in km/hr)? | [
"48 km/hr",
"56 km/hr",
"64 km/hr",
"72 km/hr"
] | A | 48 km/hr | Let the speed of the slower train be x m/s
Then, the speed of the faster train is 2x m/s
The relative speed is 3x m/s
(100 + 100)/10 = 3x
x = 20/3
So, the speed of the faster train is 40/3 = 40/3 * 18/5 = 48 km/hr
The answer is A. | aqua_rat |
What can be used to generate heat? | [
"wind",
"desire",
"knobs",
"gas"
] | D | gas | gas can be used to generate heat | qasc |
The C.P of 40 pens is equal to the S.P of 60 pens. Find his gain % or loss% | [
"25 2/3",
"32 1/3",
"33 1/3",
"25 1/3"
] | C | 33 1/3 | 40 CP = 60 SP
60 --- 20CP loss
100 --- ? => 33 1/3%
Answer: C | aqua_rat |
If x≠5 and (x^2 - 25)/(2y) = (x - 5)/4, then in terms of y, x = ? | [
"(y - 6)/2",
"(y - 10)/2",
"y - 3",
"y - 6"
] | B | (y - 10)/2 | Since (x^2 – 25)=(x-5)(x+5) the original equation can be changed into 4*(x-5)(x+5) = 2y *(x-5).
By cancelling 2(x-5) (we can do it because x≠5) we get :
2*(x+5)=y.
So x=(y-10)/2. So the answer is B). | aqua_rat |
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? | [
"388",
"277",
"245",
"288"
] | C | 245 | Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.Answer: C | aqua_rat |
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