subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | Alice and Heather are 20 miles apart and walk towards each other along the same route. Alice walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Alice, how far from the original destination has Heather walked when the two mee... | [
"4 miles",
"8 miles",
"10 miles",
"6 miles",
"12 mile"
] | Original distance between S and H = 20 miles.
Speed of A = 5+1 = 6 mph, Speed of H = 5 mph.
Time traveled by H = t hours ---> time traveled by A = t+24/60 = t+2/5 hours.
Now, the total distances traveled by A and H = 20 miles ---> 6*(t+2/5)+5*t=20 ---> t= 8/5 hours. Thus H has traveled for 8/5 hours giving you a total ... | B |
mathematics | The length of the bridge, which a train 160 meters long and travelling at 45 km/hr can cross in 30 seconds, is: | [
"239",
"277",
"215",
"88",
"232"
] | Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (160 + X)/30
= 25/2 ==> 2(160 + X) = 750 ==> X = 215 m.
Answer: C
The answer is: C | C |
mathematics | A certain tests consists 8 sections with 25 questions, numbered from 1 to 25, in each section. If a student answered all of the even-numbered questions correctly and 3/4 of the odd-numbered questions correctly, what was the total number of questions he answered correctly?
a. 150
b. 172
c. 174
d. 175
e. 176 | [
"174",
"150",
"180",
"175",
"190"
] | Each set has 12 even and 13 odd numbered questions leading to total 96 even and 104 odd questions.
96+3/4∗104=96+78=17496+3/4∗104=96+78=174
Answer: A
The answer is: A | A |
mathematics | What is the possible ways to make 3 digit numbers from 1 to 5 number(repetition is allowed)? | [
"220",
"130",
"127",
"125",
"225"
] | Repetition is allowed to make 3 digit number.So it is easy to calculate.
5*5*5=125 ways.
Answer:option D
The answer is: D | D |
mathematics | A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? | [
"2777",
"5760",
"2766",
"8987",
"2681"
] | 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
Answer: B
The answer is: B | B |
mathematics | A collection of books went on sale, and 2/3 of them were sold for $4 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold? | [
"$288",
"$135",
"$90",
"$60",
"$54"
] | Since 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($4) or $288. The best answer is therefore A.
Answer: A.
The answer is: A | A |
mathematics | A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 865 in 4 years. The sum is: | [
"s. 665",
"s. 690",
"s. 698",
"s. 700",
"s. 720"
] | S.I. for 1 year = Rs. (865 - 815) = Rs. 50.
S.I. for 3 years = Rs.(50 x 3) = Rs. 150.
Principal = Rs. (815 - 150) = Rs. 665.
Answer: Option A
The answer is: A | A |
mathematics | The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is? | [
"240",
"235",
"245",
"250",
"260"
] | Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: Option C
The answer is: C | C |
mathematics | Average of 15 results is 43. If the average of first seven results is 41 and average of last seven results is 45 Then find the eighth result? | [
"41",
"39",
"43",
"45",
"47"
] | Option 'C'
The answer is: C | C |
mathematics | In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk? | [
"32",
"36",
"38",
"40",
"50"
] | Assume that in x days, one cow will eat one bag of husk.
More cows, less days (Indirect proportion)
More bags, more days (direct proportion)
Hence we can write as
(cows)40:1
(bags)1:40
x:40
=40×1×40=1×40×x
=x=40
ANSWER : D
The answer is: D | D |
mathematics | In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 59 liters and they are all empty, how much money total will it cost to fuel all cars? | [
"320.20$",
"380.20$",
"421.20$",
"451.20$",
"481.20$"
] | Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 59 ) = 481.20
Hence answer will be (E)
The answer is: E | E |
mathematics | A basket contains 6 blue, 6 red and 6 yellow marbles. If 6 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted? | [
"2/21",
"3/25",
"1/6",
"9/34",
"11/24"
] | 18/18*12/17*6/16 = 9/34
the answer is (D)
The answer is: D | D |
mathematics | A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party T. If one registered voter has a favorable impression of both parties for every two ... | [
"15",
"20",
"30",
"35",
"45"
] | S=100
not( T and B ) =35
only T=20
(T and B)/B=1/2
let ( T and B ) =x
only B =2x
so now, 20+35+x+2x=100
x= 15
A ans
The answer is: A | A |
mathematics | 300 + 5 × 8 = ? | [
"820",
"340",
"420",
"209",
"None of these"
] | 300 + 5 × 8 = ?
or, ? = 300 + 40 = 340
Answer B
The answer is: B | B |
mathematics | In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 21 years replaced by a new boy. The age of the new boy is? | [
"14 years 8 months",
"15 years",
"16 years 4 months",
"17 years 8 months",
"17 years"
] | Total decrease = (20 x 2) months
= 3 years 4 months
Age of the new boy
= 21 years - 3 years 4 months.
= 17 years 8 months.
ANSWER:D
The answer is: D | D |
mathematics | The simple interest on a sum of money will be Rs.500 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year? | [
"700",
"800",
"900",
"1000",
"1100"
] | P --- 10 ---- 500
P --- 5 ----- 250
3P --- 5 -----750
------
=> 1000
ANSWER:D
The answer is: D | D |
mathematics | 252 can be expressed as a product of primes as: | [
"2 x 2 x 3 x 3 x 7",
"2 x 2 x 3 x 3 x 8",
"2 x 2 x 3 x 3 x 6",
"2 x 2 x 3 x 3 x 1",
"2 x 2 x 3 x 3 x 2"
] | Clearly, 252 = 2 x 2 x 3 x 3 x 7.
Answer: A
The answer is: A | A |
mathematics | Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 12 minutes more to walk to work than to ride his bike to work, then x equals? | [
"4",
"7",
"10",
"15",
"18"
] | Please follow posting guidelines, link is in my signatures.
As for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 720 (which is TIME in seconds.)... | E |
mathematics | A woman started a business investing Rs. 70,000. Roja joined him after six months with an amount of Rs. 1,05,000 and Sachin joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Akash, Roja and Sachin respectively, 3 years after Aman started the b... | [
"7:6:10",
"12:15:16",
"42:45:56",
"None of these",
"Cannot be determined"
] | Explanation :
Akash : Roja : Sachin = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24)
= 12 : 15 : 16.
Answer : B
The answer is: B | B |
mathematics | X is able to do a piece of work in 14 days and Y can do the same work in 20 days. If they can work together for 5 days, what is the fraction of work completed? | [
"15/28",
"17/28",
"13/28",
"19/28",
"11/28"
] | Explanation :
Amount of work X can do in 1 day = 1/14
Amount of work Y can do in 1 day = 1/20
Amount of work X and Y can do in 1 day = 1/14+ 1/20= 17/140
Amount of work X and Y can together do in 5 days = 5 × (17/140) = 17/28
Answer : Option B
The answer is: B | B |
mathematics | Of the 200 students at University XYZ majoring in one or more of the engineering disciplines, 140 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical coul... | [
"30 to 70",
"70 to 100",
"90 to 110",
"130 to 150",
"150 to 170"
] | if there are 140 students majoring in electrical then there must be 60 person not majoring electrical at all, since both of the student not majoring electrical and mechanical is at least 30, so the number of the student who are not majoring electrical but majoring mechanical will be at least 30.
if there are 150 studen... | C |
mathematics | Average age of students of an adult school is 46 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students. | [
"1200",
"120",
"360",
"168",
"None of these"
] | Explanation :
Let the original no. of students be x.
According to situation, 46x + 120*32 = (x + 120)36 ⇒ x = 48
So, Required no. of students after joining the new students
= x + 120 = 168.
Answer : D
The answer is: D | D |
mathematics | Find the no.of ways of arranging the boy and 9 guests at a circular table so that the boy always sits in a particular seat? | [
"3!",
"8!",
"7!",
"9!",
"11!"
] | Ans.(D)
Sol. Total number of persons = 10 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 9 places in 9P9 = 9! Ways ... The number of required arrangements = 9! x 1= 9! = 9! ways
The answer is: D | D |
mathematics | John had a stock of 800 books in his bookshop. He sold 62 on Monday, 62 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold? | [
"26.5%",
"36.5%",
"71.7%",
"56.5%",
"70.0%"
] | Let N be the total number of books sold. Hence
N = 75 + 50 + 64 + 78 + 135 = 272
Let M be the books NOT sold
M = 960 - N = 960 - 402 = 688
Percentage
Books not sold / total number of books = 688/960= 0.72 = 71.7%
correct answer C
The answer is: C | C |
mathematics | Two goods trains each 75 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? | [
"2.3 sec",
"4.2 sec",
"48 sec",
"7.2 sec",
"9 sec"
] | Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 75 + 75 = 150 m.
Required time = 150 * 6/125 = 7.2 sec.
Answer:D
The answer is: D | D |
mathematics | Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 5 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 5... | [
"21",
"22",
"23",
"24",
"25"
] | 5 minutes is 300 seconds.
Lamp A and Lamp B will flash together every 24 seconds.
300/24=12 plus remainder.
In the time period, Lamp A and Lamp B will flash together 12 times.
Lamp A and Lamp C will flash together every 30 seconds.
300/30=10.
In the time period, Lamp A and Lamp C will flash together 10 times.
Lamp B an... | C |
mathematics | A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work? | [
"22 days",
"4 days",
"13 days",
"6 days",
"9 days"
] | (A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).
B's 1 day's work =((1/4)-(1/12))=(1/6)
Hence, B alone can complete the work in 6 days.
Answer is D.
The answer is: D | D |
mathematics | A 16% stock yielding 14% is quoted at: | [
"s. 83.33",
"s. 110",
"s. 114",
"s. 120",
"s. 140"
] | Income of Rs 14 on investment of Rs 100
Income of Rs 16 on investment of ?
= (16*100)/14=114
ANSWER:C
The answer is: C | C |
mathematics | A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.40 per rake each month from March through Octobe... | [
"0.40x",
"1.20x",
"5.60x",
"1.60x",
"3.20x"
] | because we have a total of 4X
Also from Mar- Oct the rakes will be deducted by 1/8 X
so
In Apr they pay for the storage 0.4 * 4X * 7/8
In May they pay for the storage 0.4 * 4X * 6/8
In Jun they pay for the storage 0.4 * 4X * 5/8
In Jul they pay for the storage 0.4 * 4X * 4/8
In Aug they pay for the storage 0.4 * 4X * 3... | C |
mathematics | The average age of husband, wife and their child 3 years ago was 25 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is | [
"22",
"40",
"34",
"21",
"11"
] | Explanation:
Sum of the present ages of husband, wife and child = (25 x 3 + 3 x 3) years = 84 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (84 - 50) years = 34 years.
Answer: C
The answer is: C | C |
mathematics | Bani has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar? | [
"71",
"72",
"73",
"74",
"75"
] | Let there be a pennies , b nickels and c dimes
so total amount can be 1+5b+10c cents to 4+5b+10c
as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4)
So the total can never be divisible by 5 and ... | E |
mathematics | The smallest value of n, for which 2n+1 is not a prime number, is | [
"3",
"4",
"5",
"6",
"7"
] | (2×1 + 1) = 3.
(2×2 + 1) = 5.
(2×3 + 1) = 7.
(2×4 + 1) = 9.
which is not prime , n=4.
ANSWER:B
The answer is: B | B |
mathematics | A boat can travel 1.8 times the distance down the stream than up the stream in the same time. If the speed of the current is 3 KMPH, Find the speed of the boat in still water | [
"5",
"10.5",
"15",
"20",
"25"
] | Simple question, messy language.
Lets say boat's speed is B and current's speed is C.
Upstream speed : B - C
Downstream speed : B + C
Distance will be the same both times. lets say D.
given : time it takes upstream = 1.8 times time it takes downstream
D/(B + C) = 1.8 * [D/(B - C)]
Solving B = 3.5 C
given : C is 3 KMPH
... | B |
mathematics | The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of? | [
"6:6",
"6:3",
"6:5",
"6:8",
"6:1"
] | 4:5
3:2
-------
12:15:10
12:10
6:5
Answer: C
The answer is: C | C |
mathematics | Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him? | [
"$496.30",
"$512.40",
"$555.40",
"$574.90",
"$588.20"
] | 670 is the final price that is the selling price. now suppose, x is the cost price.
therefore 670 = 1.35 * x
now while doing x = 670/1.35 calculation. I saw that the answer choices begin with 5.
So i did 135 * 5 = 675. As 670 is less than 675. Therefore the quotient will be less than 5.
Which is only in the answer A.
T... | A |
mathematics | If 4 (P's Capital) = 6 (Q's Capital) = 10 (R's Capital), then out of the total profit of Rs 4650, how much R will receive? | [
"300",
"600",
"900",
"800",
"500"
] | Let P's capital be p,
Q's capital be q,
and R's capital be r
Then
4p=6q=10r2p=3q=5r⋯(A)
From (A),
q=2p/3 ⋯(1)
r=2p/5 ⋯(2)
p:q:r=p:2p/3:2p/5
=15:10:6
R's share =4650×6/31=150×6=900
Answer is C.
The answer is: C | C |
mathematics | An urn contains 8 black and 2 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black? | [
"1/5",
"28/45",
"2/5",
"3/5",
"2/7"
] | Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 8/10
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 7 black balls and two white balls left in the urn. Therefore,... | B |
mathematics | A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 70% probability that engine two will work. The third engine works... | [
"7/12",
"1/4",
"1/2",
"7/24",
"17/24"
] | In probability questions the trap answer is just the multiple of the numbers in the question.
i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer
The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer
So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they c... | E |
mathematics | One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in | [
"144 mins",
"140 mins",
"136 mins",
"132 mins",
"130 mins"
] | Explanation:
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute =1/x+3/x=1/36
=>4/x=1/36
x=36∗4=144mins
ANSWER IS A
The answer is: A | A |
mathematics | There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two socks of the same colour have been chosen? | [
"2",
"3",
"14",
"16",
"20"
] | 60% of 30 = 18.
So, there are 18 red socks and there are 12 blue socks.
Check out this possible cases once we have selected TWO socks:
case a: 2 red socks, in which case we have a pair of matching socks. DONE!
case b: 2 blue socks, in which case we have a pair of matching socks. DONE!
case c: 1 red sock and 1 blue sock... | B |
mathematics | 8, 27, 64, 100, 125, 216, 343 | [
"64",
"100",
"125",
"216",
"343"
] | The pattern is 2 cube, 3 cube, 4 cube, 5 cube, 6 cube, 7 cube. But, 100 is not a perfect cube.
answer : B
The answer is: B | B |
mathematics | How many positive integers less than 5,000 are evenly divisible by neither 15 nor 20? | [
"4,514",
"4,477",
"4,521",
"4,428",
"4,349"
] | integers less than 5000 divisible by 15 5000/15 =333.something , so 333
integers less than 5000 divisible by 20 5000/20 = 238.## , so 238
we have double counted some, so take LCM of 15 and 20 =105 and divide by 5000, we get 47. so all numbers divisible by 15 and 20 = 333 +238 -47 =524
now subtract that from 4999. 4999-... | B |
mathematics | For any positive x, y and z if x is n% of y and z is m% of y then what percentage Q must x be of z? | [
"(n/m)%",
"(m × n)%",
"(100 / [m × n]) %",
"(100 × m/n)%",
"(100 × n/m)%"
] | x is n% of y MEANS x= (n/100 )* y------------------------eq1
z is m% of y MEANS z= (m/100 )* y------------------------eq2
Find equation of xz
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
so answer Q is 100n/m %.E
The answer is: E | E |
mathematics | Car A leaves the airport at 9:00 am and travels at a constant rate of 30 km per hour. Car B leaves the airport at 9:30 am and travels in the same direction along the same highway at a constant rate of 34 km per hour. At what time will Car B be 12 km ahead of Car A? | [
"3:45 pm",
"4:00 pm",
"4:15 pm",
"4:30 pm",
"4:45 pm"
] | At 9:30 am, Car A will be 15 km ahead of Car B.
Car B travels at a rate 4 km per hour faster than Car A.
Car B needs to travel 27 km more than Car A in order to be 12 km ahead.
This will take 27 km/4 km per hour=6.75 hours.
Car B will be 12 km ahead at 4:15 pm.
The answer is C.
The answer is: C | C |
mathematics | The units digit of (35)^(87) + (93)^(46) is: | [
"2",
"4",
"6",
"8",
"0"
] | Step 1: (35)^(87) can be broken up into (5)^87 x (7)^87. Each power of 7 ends in a units digit of either a 7,9,3 or 1. Each power of 5 ends in a 5. When you multiply 5 by any odd number you will end up with a units digit of 5.
Step 2: (93)^(46) can be broken up into (3)^46 x (31)^46. Each power of 31 ends in a units di... | B |
mathematics | Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? | [
"8",
"twelve (12)",
"14",
"16",
"18"
] | Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
The answer is: B | B |
mathematics | John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3? | [
"40 ml",
"60 ml",
"70 ml",
"80 ml",
"90 ml"
] | concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)
concentration of water in pure water= 1 ...(2)
Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3
=> concentration of water in mixture2 =310
By rule of alligation,
concentration of water in m... | C |
mathematics | A 72 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume? | [
"8",
"12",
"18",
"14",
"16"
] | Amount of salt = 7.2
Assume x gallons of water are added.
7.2 / 72 + x = 8/100
720 = 8x + 576
8x = 144
x = 18
Correct Option: C
The answer is: C | C |
mathematics | A container has a capacity of 20 gallons and is full of spirit. 4 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 3 times. Find how much spirit is left in the resulting mixture finally? | [
"6(257/525) gallons",
"6(346/625) gallons",
"6.5 gallons",
"6.25 gallons",
"None of these"
] | There is a direct formula to calculate such repetition:
Left QTY / Orig QTY = ( (Orig QTY - Rep QTY) / Orig QTY )^n
where n is number of times mixing done:
Left QTY / 20 = (20 -4)^3 / 20^3
Left QTY = 20 (16/20)^3
Left QTY = 20 ( 4/5 )^3
Left QTY = 10.24
Answer is E
The answer is: E | E |
mathematics | The ratio of A and B is 5:3.After 2 years their ratio is 3:2.What is the age of B? | [
"5",
"3",
"6",
"7",
"8"
] | The ratio of A and b is 5x and 3x years.
After 2 years, their ratio will be 3 and 2.
(i.e) (5x+2)/(3x+2)=3/2
10x+4=9x+6
x=2
B's age=3x=3(2)=6 years
Answer is option C
The answer is: C | C |
mathematics | A box contains four dime coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is al... | [
"3/4",
"1/5",
"2/5",
"3/5",
"4/5"
] | There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)
How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)
Therefore probability = (number of ways to get heads from a two-headed coin)/(number of... | E |
mathematics | A cupcake recipe calls for 2 cups of sugar, and makes 2 dozen cupcakes. A caterer will supply cupcakes for 150 guests at a birthday party in which there should be at least 2 cupcakes per guest. What is the minimum amount of sugar needed? | [
"24 cups",
"75 cups",
"2 cups",
"15 cups",
"250 cups"
] | The proportion equation can be used. Let C = sugar needed.
Note: 12 = 1 dozen
Proportion: A/B = C/D
2 cups of sugar (A) makes 24 cupcakes (B).
(2)(150 guests) = 300 (D) is the least number cupcakes needed.
Proportion: 2/24 = C/300
C = (2)(300)/24 = 600/24 = 24. At least 24 cups are needed.
Answer is A
The answer is: A | A |
mathematics | A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 190 m long? | [
"44",
"99",
"88",
"77",
"21"
] | :
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 190 = 550 m
Required time = 550 * 2/25 = 44 sec
Answer:A
The answer is: A | A |
mathematics | A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days? | [
"3.75",
"4",
"2",
"8",
"7"
] | 1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
ANSWER A
The answer is: A | A |
mathematics | Jerry went to a shop and bought things worth Rs. 45, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? | [
"19",
"19.7",
"21.3",
"29.5",
"39.7"
] | Total cost of the items he purchased = Rs.45
Given that out of this Rs.45, 30 % is given as tax
=> Total tax incurred = 30 % = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (45−30/100−x)6/100 = 30/100
⇒ 6(45 −0.3 −x) = 30
⇒ (45 − 0.3 − x) = 5
⇒ x = 45 − 0.3 − 5 = 39.7
E)
The answer is: E | E |
mathematics | If the time is currently 1:30 pm, what time will it be in exactly 642 hours? | [
"3:30 am",
"4:30 am",
"5:30 am",
"6:30 am",
"7:30 am"
] | 642 = 26(24) + 18/24
The time will be 18 hours later than 1:30 pm which is 7:30 am.
The answer is E.
The answer is: E | E |
mathematics | Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $216 per week. How much does she earn in dollars per hour? | [
"11",
"10",
"9",
"8",
"6"
] | Let Sheila earn x dollars per hour
So, on Monday, Wednesday and Friday , she earns 8x each
And, on Tuesday and Thursday, she earns 6x each
In total , over the week she should earn, 3(8x) + 2(6x) = 36x
She earns $216 per week
36x =216
x =6
Correct Option : E
The answer is: E | E |
mathematics | During a Pizza buffet where A eats more times 2.4 than B, and B eats 6 times less than C.find the leat number of times all the three has to eat | [
"50",
"60",
"70",
"80",
"85"
] | A eats more than B if B eats 1 times than the ratio of A and B is A:B is 2.4:1 or 12:5 and as B eat 6 times less the C the the ratio of B : C is 5:30 the the least number of times all three has eat is the LCM of A,B,C that is 60 ..
ANSWER:B
The answer is: B | B |
mathematics | the probability of a student possessing a ball point pen in exam is 3/5 & possessing an ink pen is 2/3. find his probability of possessing at least one of them | [
"10/15",
"11/15",
"12/15",
"13/15",
"14/15"
] | the probability of a student possessing a ball point pen in exam is 3/5 .
the probability of a student not possessing a ball point pen in exam is 2/5 & possessing an ink pen is 2/3.
& not possessing an ink pen is 1/3.
his probability of possessing none of them =2/5*1/3=2/15
his probability of possessing one of them =1-... | D |
mathematics | A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 50 percent of the drive from the center, what percent of the round-trip has the technician completed? | [
"70",
"65",
"60",
"75",
"80"
] | round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 50% of 50% i.e 25%. so he completed 50 +25 =75 % of total trip.
D
The answer is: D | D |
mathematics | 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 4 employees to 2 different offices? | [
"10",
"15",
"14",
"16",
"18"
] | Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2*2=2^4=16.
Answer: D.
The answer is: D | D |
mathematics | The price of a certain painting increased by 20% during the first year and decreased by 25% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price? | [
"102%",
"90%",
"120%",
"85%",
"95%"
] | Easiest thing to do: Assume that price is 100
Price at the end of yr 1: 100+ 20 = 120
Price at the end of year 2 = 120 - 120*0.25 = 120*0.75 = 90
Hence required answer = (90/100)*100% = 90%
Answer is B.
The answer is: B | B |
mathematics | In school there are some bicycles and 4 wheeler wagons.one Tuesday there are 190 wheels in the campus.How many bicycles are there? | [
"35",
"36",
"37",
"38",
"39"
] | Let no. of bicycles be x
& no. of wagons be y
so, 2x+4y=190
by solving, we get
no. of bicycles=39 (wheels=>2*39=78)
no. of wagons=28 (wheels=>4*28=112)
ANSWER:E
The answer is: E | E |
mathematics | The smallest value of n, for which 2n is not a prime number, is | [
"2,3,4",
"1,3,5",
"2,5,6",
"4,8,9",
"12,14,16"
] | (2×1) = 2.
(2×2) = 4.
(2×3) = 6.
(2×4) = 8.
which is not prime , n=2,3,4.
ANSWER:A
The answer is: A | A |
mathematics | In a class of 52 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German? | [
"30",
"10",
"18",
"28",
"32"
] | Total=English+German-Both+Neither --> 52=English+22-12+0 --> English=42 --> Only English=English-Both=42-12=30
Answer: A.
The answer is: A | A |
mathematics | A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 600 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours... | [
"2880.",
"4860.",
"5780",
"4320",
"6380."
] | Normal Day = 600 kw/h
Stormy Day = 600*1.2=720 kw/h
3 windmills for 2 hours on stormy day
720*3*2=4320
Answer: D
The answer is: D | D |
mathematics | In a certain corporation, there are 300 male employees and 150 female employees. It is known that 40% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female? | [
"1/2",
"2/3",
"3/5",
"7/10",
"11/15"
] | P(female) = 150/450 = 1/3
P(male with advanced degree) = 0.4*300/450 = 120/450 = 4/15
The sum of the probabilities is 9/15 = 3/5
The answer is C.
The answer is: C | C |
mathematics | The average age of 3 girls is 16 years and their ages are in the proportion 1:2:3. The age of the youngest girl is? | [
"12 years",
"7 years",
"9 years",
"10 years",
"8 years"
] | Total age of 3 boys = 16*3 =48
ratio of their ages = 1:2:3
Age of the youngest =48*1/6 = 8 years
Answer is E
The answer is: E | E |
mathematics | (51+52+53+………+100) is equal to: | [
"2525",
"2975",
"3225",
"3775",
"3885"
] | (51+52+53+………+100) = (1+2+3+…….+100)- (1+2+3+4+……+50)
= (100*101)/2 - (50*51)/2
= (5050-1275)= 3775.
Answer: D
The answer is: D | D |
mathematics | Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? | [
"Rs.16.90",
"Rs.16.59",
"Rs.16.60",
"Rs.16.50",
"Rs.18.50"
] | Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) ... | D |
mathematics | If the price of a certain computer increased 30 percent from y dollars to 351 dollars, then 2y = | [
"540",
"570",
"619",
"649",
"700"
] | Before Price increase Price = y
After 30% Price increase Price = y+(30/100)*y= 1.3y = 351 (Given)
i.e. y= 351/1.3 = $270
i.e. 2y = 2*270 = 540
Answer: option A
The answer is: A | A |
mathematics | Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 400 funds on the list have 3-star ratings, how many funds are on the list? | [
"500",
"750",
"1,000",
"1,200",
"1,500"
] | C
Fraction of 5- and 4-star funds: 1/3 + (2/5)*(2/3) = 5/15 + 4/15 = 9/15
Fraction of 3-star funds = 1 - 9/15 = 6/15
(6/15)*Total = 400
Total = 1000
The answer is: C | C |
mathematics | A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 10 were to be added to each score, which of these three statistics would change? | [
"The mean only",
"The median only",
"The mean and the median",
"The standard deviation only",
"The mean and the standard deviation"
] | The correct answer is C.
The answer is: C | C |
mathematics | For a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease? | [
"22%",
"40%",
"60%",
"84%",
"94%"
] | Again, the exact dimensions of the cylinder do not matter, as long as every length increases by the same percent or same ratio. We now have a percent decrease, which means we subtract to construct our multiplier. A 60% decrease means we have a multiplier of 1 – 0.60 = 0.4, and so k = 0.4 as well. For volume we need to ... | E |
mathematics | A boy has 5 pens out of which a pair is to be selected for an examination. At most, how many different pairs are possible? | [
"20",
"10",
"5",
"40",
"10"
] | N=5C2=5!/(3!2!)=5*2=10
Correct Option: E
The answer is: E | E |
mathematics | If a certain sample of data has a mean of 15.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean? | [
"(8.0; 16.5)",
"(8.5; 21.0)",
"(14.0; 26.5)",
"(16.5; 26.0)",
"(21.0; 26.5)"
] | 2.5 standard deviation equals to 2.5*2=5;
2.5 standard deviations from the mean, so5 points, from the mean is the range from {mean-5} to {mean+5}, so from 10 to 20.
The correct answer choice must cover all this range: only answer choice B does this.
Answer: B.
The answer is: B | B |
mathematics | If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers i | [
"2 : 3",
"3 : 4",
"3 : 20",
"20 : 3",
"None"
] | Sol.
0.4A = 0.06 B ⇔ A / B = 0.06 / 0.40 = 6/40 = 3/20.
∴ A : B = 3 : 20.
Answer C
The answer is: C | C |
mathematics | When a plot is sold Rs. 18,700, the owner loses 15%. At what price must the plot be sold in order to gain 15%? | [
"Rs. 21,000",
"Rs. 22,500",
"Rs. 25,300",
"Rs. 25,800",
"None"
] | Solution
85 : 18700 = 115 : x or x = (18700 x 115 / 85)
= 25300.
Hence, S.P. = Rs. 25300.
Answer C
The answer is: C | C |
mathematics | In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 161 hats in this group, how many of these hats are not blue? | [
"28",
"42",
"48",
"112",
"76"
] | Since the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be
7x+4x+12x=161 or 23x=161...here 7x,4x and 12x represent hats of each type
23x=161 so x=7...Blue hats =7*7=49...Not blue will be 161-49=112.
Ans D
The answer is: D | D |
mathematics | Rs.1010/- distributed among A,B and C such that on decreasing their shares by RS.25,RS.10 and RS.15 respectively, The balance money would be divided among them in the ratio 3:2:5. Then, A’s share is:? | [
"Rs.255/-",
"Rs.313/-",
"Rs.365/-",
"Rs.355/-",
"Rs.345/-"
] | A:B:C = 3:2:5
Total parts = 10
A's share is = 3 parts
10 -----> Rs.960/-
3 -----> Rs.288/-
A's total =288 + 25 = Rs.313/-
B)
The answer is: B | B |
mathematics | A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent? | [
"28%",
"20%",
"29%",
"27%",
"10%"
] | 900 ---- 180
100 ---- ? => 20%
Answer:B
The answer is: B | B |
mathematics | Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has twu iron coins and twu copper coins, how many different sums from 1¢ to 14¢ can he make with a combination of his coins? | [
"8",
"11",
"9",
"4",
"12"
] | The total sum is 2*2 + 2*5 = 14¢. If you can make each sum from 1 to 14 (1¢, 2¢, 3¢, ..., 14¢), then the answer would be 14 (maximum possible).
Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 13¢ and 11¢ (since total sum is 14¢ we cannot remove 1¢ or 3¢ to get 13¢ or 11¢).
Also discarded 6 and 8, for ... | A |
mathematics | The radius of the base of cone is 3 cm and height is 4 cm. Find the volume of the cone? | [
"12",
"75",
"97",
"15",
"91"
] | 1/3 * π * 3 * 3 * 4
= 12 π
Answer:A
The answer is: A | A |
mathematics | Steve traveled the first 2 hours of his journey at 50 mph and the last 3 hours of his journey at 80 mph. What is his average speed of travel for the entire journey? | [
"60 mph",
"68 mph",
"53.33 mph",
"64 mph",
"66.67 mph"
] | Answer
Average speed of travel = Total distance travelled/Total time taken
Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours.
Distance covered in the first 2 hours = speed * time = 50 * 2 = 100 miles.
Distance covered in the next 3 hours = speed * time = 80 ... | B |
mathematics | Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip? | [
"1",
"8",
"9",
"2",
"7"
] | Explanation:
Amy can travel clockwise or anticlockwise on the diagram.
Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.
Similarly, anticlockwise sh
Answer: B) 8
The answer is: B | B |
mathematics | Car X began traveling at an average speed of 35 miles per hour. After 48 minutes, car Y began traveling at an average speed of 39 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped? | [
"105",
"140",
"175",
"210",
"245"
] | In 48 minutes, car X travels 28 miles.
Car Y gains 4 miles each hour, so it takes 7 hours to catch car X.
In 7 hours, car X travels 245 miles.
The answer is E.
The answer is: E | E |
mathematics | 1100 boys and 700 girls are examined in a test; 31% of the boys and 23% of the girls pass. The percentage of the total who failed is ? | [
"A)63.3%",
"B)52.4%",
"C)81.2%",
"D)75.4%",
"E)72.11%"
] | Total number of students = 1100+700 = 1800
Number of students passed = (31% of 1100+23% of 700) = 341+161 = 502
number of failures = 1298*100/1800= 72.11%
Answer is E
The answer is: E | E |
mathematics | A sum of Rs. 2678 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum? | [
"1629",
"1648",
"2677",
"2986",
"2679"
] | (x*8*3)/100 = ((2678 - x)*3*5)/100
24x/100 = 40170/100 - 15x/100
39x = 40170 => x = 1030
Second sum = 2678 – 1030 = 1648
Answer:B
The answer is: B | B |
mathematics | F and E are midpoints of AB and AD respectively. If the side of square ABCD is 8, what is the area of triangle CEF? | [
"8√2",
"9√3",
"18",
"16√2",
"24"
] | Area of Shaded figure = Area of Square - (Area of Triangle AEF + Area of Triangle FBC + Area of Triangle EDC )
= 8*8 - (1/2 * 4 * 4 + 1/2 * 4 * 8 + 1/2 * 4 * 8 )
= 24.
Answer E.
The answer is: E | E |
mathematics | Two-third of a positive number and 16/216 of its reciprocal are equal. Find the positive number. | [
"9/25",
"14/4",
"4 /12",
"144/25",
"144/29"
] | Explanation:
Let the positive number be x.
Then, 2/3 x = 16/216 * 1/x
x2 = 16/216 * 3/2
= 16/144
x = √16/144 =4 /12.
ANSWER:C
The answer is: C | C |
mathematics | Of the 60 electronics components that a factory must manufacture, 80 percent would be most e¢ ciently manufactured by Machine A and the remaining 20 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 60 components. If 40 percent of the components were manufac... | [
"30",
"32",
"33",
"35",
"36"
] | A can manufacture 80 % of 60 efficiently, which is 48.
B can manufacure 20 % of 60 efficiently, which is 12.
Now 40 % of 60 are produced by A. This means 24 parts. Since A can produce 48 efficiently, all 24 are produced efficiently. Rest (36) is produced by B, which can produce max. 12 parts efficiently.
Hence parts th... | E |
mathematics | In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes. | [
"10",
"12",
"16",
"17",
"18"
] | Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
B
The answer is: B | B |
mathematics | Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 31, 56, 93 | [
"2",
"6",
"15",
"93",
"91"
] | 1(result) + (1*1) = 2.
2(result) + (2*2) = 6.
6(result) + (3*3) = 15.
15(result) + (4*4) = 31.
31(result) + (5*5) = 56.
56(result) + (6*6) = 92.
Now we are getting 92 not 93.. So 93 is the wrong number of the given.
answer : D
The answer is: D | D |
mathematics | Wendy begins sanding a kitchen floor by herself and works for 7 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself? | [
"9/80 hours",
"3/20 hours",
"20/3 hours",
"80/9 hours",
"10 hours"
] | Let Wendy finishes sanding the floor alone in W hours while B be the hours for Bruce.
Thus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.
If wendy works for 7 hours and is then joined by Bruce to finish the work in 2 more hours,
7/W + 2/W+2/B = 1 (1 denotes the total amount of work)
9/W ... | E |
mathematics | If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first? | [
"67%",
"70%",
"60%",
"62%",
"65%"
] | Given ratio
= 1/8 : 1/5 = 5 : 8
Let first number be 5x and the second number be 8x.
The second number is more than first number by 3x.
Required percentage
= 3x/5x * 100 = 60%.
Answer:C
The answer is: C | C |
mathematics | The regular price per can of a certain brand of soda is $0.55. If the regular price per can is discounted 25 percent when the soda is purchased in 24-can cases, what is the price of 70 cans of this brand of soda purchased in 24-can cases? | [
"$16.32",
"$18.00",
"$21.60",
"$24.48",
"$28.87"
] | The discounted price of one can of soda is (0.75)($0.55), or $0.4125
Therefore, the price of 70 cans of soda at the discounted price would be (70)($0.4125) = 28.875
Answer: E
The answer is: E | E |
mathematics | √1.5625 = ? | [
"1.05",
"1.25",
"1.45",
"1.55",
"1.65"
] | Explanation:
1|1.5625( 1.25
|1
|-------
22| 56
| 44
|-------
245| 1225
| 1225
|-------
| X
|-------
1.5625 = 1.25.
ANSWER IS B
The answer is: B | B |
mathematics | A hostel had provisions for 250 men for 44 days. If 50 men left the hostel, how long will the food last at the same rate? | [
"55",
"40",
"50",
"60",
"65"
] | A hostel had provisions for 250 men for 44 days
If 50 men leaves the hostel, remaining men = 250 - 50 = 200
We need to find out how long the food will last for these 200 men.
Let the required number of days = x days
More men, Less days (Indirect Proportion)
(men) 250 : 200 :: x : 44
250×44=200x
5×44=4x
x=5×11=55
ANSWER... | A |
mathematics | The rate of Interest on a sum of money is 9% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is | [
"1,125",
"2,000",
"2,100",
"2,250",
"2,540"
] | Explanation:
I1 = (P x 3 x 9)/100 = 10P/37
I2 = (P x 4 x 4)/100 = 4P/25
I3 = (P x 1 x 5)/100 = P/20
10P/37 + 4P/25 + P/20 = 540
12P/25 = 540
P = 1125
Answer: Option A
The answer is: A | A |
mathematics | For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 74, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement? | [
"K+37",
"2K+37",
"(74+K)/2",
"(74-K)/2",
"2(74-K)"
] | Let y be the years of service at the company.
After y years of service, Sue's age will be K + y.
Sue can retire when (K+y) + y = 74
y = (74 - K)/2
Then Sue's age will be K + y = K + (74 - K)/2 = (74+K) / 2
The answer is C.
The answer is: C | C |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.