mathewhe/aqua_rat huggingface dataset:
Question: A coin is weighted so that the probability of heads on any flip is 0.4, while the probability of tails is 0.6. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?
(A) (0.4)^5 + 5(0.4)^4(0.6) + 10(0.4)^3(0.6)^2
(B) (0.6)^5 + 4(0.6)^4(0.4) + 6(0.6)^3(0.4)^2
(C) (0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2
(D) (0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2
(E) (0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2
Rationale: Probability of Head, P(H) = 0.4
Probability of Tail, P(T) = 0.6
Tail will appear NO more than twice
i.e. favourable cases
2 Tails and 3 Heads, Probability = 5C2*(0.4)^3*(0.6)^2
1 Tail and 4 Heads, Probability = 5C1*(0.4)^4*(0.6)^2
0 Tail and 5 Heads, Probability = (0.4)^5
Required Probability = Sum of all Favourable cases = (0.4)^5 + 5(0.4)^4(0.6) + 10(0.4)^3(0.6)^2
Answer: option A
Answer: (A) (0.4)^5 + 5(0.4)^4(0.6) + 10(0.4)^3(0.6)^2
Question: train start from mumbai to delhi at 12.00am with speed of 60km/hr another train starts from delhi to mumbai at 1.30 with speed of 80km/hr find time when they meet.
(A) 5am
(B) 6am
(C) 7am
(D) 8am
(E) 9am
Rationale: 1 train 12.00 = 60km ; 2 train 1.30 = 80km;
1 train travel till 1.30 = 90 km.
1 2
150 80 -2.30
210 160 3.30
270 240 4.30
330 320 5.30
360 360 6.00
so they meat at 6am
ANSWER:B
Answer: (B) 6am
Question: What is the smallest positive integer x such that 720-x is the cube of a positive integer
(A) 5
(B) 7
(C) 47
(D) 9
(E) 12
Rationale: Given 738-x is a perfect cube
so we will take 729 = 9*9*9
738-x = 729
x =738-729 = 9
correct option is D
Answer: (D) 9
Question: In a candy dish the ratio of red to yellow candies is 2:5, the ratio of red to green candies is 3:8, and the ratio of yellow ot blue candies is 9:2.what is the maximum total number T of yellow and green candies combined if the maximum combined number of red and blue candies is fewer than 85?
(A) 144
(B) 189
(C) 234
(D) 279
(E) 309
Rationale: Given that Red is to yellow is 2:5, Red is to green is 3:8 and Yellow is to blue is 9:2.
Therefore, the total number of red, yellow, blue and green balls will be 18x, 45x, 10x and 48x respectively, where x is a constant.
If the combined number of red and blue balls is fewer than 85, i.e. max 84 balls, then the maximum number of yellow and green balls will be 279.
(10x+18x) < 85.
28x < 85, i.e. 28x <= 84 (Since number of balls cannot be in fraction). Thus, x<=3.
(45x+48x) = 93x.
Max (93x) T= 279.
Answer is D.
Answer: (D) 279
Question: The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 50%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?
(A) 20%
(B) 24%
(C) 30%
(D) 32%
(E) 39%
Rationale: take it as original output =100.
to meet demand increase by 10%, then output=110.
to meet holiday demand , new output increase by 50% then output equals 165
To restore new holidy demand output to original 100.
final -initial/final*100
=65/165*100=39% approxiamately.
option E is correct.
Answer: (E) 39%
Question: A is half good a work man as B and together they finish a job in 32 days. In how many days working alone B finish the job?
(A) 98 days
(B) 21 days
(C) 48 days
(D) 18 days
(E) 19 days
Rationale: WC = 1:2
2x + x = 1/32 => x = 1/96
2x = 1/96 => 48 days
Answer:C
Answer: (C) 48 days
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
(A) 22
(B) 28
(C) 25
(D) 77
(E) 88
Rationale: D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec
Answer: C
Answer: (C) 25
Question: At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 160 male associates, how many female managers are there?
(A) 40
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: 250 Employees:
90 Male, 160 Female
40 Managers, 210 Associates
160 Male Associates implies 50 Female Associates which means the remaining 40 females must be Managers
A. 40
Answer: (A) 40
Question: A tradesman sold an article at a loss of 10%. If the selling price had been increased by $50, there would have been a gain of 10%. What was the cost price of the article ?
(A) $100
(B) $250
(C) $200
(D) $150
(E) $300
Rationale: Let C.P. be $x
then, (110% of x)-(90% of x) = 50 or 20% of x=100
x/5 = 50
x=250
C.P. = $250
correct option is B
Answer: (B) $250
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
(A) 39, 30
(B) 41, 32
(C) 42, 33
(D) 43, 34
(E) 40, 32
Rationale: Let their marks be (x + 9) and x.
Then, x + 9 =	56	/100(x + 9 + x)
=25(x + 9) = 14(2x + 9)
= 3x = 99
=x = 33
So, their marks are 42 and 33.
ANSWER IS C
Answer: (C) 42, 33
Question: Larry, Michael, and Peter have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?
(A)  21
(B)  42
(C)  120
(D)  504
(E)  5040
Rationale: Larry, Michael, and Peter have five donuts to share.to get the answer, see how can we get sum5with 3 numbers.
1) 0,0,5 = 3 combinations or 3! /2!
2) 0,1,4 = 6 combinations or 3!
similarly
3) 0,2,3 = 6 combinations
4) 1,1,3 = 3 combination
5) 2,2,1 = 3 combination
total =21=A
Answer: (A)  21
Question: If n is a natural number, then (6n2 + 6n) is always divisible by:
(A) 6 only
(B) 12 only
(C) 6 and 12 both
(D) by 18 only
(E) 15 only
Rationale: (6n^2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
Answer C) 6 and 12 both.
Answer: (C) 6 and 12 both
Question: What is the average of all the multiples of ten from 10 to 200 inclusive?
(A) 90
(B) 95
(C) 100
(D) 105
(E) 110
Rationale: The multiples of ten from 10 to 190 inclusive would be an evenly spaced set with 19 terms - 10, 20, 30,.......190
So average = (First term + Last Term)/2 = (10 + 200)/2 = 210/2 = 105
Hence, the correct answer is D.
Answer: (D) 105
Question: Jill has 28 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?
(A) 3
(B) 6
(C) 48
(D) 12
(E) 14
Rationale: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 28 1 3/4w = 28w=16The total number of jars = 3w =48Answer: C
Answer: (C) 48
Question: Three candidates contested an election and received 1136, 7636 and 15628 votes respectively. What percentage of the total votes did the winning candidate got?
(A) 55%
(B) 64%
(C) 57%
(D) 58%
(E) 59%
Rationale: Total number of votes polled = (1136 + 7636 + 15628) = 24400
So, Required percentage = 15628/24400 * 100 = 64%
ANSWER : B
Answer: (B) 64%
Question: How many seconds will a 500 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
(A) 33
(B) 87
(C) 30
(D) 88
(E) 77
Rationale: Explanation:
Distance = 500 m
Speed of the train relative to man= ( 63 - 3 ) km/hr = 60 km/hr
= m/s = m/s
Time taken to pass the man = distance/speed = sec = 30 sec
Answer: C) 30
Answer: (C) 30
Question: What will be the fraction of 10%
(A) 1/10
(B) 1/50
(C) 1/75
(D) 1/25
(E) None of these
Rationale: Explanation:
10*1/100 = 1/10
Option A
Answer: (A) 1/10
Question: My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then what was the age of my father when my brother was born?
(A) 25
(B) 27
(C) 31
(D) 33
(E) 32
Rationale: Father's age was 28 years when my sister was born.
My sister's age was 4 years when my brother was born.
Therefore, father's age was 28+4=32 years when my brother was born.
Answer is E.
Answer: (E) 32
Question: A computer factory produces 3024 computers per month at a constant rate, how many computers are built every 30 minutes assuming that there are 28 days in one month?
(A) 2.25.
(B) 3.125.
(C) 4.5.
(D) 5.225.
(E) 6.25.
Rationale: Number of hours in 28 days = 28*24
Number of 30 mins in 28 days = 28*24*2
Number of computers built every 30 mins = 3024/( 28*24*2) = 2.25
Answer A
Answer: (A) 2.25.
Question: A train travels 290 km in 4.5 hours and 400 km in 5.5 hours.find the average speed of train.
(A) 80 kmph
(B) 69 kmph
(C) 70 kmph
(D) 90 kmph
(E) None of these
Rationale: As we know that Speed = Distance / Time
for average speed = Total Distance / Total Time Taken
Thus, Total Distance = 290 + 400 = 690 km
Thus, Total Speed = 10 hrs
or,Average Speed = 690/10
or, 69 kmph.
ANSWER:B
Answer: (B) 69 kmph
Question: 6 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
(A) 12/9 days
(B) 6 days
(C) 82/8 days
(D) 22/76 days
(E) 22/2 days
Rationale: 6M = 6W ---- 20 days
12M + 8W -----?
12W + 8 W = 20W ---?
6W ---- 20 20 -----?
6 * 20 = 20 * x => x = 6 days
Answer:B
Answer: (B) 6 days
Question: In an election, candidate Douglas won 54 percent of the total vote in Counties X and Y. He won 62 percent of the vote in County X. If the ratio of people who voted in County X to County Y is 2: 1, what percent of the vote did candidate Douglas win in County Y?
(A) 25%
(B) 28%
(C) 32%
(D) 38%
(E) 40%
Rationale: given voters in ratio 2:1
let X has 200 votersY has 100 voters
for X 62% voted means 62*200=124 votes
combined for XY has 300 voters and voted 54% so total votes =162
balance votes=162-124=38
As Y has 100 voters so 38 votes means 38% of votes required
Ans D
Answer: (D) 38%
Question: An engineer undertakes a project to build a road 10 km long in 150 days and employs 30 men for the purpose. After 50 days, he finds only 2 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
(A) 22
(B) 30
(C) 15
(D) 18
(E) 20
Rationale: 30 workers working already
Let x be the total men required to finish the task in next 100 days
2 km done hence remaining is 8 km
Also, work has to be completed in next 100 days (150 - 50 = 100)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X = (30 * 8 * 50) / (2 *100)
thus, X = 60
Thus, more men needed to finish the task = 60-30=30
Answer : B
Answer: (B) 30
Question: Can you find the last number in the number sequence given below?
10 : 10 : 20 : 45 : 110 : 300 : ?
(A) 920
(B) 930
(C) 940
(D) 950
(E) None
Rationale: Solution:
930
Explanation:
New number = Last number * multiplication factor (increased by 0.5 every time) + sum factor (increased by 5 every time)
10
10 * 0.5 + 5 => 10
10 * 1.0 + 10 => 20
20 * 1.5 + 15 => 45
45 * 2.0 + 20 => 110
110 * 2.5 + 25 => 300
300 * 3.0 + 30 => 930 , desired answer
Answer B
Answer: (B) 930
Question: When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.?
(A) 4.5
(B) 5
(C) 4.8
(D) 5.6
(E) 5.9
Rationale: if $x$ is the number, x/6 * 12 = 9
=> 2x = 9
=> x = 4.5
A
Answer: (A) 4.5
Question: A completes a work in 4 days and B complete the same work in 12 days. If both of them work together, then the number of days required to complete the work will be?
(A) 3 days
(B) 11 days
(C) 21 days
(D) 22 days
(E) 24 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 4 Ã— 12/ 16 = 3 days.
Option 'A'
Answer: (A) 3 days
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5
(A) 145
(B) 148
(C) 150
(D) 153
(E) 158
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
Answer: (D) 153
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a girl sitting at window seat in the slower train in 32 seconds. Find the length of the faster train ?
(A) 170 m
(B) 100 m
(C) 270 m
(D) 320 m
(E) 350 m
Rationale: Explanation:
Relative speed = (72 - 36) x 5/18 = 2 x 5 = 10 mps.
Distance covered in 32 sec = 32 x 10 = 320 m.
The length of the faster train = 320 m.
ANSWER IS D
Answer: (D) 320 m
Question: On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took their cars abroad the ship. If 50 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship's passengers held round-trip tickets?
(A) 33.3%
(B) 40%
(C) 50%
(D) 60%
(E) 66.6%
Rationale: 0.20P = RT + C
0.5(RT) = no C
=> 0.50(RT) had C
0.20P = 0.50(RT)
RT/P = 40%
Answer - B
Answer: (B) 40%
Question: Two quarts containing 7⁄8 water and 1/8 formula are mixed with three quarts containing 7⁄10 water and 2⁄10 formula. Approximately what percent of the combined five-quart mixture is water?
(A) 60%
(B) 55%
(C) 65%
(D) 77%
(E) 70%
Rationale: 7/8 of 2 quarts = 14/8 quarts of water
7/10 of 3 quarts = 21/10 quarts of water
14/8 = 1.75
21/10 = 2.10
Total water = 1.75 + 2.10= 3.85
Total quarts = 5
3.85/5 = 77%
Answer : D
Answer: (D) 77%
Question: If two letters are chosen at random (without replacement) from the word COMPUTER, what is the probability that none of the letters are vowels?
(A) 2/7
(B) 3/7
(C) 3/14
(D) 5/14
(E) 11/28
Rationale: The number of ways to choose two letters is 8C2 = 28
The number of ways to choose two consonants is 5C2 = 10.
P(no vowels) = 10/28 = 5/14
The answer is D.
Answer: (D) 5/14
Question: The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If e of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?
(A)  y/R
(B)  y/(R-x)
(C)  xy/(R-x)
(D)  ey/(R(R-e))
(E)  y/(R(R-x))
Rationale: y/(R-e)- y/R
if we simplify this we get choice D, which is the correct answer.
Answer: (D)  ey/(R(R-e))
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 20%, then the cost price of the article is:
(A) 500
(B) 277
(C) 466.7
(D) 297
(E) 111
Rationale: Explanation:
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (100 * 560)/120 = Rs. 466.7
Answer:C
Answer: (C) 466.7
Question: One fourth of a solution that was 10 percent oats by weight was replaced by a second solution resulting in a solution that was 16 percent oats by weight. The second solution was what percent oats by weight ?
(A) 34%
(B) 24%
(C) 22%
(D) 18%
(E) 8.5%
Rationale: EQ can be written as ...
let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of oats in 2nd sol)=34%=A
Answer: (A) 34%
Question: Express a speed of 18 kmph in meters per second?
(A) 5 mps
(B) 10 mps
(C) 6 mps
(D) 7 mps
(E) 12 mps
Rationale: 18 * 5/18
= 5 mps
Answer:A
Answer: (A) 5 mps
Question: In a garden, there are five blue flowers, five red flowers,five green flowers, and five pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?
(A) 11/10
(B) 3/95
(C) 31/10
(D) 3/55
(E) 1/16
Rationale: P(all the same color) = P(1st flower is ANY colorAND2nd flower is same as firstAND3rd flower is also the same color)
= P(1st flower is ANY color)xP(2nd flower is same as 1st)ANDP(3rd flower is the same color)
= 1x4/20x3/19
= 3/95
Answer: B
Answer: (B) 3/95
Question: An electrical appliances store sold this month 400% more than the average of all the other months in the year. The sales total for this month was approximately what percent of total sales for this year?
(A) 14%
(B) 21%.
(C) 31%.
(D) 37%.
(E) 43%.
Rationale: The average sales for all the other months (11 months) of the year is x.
So, the total sales of those 11 months will be= 11x
Now, this month's sales, which is 400% more than the average of other months' sales, is 5x, (x+400% of x).
Thus, this month's' sales are (5x/16x)*100=31.25% of the total yearly sales. [Total sales=11x+5x=16x]
Answer is B
Answer: (B) 21%.
Question: If m=9^(x−1), then in terms of m, 3^(4x−3) must be which of the following?
(A) m/3
(B) 9m
(C) 3m^2
(D) m^2/3
(E) m^2/9
Rationale: m = 9 ^ (X-1)
m = 3 ^ (2x-2)
m^2 = 3 ^ (4x-4)
3m^2 = 3 ^ (4x-3)
Answer C
Answer: (C) 3m^2
Question: A can do a piece of work in 12 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
(A) 15 5/8 days
(B) 10 5/8 days
(C) 12 5/8 days
(D) 19 5/8 days
(E) 13 5/8 days
Rationale: B
(x â€“ 5)/12 + x/20 = 1
x = 10 5/8 days
Answer: (B) 10 5/8 days
Question: the egg vendor calls on his 1st customer and sells his half his eggs and half an egg.to the 2nd customer he sells half of what he had left and half an egg,and to the 3rd customer he sells half of what he had then left and half an egg.by the way he did not break any eggs.in the end 3 eggs were remainig.how many did he start out with?
(A) 21
(B) 31
(C) 41
(D) 51
(E) 61
Rationale: He start out with 31eggs.
In the end, he have 3eggs left.
So,
3*2 +1= 7
7*2 +1= 15
15*2 +1= 31
31eggs he had initially.
ANSWER:B
Answer: (B) 31
Question: Consider the formula M = 4c^2/d. If c is doubled and d is increased by a factor of 2, by what factor is M increased?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: We have,
M = 4c^2/d
If c is doubled and d is increased by a factor of 2, the formula changes to:
M = 4*{(2c)^2}/(2d)
M = 4*{4c^2}/(2d)
M = 4*[2c^2/d]
At first, M = 4c^2/d
After changing c and d, M = 2*4c^2/d
Hence, M changes by a factor of 2.
Answer = B = 2
Answer: (B) 2
Question: A team of seven entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
(A) 288
(B) 581
(C) 168
(D) 127
(E) 664
Rationale: Explanation:
7 * 84 = 588 - 7 = 581
Answer:B
Answer: (B) 581
Question: P beats Q by 125 meter in a kilometer race. Find Q's speed if P's speed is 24 meter/sec.
(A) 21 meter/sec
(B) 7 meter/sec
(C) 14 meter/sec
(D) 18 meter/sec
(E) 28 meter/sec
Rationale: P's speed = 24 m/s
P's distance = 1000m (as it is a km race)
t = 1000/24 = 41.7 sec
Q's distance = 1000-125= 875m
Q's time to complete this distance is also 62.5 sec.
Q's speed = dist/time = 875/41.7 = 21 m/s
Hence A is the answer.
Answer: (A) 21 meter/sec
Question: A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000
Rationale: No. of ways select first digit (other than 0) * No of wasy select second digit (exclude first digit selected) * no of ways select 3rd digit (exclude first 2) * no of ways to select 4 th digit (excllude first 3 digits)
= 9*9*8*6= 4536
ANSWER:B
Answer: (B) 4,536
Question: 90, 180, 12, 50, 100, 100, ?, 3, 25, 4, 25, 2, 6, 30, 3
(A) 100
(B) 85
(C) 75
(D) 66
(E) 77
Rationale: 30*3=90
6*30=180
6*2=12
25*2=50
4*25=100
25*4=100
3*25=75 ans is 75
ANSWER:C
Answer: (C) 75
Question: Of the science books in a certain supply room, 40 are on botany, 45 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same area science?
(A) 186
(B) 225
(C) 294
(D) 302
(E) 314
Rationale: The worst case scenario is to remove all the books on botany, zoology, and geology.
Also we can remove 79 books each from physics and chemistry.
The total is 40 + 45 + 50 + 79 + 79 = 293.
The next book removed must either be physics or chemistry, ensuring 80 books in that subject.
The answer is C.
Answer: (C) 294
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 8500. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 30.05%
(B) 13.15%
(C) 40%
(D) 27.15%
(E) None of these
Rationale: The total CP = Rs. 16000 + Rs. 8500 = Rs. 24500 and SP = Rs. 31150
Profit(%) = (31150 - 24500 )/24500* 100 = 27.15%
ANSWER:D
Answer: (D) 27.15%
Question: At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
(A) 4%
(B) 8%
(C) 4.2%
(D) 4.8%
(E) 5%
Rationale: Let's say there is a TOTAL of100students at this college.
60 percent of the total number of students are freshmen.
# of freshmen = 60% of 100 =60
40 percent of the fresh-men are enrolled in the school of liberal arts...
Number of liberal arts freshmen = 40% of 60 =24
...and, of these, 20 percent are psychology majors...
Number of liberal arts freshmen who are psychology majors = 20% of 24=4.8
What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
4.8/100= 4.8%
Answer:D
Answer: (D) 4.8%
Question: In the coordinate plane, rectangular region R has vertices at (0,0), (0,3), (4,3), and (4,0). If a point in region R is randomly selected, what is the probability that the point's y-coordinate will be greater than its x-coordinate?
(A) 7/12
(B) 5/12
(C) 3/8
(D) 1/3
(E) 1/4
Rationale: Now, rectangle R has an area of 3*4=12. All point that has y-coordinate greater than x-coordinate lie above the line y=xy=x, so in yellow triangle, which has an area of 1/2*3*3=4.5. So, the probability equals to favorable outcomes/total=yellow triangle/rectangle R=4.5/12=3/8.
Answer: C.
Answer: (C) 3/8
Question: A shop sells bicycles and tricycles. In total there are 9 cycles (cycles include both bicycles and tricycles) and 21 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.
(A) b=2,t=3
(B) b=5,t=3
(C) b=6,t=3
(D) b=2,t=5
(E) b=3,t=4
Rationale: Let b be the number of bicycles and let t be the number of tricycles.
Set up the equations
b+t=9............(1)
2b+3t=21............(2)
Rearrange equation (1) and substitute into equation (2)
2b+27-3b=21
-b=-6
b=6
Calculate the number of tricycles t
t=9−b
=9−6
=3
There are 3 tricycles and 6 bicycles.
Answer is C.
Answer: (C) b=6,t=3
Question: One copy machine can make 25 copies a minute, and a second copy machine makes 35 copies a minute. If the two copiers work together, how long would it take them to make 4,800 copies?
(A) 30 minutes
(B) 40 minutes
(C) 60 minutes
(D) 70 minutes
(E) 80 minutes
Rationale: Total work done by both machines in a minute = 25 + 35 = 60 copies
Total number of copies required = 6000
Time = 4800/60 = 80 mins
Answer E
Answer: (E) 80 minutes
Question: By selling 15 pencils for a rupee a man loses 60%. How many for a rupee should he sell in order to gain 60%?
(A) 2.15
(B) 4.2
(C) 5.18
(D) 3.75
(E) 4.2
Rationale: 40% --- 15
160% --- ?
40/160 * 15 = 3.75
Answer: D
Answer: (D) 3.75
Question: A set of numbers has the property that for any number t in the set,t+3 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 2
II. 5
III. 7
(A) II only
(B) I only
(C) I,II only
(D) II,III only
(E) III only
Rationale: question is asking for must be there elements.
According to the question if t is there t+3 must be there.
if -1 is the starting element the sequence is as follows.
S ={-1,2,5,8,11....}
if -1 is not the starting element the sequence is as follows
S = {...-4,-1,2,5,8,11...}
By observing the above two sequences we can say that 2,5 must be there in set S.
Answer : C
Answer: (C) I,II only
Question: Nine persons went to a hotel for taking their meals 8 of them spent Rs.12 each on their meals and the ninth spent Rs.8 more than the average expenditure of all the nine.What was the total money spent by them?
(A) Rs.117
(B) Rs.100
(C) Rs.110
(D) Rs.107
(E) Rs.98
Rationale: Let the average expenditure of all nine be Rs.x
Then 12*8+(x+8)=9x or 8x=104 or x=13.
Total money spent = 9x=Rs.(9*13)=Rs.117.
Answer is A.
Answer: (A) Rs.117