divelab/Sys2Bench huggingface dataset:
Question: At the opening of a trading day at a certain stock exchange, the price per share of stock K was $6. If the price per share of stock K was $8 at the closing of the day, what was the percent increase in the price per share of stock K for that day?
Options:
A)1.4%
B)5.9%
C)11.1%
D)12.5%
E)33.33%
Rationale: Opening = 6
Closing = 8
Rise in price = 2
So, percent increase = 2/6*100 =33.33%
Answer : E
Answer: E
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
Options:
A)2
B)3
C)5
D)81
E)6
Rationale: :
1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
1/4 + 9/20 = 14/20
1 h ---- 1/20
? ----- 14/20
14 hours ==> 5 PM.Answer: D
Answer: D
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation h of the mean, what percent of the distribution is less than m+h?
Options:
A) 16%
B) 32%
C) 48%
D) 84%
E) 92%
Rationale: 16%
________________________________________________ m+h
34%
________________________________________________ m
34%
________________________________________________ m-h
16%
since 68% lies one standard deviation from mean m, => 50% of 68% lies on either side as it is symmetric about m.
thus 16% lie below m-h and 16% lie above m+h
now below m+h = 16+34+34 = 84%
hence D
Answer: D
Question: Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married ?
Options:
A)23 years
B)25 years
C)33 years
D)35 years
E)45 years
Rationale: Ayush's present age = 10 years.
His mother's present age = (10 + 20) years = 30 years.
Ayush's father's present age = (30 + 5) years = 35 years.
Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years.
Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.
ANSWER:A
Answer: A
Question: The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
Options:
A)9 : 29
B)9 : 23
C)9 : 24
D)9 : 25
E)9 : 21
Rationale: a13 : a23 = 27 : 125
a1 : a2 = 3 : 5
6 a12 : 6 a22
a12 : a22 = 9 : 25
Answer: C
Answer: C
Question: A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/8 of th area of the garden. What is the radius of the circular garden?
Options:
A)1
B)2
C)4
D)8
E)16
Rationale: as per the question-- width is negligible
now,
let L be the length of the fence =2pir
L=1/8(pir^2)
pir^2=16pir
r=16
Answer : E
Answer: E
Question: 107 x 107 + 93 x 93 =?
Options:
A)19578
B)19418
C)20098
D)21908
E)None of them
Rationale: =(107)^2+(93)^2
=(100+7)^2+(100-7)^2
=2 x [(100)^2+7^2]
=2[10000+49]
=2 x 10049 = 20098
Answer is C
Answer: C
Question: What quantity of water should taken out to concentrate 18 liters of 40% acidic liquid to 60% acidic liquid?
Options:
A)5liters
B)10liters
C)15liters
D)8liters
E)6liters
Rationale: Required answer is = 18(60-40)/60 = 6 liters
Answer is E
Answer: E
Question: To furnish a room in a model home an interior decorator is to select 3 chairs and 3 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 6 chairs in the warehouse and if 80 different combinations are possible, how many tables are there in the warehouse?
Options:
A)A)4
B)B)8
C)C)10
D)D)15
E)E)30
Rationale: Total number of ways to choose 3 chairs from 6= 6C3=20
Total number of combination=80
That means we need get 4 combinations from the selection of tables....
Screening through the answers.... 4C3=4..... 4*20=80
Answer is 6... A
Answer: A
Question: A and B began business with Rs.6000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
Options:
A)240
B)288
C)277
D)357
E)361
Rationale: (6*8 + 5*4):(4*8 + 5*4)
17:13
17/30 * 630 = 357
Answer: D
Answer: D
Question: If x and y are non-zero integers, and 25x^4 – 4y^4 = 5x^2 + 2y^2, which of the following could be the value of x2 in terms of y?
Options:
A)2y^2+1/6
B)2y^2/5
C)2y^2
D)2y^2+1/5
E)2y
Rationale: 25x^4 – 4y^4 = 5x^2 + 2y^2
(5x^2 + 2y^2) (5x^2 - 2y^2) = 5x^2 + 2y^2
5x^2 - 2y^2 = 1
5x^2 = 2y^2+1
x^2 = 2y^2+1/5
Answer : D
Answer: D
Question: If four coins are tossed, the probability of getting two heads and two tails is?
Options:
A)3/8
B)3/5
C)3/9
D)3/3
E)3/1
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24
= 3/8
Answer: A
Answer: A
Question: A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 45 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?
Options:
A)40
B)45
C)50
D)55
E)60
Rationale: A- B = 120 Miles
B - C = 60 Miles
Avg Speed = 45 Miles
Time taken for A-B 3t and B-C be t
avg speed = (120+60) / Total time
45 = 180/4t
t = 60
B-C = 60 mph
Answer E
Answer: E
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5
B)2.3
C)2.4
D)2.1
E)2.6
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: A
Answer: A
Question: x and y are positive integers. If xy + x is even, then which of the following must be even?
Options:
A)x
B)y
C)x + y
D)y+1
E)x^2 − y
Rationale: Given that xy + x is even, which means x(y+1) is even.
Product of two nos. will be even only if both the nos. are odd.
Hence x is odd, y+1 is also even.
y+1 is even. Answer will be D.
Answer: D
Question: A certain club has 8 members, including Harry. One of the 8 members is to be chosen at random to be the president, one of the remaining 7 members is to be chosen at random to be the secretary, and one of the remaining 6 members is to be chosen at random to be the treasurer. What is the probability that Harry will either be the secretary or the member chosen to be the treasurer?
Options:
A)1/4
B)2/4
C)3/4
D)1
E)5/4
Rationale: Each member out of 8, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/8 and the probability that Harry will be selected to be the treasurer is also 1/8. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/8+1/8=2/8.
Answer: A.
Answer: A
Question: The grade point average of one third of the classroom is 45; the grade point average of the rest is 60. What is the grade point average of the whole class?
Options:
A)54
B)55
C)60
D)65
E)70
Rationale: Let n=total students in class
total points for 1/3 class=45n/3=15n
total points for 2/3 class=60*2n/3=40n
total points for whole class=15n+40n=55n
63n total class points/n total students=55 grade point average for total class
Answer : B
Answer: B
Question: Pipe A and pipe B fill water into a tank of capacity 5000 litres, at a rate of 200 l/min and 50 l/min. Pipe C drains at a rate of 25 l/min. Pipe A is open for 1 min and closed, then pipe B is open for 2 min and closed. Further the pipe c is opened and drained for another 2 min. This process is repeated until the tank is filled. How long will it take to fill the tank?
Options:
A)120
B)100
C)140
D)80
E)90
Rationale: tank capacity: 5000 L,
1st- 200 l/min for 1 min, volume filled: 200 L
2nd- 100 l/min for 2 min, volume filled: 100 L
3rd (water draining) : 25 l/min*2 : 50 L
total : (200+100)-50 =250 L filled for 1 cycle
number of 250 in 5000 L tank :1000/250 = 20
time taken to fill: 20* total time= 20*5 = 100 (option B)
Answer: B
Question: The ratio between the present age of P and Q is 6:7. If Q is 4 years old than P,What will be the ratio of the ages of P and Q after 4 years?
Options:
A)8:7
B)7:8
C)8:6
D)6:7
E)6:8
Rationale: Let p and q's age is 6x and 7 x years respectively .7x-6x=4
x=4
Required ratio =(6x+4):(7x+4)
=28:32
=7:8
option A is answer
Answer: A
Question: Of the 250 employees at company X, 80 are full-time, and 175 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
Options:
A)25
B)30
C)50
D)80
E)100
Rationale: 250 employees
80 are full-time
175 have worked at company X for at least a year
20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year.
How many full-time employees of company X have worked at the company for at least a year?
250-80=170 employees not full time
170-20= 150 employees not full time who worked over a year
175 employees have worked at company X for at least a year-150 employees not full time who worked over a year = 25 full-time employees of company X have worked at the company for at least a year
ans A
Answer: A
Question: There are 3 red shoes & 7 green shoes . If two of red shoes are drawn what is the probability of getting red shoes
Options:
A)1/13
B)1/14
C)1/12
D)1/15
E)1/16
Rationale: taking 2 red shoe the probablity is 3C2
from 10 shoes probablity of taking 2 red shoe is 3C2/10C2=1/15
ANSWER:D
Answer: D
Question: A car was driving at 80 Km/h for 40 minutes, and then at 60 Km/h for another 40 minutes. What was its average speed?
Options:
A)113.33.
B)103.33
C)93.33
D)83.33
E)73.33
Rationale: driving at 80 Km/h for 40 minutes ,distance covered = 80*2/3=53.33 km
driving at 90 km/h for 40 minutes ,distance covered = 90*2/3=60 km
average speed = total distance/total time = 113.33/1 = 113.33 km/h
Answer: 113.33 km/h
Answer: A
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Options:
A)22
B)88
C)16
D)83
E)82
Rationale: 10 * 15 + 36 – 26 = 160/10 = 16
Answer: C
Answer: C
Question: How many total number of ways in which c distinct objects can be put into two different boxes is
Options:
A)n2
B)2c
C)2n
D)3n
E)None of these
Rationale: Let the two boxes be B1 and B2. There are two choices for each of the c objects. So, the total number of ways is
2 × 2 ×.....× 2 (c times ) = 2c
Answer B
Answer: B
Question: In a party every person shakes hands with every other person. If there were a total of 153 handshakes in the party then what is the number of persons present in the party ?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: Explanation :
Let the number of persons be n
âˆ´ total handshakes = nC2 = 153
n(n-1)/2 = 153 âˆ´ n = 18
Answer : Option D
Answer: D
Question: Find the value of X: 3x^2-6x+3 = 0
Options:
A)-1
B)1
C)2
D)3
E)4
Rationale: a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Answer: B
Question: In an election between two candidates first candidate got 50% of votes polled and second Candidate got 2800 votes. The total number of votes polled was?
Options:
A)5600 votes
B)5800 votes
C)5900 votes
D)5980 votes
E)5990 votes
Rationale: Total = 100 %,
First person got 50%
second person got remaining 50 % of votes.
than 50 % = 2800
50% = 50Ã—56 = 2800
100% =100Ã—56 =5600 votes
A
Answer: A
Question: What is the units digit of the expression 14^7−20^4?
Options:
A) 8
B) 3
C) 4
D) 6
E) 0
Rationale: I think answer on this one should be A too. Since we know that 14^7>20^4, as Will said one should always check if the number is positive.
Answer: A
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 22% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
Options:
A)10.5%
B)12.8%
C)15%
D)22%
E)30%
Rationale: Answer is B.
This question is in the OG and thus well explained by ets.
those who exceed : X
so X = 10%+0,22X
id est X = 12,8%
Answer: B
Question: A man purchases 2 watches for $ 540. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
Options:
A)$ 260 and $ 300
B)$216 and $ 324
C)$224 and $336
D)$560 and $560
E)$224 and $ 350
Rationale: x + y = 540 --- (1)
1.15x + 0.9y = 540 --- (2)
(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*108)/(3*108) = 216/324
Answer: B
Answer: B
Question: A box contains four gold 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 also a head.
Options:
A)2/5
B)3/5
C)4/5
D)1/5
E)3/4
Rationale: 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 = 4/5
Option C
Answer: C
Question: The lowest number which should be added to 1277 so that the sum is exactly divisible by 3, 2, 5, 4 and 7 is:
Options:
A)303
B)403
C)203
D)453
E)203
Rationale: L.C.M. of 5, 6, 4 and 3 = 420.
On dividing 1277 by 420, the remainder is 17.
Number to be added = (420 - 17) = 403. Answer: Option 'B'
Answer: B
Question: A 10 kg dry mixture is composed of 40 % sugar and rest salt. How much sugar (in kg) must be added to this mixture so that salt and sugar are in same proportion?
Options:
A)2
B)3
C)5
D)7
E)8
Rationale: Total mass of the mixture is 10 kg out of which sugar is 40 %, means the mass of the sugar is 4 kg and the rest is salt, this means the salt content is 6 kg.
Suppose x kg of sugar is added so as to equalise the proportion of salt and sugar in the mixture.
After adding x kg sugar, the sugar content becomes (4 + x) kg and the salt content is the same 6 kg.
Now in the new mixture we desire the salt and sugar content to be same, this means we want their masses to be same.
This means ( 4 + x ) = 6
Solving we get x = 2.
Ans A
Answer: A
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
Options:
A)Rs.3944
B)Rs.3918
C)Rs.3928
D)Rs.3929
E)Rs.3289
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58
= Rs.3944.
Answer: A
Answer: A
Question: A physics class has 25 students, two of whom are Alex and Justin. Three students are chosen
uniformly at random for a lab demonstration. What is the probability that at least one of Alex
and Justin is chosen?
Options:
A)0.3
B)0.25
C)0.19
D)0.23
E)0.2
Rationale: We first calculate the probability that neither Alex nor Justin is chosen. The number
of ways to choose 3 people in the class is
􀀀25
3
. If neither Alex nor Justin can be chosen, there are
23 students that can be chosen and hence
􀀀23
3
ways to choose them. Therefore, the probability
that neither Alex nor Justin is chosen is
􀀀23
3
􀀀25
3
(=
23*22*21
3!
25*24*23
)=
23 *22 * 21/25 * 24 *23=
22 * 21/25 *24=
77/100,
so the probability that at least one of them is chosen is
1 -
77/100=
23/100=0.23
correct answer D
Answer: D
Question: On a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The first box contains $3, the second $300, and the third $3000. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. Mention the probability that a contestant will win more than $3000?
Options:
A)1/6
B)1/8
C)1/7
D)1/3
E)1/2
Rationale: Let's call the boxes that contain $3, $300, and $3000, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.
We want to know the probability of winning more than $3000. Notice that if the distribution of keys is:
Box A = Key B
Box B = Key A
Box C = Key C
then the contestant wins exactly $3000, not more than $3000. The only configuration that leads to winning more than $1000 is:
Box A = Key A
Box B = Key B
Box C = Key C
i.e., getting all three keys correct. That's the only way to be more than $3000. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?
Well, for a set of three items, the number of possible permutations is 3! = 3*2*1 = 6.
Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is
Probability = 1/6
Answer = A
Answer: A
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
Options:
A)1/48
B)5/16
C)11/12
D)11/16
E)23/48
Rationale: Event(1): Probability of getting head in a flip of coin = 1/2
Event(2): Probability of getting 6 in a roll of dice = 1/6
Event(3): Probability of getting spade in a pack of card = 1/4
Probability of winning is having exactly one successful event is:
P(success 1)* P(Fail 2)* P(Fail 3) + P(Fail 1)* P(Success 2)* P(Fail 3) + P(Fail 1)* P(Fail 2)* P(Success 3)
= 1/2*5/6*3/4 +1/2*1/6*3/4 +1/2*5/6*1/4
=15/48 + 3/48 +5/48
=23/48
Answer :E
Answer: E
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)6 hours
B)8 hours
C)3 hours
D)9 hours
E)1 hours
Rationale: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3
All the three pipes together will fill the tank in 3 hours.
Answer: C
Answer: C
Question: A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 5 hours longer than the first half, how many hours did it take the runner to run the second half?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2.
The time T2 to run the second half must be twice the time T1 to run the first half.
T2 = 2*T1 = T1+5
T1 = 5 and so T2 = 10.
The answer is C.
Answer: C
Question: What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
Options:
A)34
B)42
C)48
D)49
E)53
Rationale: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Answer: B
Question: If 7687 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?
Options:
A)27 books
B)1 book
C)28 books
D)0 books
E)8 books
Rationale: The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 7687.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 7687 =28 and 27 is divisible by 9.
Hence, we need to remove 1 to this number for it to be divisible by 9
Correct Option:B
Answer: B
Question: What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years.
Options:
A)2:3
B)2:5
C)1:3
D)2:3
E)None of these
Rationale: Explanation:
Let the principal be P and rate be R
then
ratio = [(P∗R∗4/100) /(P∗R∗12/100)]
=4PR /12PR=1:3
Option C
Answer: C
Question: A, B and C start swimming in a pool simultaneously from the same end. To complete 10 laps, A takes 10 minutes, B takes 8 minutes and C takes 4 minutes. What is the ratio of speeds A:B:C?
Options:
A)3:4:5
B)12:15:20
C)5:4:3
D)4:5:10
E)12:15:25
Rationale: The slowest one is A, then comes B and the fastest one is C. So, the the ratio of speeds A:B:C must be in ascending order. Eliminate options C, D, and E.
A's speed (distance)/(time) = 10/10 = 1 lap per minute = 4laps in 4 minute;
B's speed (distance)/(time) = 10/8 = 5/4 lap per minute = 5 laps in 4 minutes;
C's speed (distance)/(time) = 10/4 = 5/2 lap per minute = 10 laps in 4 minutes/
Therefore, the the ratio of speeds A:B:C is 4: 5:10.
Answer: D.
Answer: D
Question: When n is divided by 15, the remainder is 6. When n is divided by 12, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: N = 159 q + 6
N = 12 z + 6
Equating
15 Q + 6 = 12z+6
12z=15q
12z/15 = q
since q is an integer Z must be divisible by 15.
Hence C
Answer: C
Question: During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 15 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?
Options:
A)80%
B)100%
C)116.7%
D)120%
E)160%
Rationale: Kim purchased 20 gallons of gas. She paid for 15 + 0.9*5 = 19.5 gallons, so the overall discount she got was 0.5/20 = 0.025.
Isabella purchased 25 gallons of gas. She paid for 15 + 0.9*10 = 24 gallons, so the overall discount she got was 1/25 = 0.04.
4/2.5*100 = 160%
Answer: E.
Answer: E
Question: The population of a town is 176400. If it increase at the rate of 5% per annum. What will be its population for 2years hence?
Options:
A)200000
B)215600
C)194582
D)194481
E)215460
Rationale: population after 2years = 176400*(1+ 5/100)^2 = 194481
Answer is D
Answer: D
Question: In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?
Options:
A)1:0
B)1:3
C)1:9
D)1:6
E)1:5
Rationale: Explanation:
33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3
Answer: B) 1:3
Answer: B