mathewhe/aqua_rat huggingface dataset:
Question: seven balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?
(A) 60
(B) 90
(C) 240
(D) 150
(E) 180
Rationale: Since the balls are all of different colors, let's permute them and then decide how many balls we put in each box.
For example, arrange in a row the balls, then decide: two balls go into the first box, next two in the second box, and the last ball goes to the third box.
Since in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes.
For the 2,2,1 type arrangements, we have [5!/(2!2!1!)]*3 = 90 possibilities. Inside a box, it doesn't matter the order of the balls.
For the 3,1,1 type arrangements, we have [5!/(3!1!1!)]*3 = 60 possibilities.
Total of 150 + 90 =240 possibilities.
Answer C.
Answer: (C) 240
Question: A hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 12 kilometers per hour. The cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: In 5 minutes, the cyclist travels a distance of (5/60)*12 = 1 km.
The time it takes the hiker to complete this distance is 1/4 hours = 15 minutes
The cyclist needs to wait 15 - 5 = 10 minutes
The answer is A.
Answer: (A) 10
Question: Rs 3400 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part.
(A) s 4000
(B) s 1800
(C) s 800
(D) s 500
(E) s 1300
Rationale: Explanation :
Average rate = (144/3400)*100 = 4.24
Ratio = 7.65: 12.35
So, first part = (7.65/20)*3400 = Rs 1300.
Answer : E
Answer: (E) s 1300
Question: Sam invests $1000 in an account that pays 12% annual interest: the interest is paid once, at the end of the year. Kody invests $1000 in an account that pays 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Sam's account, approximately how much more does Kody’s account have?
(A) Zero
(B) $682.5
(C) $68.25
(D) $6.825
(E) $0.6825
Rationale: Sam's interest= $1000*0.12 = $120 or $10 each month.
Kody’s interest, 12%/12 = 1% each month:
For the 1st month = $1000*0.01 = $10;
For the 2nd month = $10 + 1% of 10 = $10.1, so we would have interest earned on interest (very small amount);
For the 3rd month = $10.1 + 1% of 10.1 = ~$10.2;
For the 4th month = $10.201 + 1% of 10.201 = ~$10.3;
...
For the 12th month = $11+ 1% of 11 = ~$11.1.
The difference between Sam's interest and Kody’s interest = ~(0.10 + 0.20 + ... + 1.10) = $6.6.
Answer: D.
Answer: (D) $6.825
Question: plot ABCD is as shown in figure, where AF = 30 m, CE = 40 m, ED = 50 m, AE = 120 m. Find the area of the plot ABCD?
(A) 2978 sq.m
(B) 6289 sq.m
(C) 2989 sq.m
(D) 7200 sq.m
(E) 1551 sq.m
Rationale: Area of plot ABCD = Area of ADE + Area of AFB + Area of BCEF
= 1/2 * 50 * 120 + 1/2 * 40 * 30 + 40 * 90
= 3000 + 600 + 3600
= 7200 sq.m
Answer:D
Answer: (D) 7200 sq.m
Question: Chances of Mr. Button winning the local lottery in 8%. All participants lined up and Mr. Button is 3rd in the row. The first two participants lose the lottery.
What is the chance of Samuel Mr. Button now?
(A) 8%
(B) 5%
(C) 10%
(D) 50%
(E) 40%
Rationale: The winning chance probability is still 8% as the outcome of Mr.Bitton winning the lottery is a separate event from rest losing the lottery.correct answer is A)8%
Answer: (A) 8%
Question: There are 16 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?
(A) 20
(B) 24
(C) 28
(D) 36
(E) 48
Rationale: Note that each handshake includes two people.
The total number of handshakes is 16*3/2 = 24
The answer is B.
Answer: (B) 24
Question: What percent of 60 is 90?
(A) 133 1⁄3
(B) 150
(C) 60
(D) 33 1⁄3
(E) 25
Rationale: % of 60 is 90?
= 90/60 = 3/2 = 150%
Thus B is the correct answer.
Answer: (B) 150
Question: Suppose son name is 120,his brother name is 150 and his mother name is 210.find out his father's name???
(A) 190
(B) 210
(C) 230
(D) 240
(E) 250
Rationale: since difference between all name is =30
so father's name will be 210+30=240.
ANSWER:D
Answer: (D) 240
Question: The number of number - pairs lying between 40 and 100 with their H.C.F. as 15 is :
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Explanation:
Numbers with H.C.F.15 must contain 15 as a factor.
Now, multiples of 15 between 40 and 100 are 45, 60, 75 and 90.
âˆ´
Number pairs with H.C.F. 15 are (45, 60), (45, 75), (60, 75) and (75, 90).
[
âˆ´
H.C.F. of (60, 00) is 30 and that Of (45, 90) is 45]
Clearly, there are 4 such pairs.
ANSWER IS B
Answer: (B) 4
Question: In Orange County one third of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
(A) 60.
(B) 42.
(C) 85.
(D) 140.
(E) 252.
Rationale: The number must be an integer and multiple of both 3 and 7.
Only option B fulfill this condition and hence is the answer.
Answer: (B) 42.
Question: Of the 25 cupcakes in the bakery, 20 percent are chocolate. How many vanilla cupcakes must be sold in order to bring the number of chocolate cupcakes up to 50 percent of the cupcakes in the bakery?
(A) 1
(B) 5
(C) 10
(D) 15
(E) 20
Rationale: Now, there are 5 chocolate cupcakes (20% of 25) and 25-5=20 vanilla cupcakes at the bakery. We need there to be 5 chocolate and 5 vanilla cupcakes, in this case there will be 50% chocolate and 50% vanilla.
Therefore 20-5=15 vanilla cupcakes must be sold.
Answer: D.
Answer: (D) 15
Question: A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 840 in 4 years. The
rate on interest per annum is.
(A) 4%
(B) 5%
(C) 6%
(D) 7%
(E) 8%
Rationale: Explanation:
S.I. on Rs 800 for 1 year = 40
Rate = (100*40)/(800*1) = 5%
Answer: B
Answer: (B) 5%
Question: 10 men, working 7 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the same work in 12 days?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: The number of hours required to complete the work is 10*7*18 = 1260
15 × 12 × (x) = 1260
x = 7
The answer is B.
Answer: (B) 7
Question: How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,Q,R,S,and T so that letter P is to the left of letter R?
(A) 120
(B) 60
(C) 48
(D) 24
(E) 12
Rationale: Considering that there are 5 distinct letters - P,Q,R,S,T
Number of words - 5!/2 = 120/2=60
ANSWER:B
Answer: (B) 60
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made?
(A) Rs. 1,10,000
(B) Rs. 1,20,000
(C) Rs. 1,24,000
(D) Rs. 1,21,000
(E) None of these
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000
ANSWER:B
Answer: (B) Rs. 1,20,000
Question: Carrie likes to buy t-shirts at the local clothing store. They cost $9.15 each. One day, she bought 22 t-shirts. How much money did she spend?
(A) $150
(B) $248.75
(C) $200
(D) $201.3
(E) $190
Rationale: $9.15*22=$201.3. Answer is D.
Answer: (D) $201.3
Question: A glass was filled with 10 ounces of water, and 0.06 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period?
(A) 0.002%
(B) 0.02%
(C) 0.2%
(D) 12%
(E) 20%
Rationale: We are given that 0.06 ounces of water evaporated EACH DAY. Furthermore, we know that this process happened over a 20-DAY PERIOD. To calculate the total amount of water that evaporated during this time frame we need to multiply 0.06 by 20. This gives us:
0.06 x 20 = 1.2 ounces
Finally, we are asked for “What percent” of the original amount of water evaporated during this period. To determine this percentage, we have to make sure we translate the expression correctly. We can translate it to:
(Amount Evaporated/Original Amount) x 100%
(1.2/10) x 100%
(12/100) x 100% = 12%
Answer D
Answer: (D) 12%
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
(A) 6.888 kg
(B) 6.892 kg
(C) 9.832 kg
(D) 6.832 kg
(E) 4.832 kg
Rationale: 52 * 40 * 29 = 60320
48 * 36 * 27 = 46650
------------
13664
13664 * 1/2 = 6832 => 6.832 kg
Answer: D
Answer: (D) 6.832 kg
Question: Jill, who lives in City C, plans to visit 4 different cities, M,N, L, and S. She plans to visit each city exactly once and return to City C after the 4 visits. She can visit the cities in any order. In how many different orders can she visit the 4 cities?
(A)  3
(B)  24
(C)  8
(D)  9
(E)  12
Rationale: 4! = 24 =B
Answer: (B)  24
Question: The area of a sector of a circle of radius 4 cm formed by an arc of length 4.5 cm is?
(A) 8.78
(B) 8.67
(C) 8.75
(D) 8.98
(E) 9
Rationale: (4 * 4.5)/2
= 9
Answer:E
Answer: (E) 9
Question: Rani took a loan of Rs. 1600 with simple interest for as many years as the rate of interest. If she paid Rs. 256 as interest at the end of the loan period, what was the rate of interest?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let rate = R% and time = R years.
Then, (1600 * R * R) / 100 = 256
16R2 = 256
R2 = 16 => R = 4
Answer:B
Answer: (B) 4
Question: A is half good a work man as B and together they finish a job in 12 days. In how many days working alone B finish the job?
(A) 23
(B) 22
(C) 18
(D) 36
(E) 48
Rationale: C
18
WC = 1:2
2x + x = 1/12 => x = 1/36
2x = 1/18 => 18 days
Answer: (C) 18
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
(A) 5%
(B) 3%
(C) 7%
(D) 6%
(E) 1%
Rationale: 160 = (180*4*R)/100
R = 5%
Answer:A
Answer: (A) 5%
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
(A) 20
(B) 89
(C) 100
(D) 200
(E) 80
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Option C
Answer: (C) 100
Question: Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 3 pages a minute more than printer A ?
(A) 600
(B) 800
(C) 1000
(D) 360
(E) 1500
Rationale: Answer: D.
Answer: (D) 360
Question: The integer x is divisible by both 10 and 15. Which of the following must be an integer?
(A) x/50
(B) x/30
(C) x/10
(D) x/40
(E) x/20
Rationale: Prime factorization of 10 = 5*2
Prime factorization of 15= 5*3
LCM of 10 and 15 = 5*2*3 = 30
Therefore x/30 must be an integer
Answer B
Answer: (B) x/30
Question: In a hotel we can order two types of varieties, but we can make 7 more varieties in home. One can choose the four varieties with two from hotel as must. Find how many ways one can order.
(A) 14
(B) 15
(C) 56
(D) 21
(E) 29
Rationale: 2c2*7c2=21ways
ANSWER:D
Answer: (D) 21
Question: If a sample of data has mean of 20 and SD of 3, which of the following values is more than 2.8 SDs from the mean?
(A) 16
(B) 15
(C) 14
(D) 13
(E) 11
Rationale: 2.8 SD's mean is equal to: +/- 2.8*3 = +/- 8.4
ie. 11.6 to 28.4
Answer is: E
Answer: (E) 11
Question: We bought orange juice and apple juice at the store. A bottle of orange juice costs 70 cents and a bottle of apple juice costs 60 cents. We bought a total of 70 bottles for $46.20. How many bottles of orange juice did we buy?
(A) 32
(B) 36
(C) 38
(D) 42
(E) 48
Rationale: Let OJ be the bottles of orange juice and let AJ be the bottles of apple juice.
(OJ) + AJ = 70.
AJ = 70 - (OJ).
70(OJ) + 60AJ = 4620.
70(OJ) +60(70-OJ) = 4620.
10(OJ) + 4200 = 4620.
OJ = 42.
The answer is D.
Answer: (D) 42
Question: If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.
x = 2.
A
Answer: (A) 2
Question: Roses can be purchased individually for $2.30, one dozen for $36, or two dozen for $50. What is the greatest number of roses that can be purchased for $680?
(A)  156
(B)  162
(C)  325
(D)  324
(E)  326
Rationale: Buy as many $50 deals as possible. We can by 650/50=13 two dozen roses, thus total of 13*24 = 312 roses.
We are left with 680 - 650 = $30. We can buy 30/2.3 = ~13 roses for that amount.
Total = 312 + 13 = 325.
Answer: C.
Answer: (C)  325
Question: For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 15 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
(A) 12%
(B) 26%
(C) 23%
(D) 30%
(E) 60%
Rationale: In the first plot 15% of 300 seeds germinated, so 0.15 x 300 = 45 seeds germinated.
In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated.
Since 45 + 70 = 115 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (115/500) x 100%, or 23%.
Answer: C.
Answer: (C) 23%
Question: The perimeter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
(A) 23.57
(B) 25.54
(C) 26.5
(D) 26.55
(E) 26.71
Rationale: Let the side of the square be a cm.
Perimeter of the rectangle = 2(20 + 14) = 68 cm
Perimeter of the square = 68 cm
i.e. 4a = 68
A = 17
Diameter of the semicircle = 17 cm
Circumference of the semicircle
= 1/2(∏)(17)
= 1/2(22/7)(17) = 26.71 cm to two decimal places
Answer: E
Answer: (E) 26.71
Question: On average, the bottle-nosed dolphin comes up for air once every six minutes; the beluga whale, a close relative, comes up for air on average once every nine minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period?
(A) 150%
(B) 175%
(C) 200%
(D) 225%
(E) 250%
Rationale: Dolphin once in 6 min;
Beluga once in 9 min;
So, dolphin comes up 1.5 times frequently than beluga, which is 150% (9-6)/2*100.
Answer: A.
Answer: (A) 150%
Question: an operation * is defined by the equation:
a*b=a-b/a+b, for all numbers a and b such that a is not equal to -b, if a is not equal to -q and a*q=0, then q=?
(A) a) -a
(B) b) -1/a
(C) c) 1/a
(D) d)0
(E) e)a
Rationale: If a*q=0 and a=-q then a-q = o of a=q, so answer E
Answer: (E) e)a
Question: Two dice are rolled. What is the probability the sum will be greater than 10?
(A) 1/5.
(B) 1/6
(C) 5/3
(D) 1/12
(E) 1/9
Rationale: 3 possible rolls greater than 10. 5/6, 6/5, and 6/6
There are 36 possible combinations of rolling 2 dice.
3/36 = 1/12
hence:D
Answer: (D) 1/12
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job.How long should it take both A and B, working together but independently, to do the same job?
(A) 20/6 days
(B) 15/4 days
(C) 40/9 days
(D) 40/3 days
(E) 45/7 days
Rationale: A’s 1 hour's work = 1/8
B's 1 hour's work = 1/10
(A + B)'s 1 hour's work = (1/8) +(1/10)=9/40
Both A and B will finish the work in 40/9 days
Answer is C.
Answer: (C) 40/9 days
Question: The ages of X and Y are in the proportion of 6:5 and total of their ages is 44 years. The proportion of their ages after 8 years will be
(A) 8:7
(B) 6:9
(C) 4:9
(D) 3:6
(E) 1:9
Rationale: A
8:7
Let current ages of X and Y correspondingly, is 6A & 5A
Given: 6A + 5A = 44
=> A = 4
Proportion of ages after 0.8 decades will be
6A + 8 : 5A + 8
or, 32:28 or, 8:7
Answer: (A) 8:7
Question: Find the number of ways in which 4 different beads can be arranged to form a necklace.
(A) 30
(B) 20
(C) 3
(D) 60
(E) 80
Rationale: Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,4 beads can be arranged to form a necklace in(4-1)! /2ways
= 3*2/2 = 3 ways
Answer is C
Answer: (C) 3
Question: What is the maximum number of false trials that can be made before the lock is opened?
(A) 3*26C6
(B) (26C6)3
(C) 26C6. 3!
(D) 215
(E) 235
Rationale: Maximum possible permutation of letters= 6*6*6= 216
Out of 216 different permutations only 1 is correct.
Maximum number of false trials= 216-1= 215
ANSWER:D
Answer: (D) 215
Question: A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:
(A) 59 7/12 min. past 3
(B) 4 p.m.
(C) 58 7/12 min. past 3
(D) 58 7/11 min. past 4
(E) 2 3/11 min. past 4
Rationale: Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. =	37/4	hrs.
3 min. 5 sec. of this clock = 3 min. of the correct clock.
37/720 hrs of this clock =1/20 hrs of the correct clock.
37/4	hrs of this clock =1/20 x 720/37 x 37/4 hrs of the correct clock.
= 9 hrs of the correct clock.
The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.
Answer: B
Answer: (B) 4 p.m.
Question: Solve the equation :
A) (5x - 4)/2 = (0.5x + 1)/3,
B) 1 –[(x - 3)/5] = ( -3x + 3)/3,
C) (x + 1)/3 – (2x + 5)/2 = -3,
D) [3.(x - 1)]/2 + [2(x + 2)]/4 = (3x + 4.5)/5
(A) 1, - 3/4, 5/4, 1
(B) 1, - 3/4, 5/4, 2
(C) 3, - 3/4, 5/4, 1
(D) 1, - 3/4, 5/4, 4
(E) None
Rationale: Solution:
A) (5x - 4)/2 – (0.5x + 1)/3 <=>
3(5x - 4) = 2(0.5x + 1) <=>
15x - 12 = x + 2 <=>
15x – x = 12 + 2<=>
14x = 14 <=> x = 1
B) 1 – [(x - 3)/5] = 3.(1 - x)/3<=>
1 –[(x - 3)/5] = 1 – x<=>
-x + 3 = - 5x <=>
5x – x = - 3 <=>
x = - 3/4
C) [3.(x - 1)]/2 + [2(x + 2)]/4 = (3x + 4.5)/5 <=>
[2(x + 1) - 3(2x + 5)]/6 = - 3 <=>
(2x + 2 - 6x -15) / 6 = - 3 <=>
-4x - 13 = -18 <=>
-4x = -18 + 13 <=>
-4x = -5 <=> x = 5/4
D) We reduce to common denominator, which for 2, 4 and 5 is 20
[3.(x - 1)] / 2 + [2(x + 2)] / 4 = (3x + 4.5) / 5 <=>
30(x - 1) + 10(x + 2) = 4(3x + 4.5) <=>
30x - 30 + 10x + 20 = 12x + 18 <=>
40x - 12x = 18 + 10 <=>
28x = 28 <=> x = 1
Answer A
Answer: (A) 1, - 3/4, 5/4, 1
Question: A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $19000 left with him. find salary..
(A) $10900
(B) $19000
(C) $190000
(D) $1900
(E) None
Rationale: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount
[1-(1/5 + 1/10 + 3/5)} * total salary= $19000, = [1-9/10] * Total salary = $19000, Total salary = $19000*10 = $190000, correct answer (C)
Answer: (C) $190000
Question: A rectangle with width 8 and diagonal 30. find the area?
(A) 240square units
(B) 180square units
(C) 100square units
(D) 150square units
(E) 160square units
Rationale: Then the area is: 8" x 30" = 240 square inches, or 240 square units
hence A
Answer: (A) 240square units
Question: At an elementary school, 70% of the faculty members are women and 60% of the faculty members are married. If 2⁄3 of the men are single, what fraction of the women are married?
(A) 5⁄7
(B) 7⁄10
(C) 1⁄3
(D) 7⁄30
(E) 5⁄70
Rationale: Plugging in numbers for this. Assume 100 faculty members.
70 faculty members are women
30 faculty members are men
60 total faculty members are married
1/3 of men are married (10), which means 20 men are single
10 of the 60 married faculty members are men, which means that 50 women are married.
50/70 women are married, reduced to 5/7
Ans A
Answer: (A) 5⁄7
Question: A librarian has a set of ten books, including four different books about Abraham Lincoln. The librarian wants to put the ten books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other six books. How many different arrangements of the ten books are possible?
(A) (10!)/(4!)
(B) (4!)(6!)
(C) (4!)(7!)
(D) (4!)(10!)
(E) (4!)(6!)(10!)
Rationale: You can club the four Lincoln books as one, which leaves us with six other books plus this one to think about. So, these seven items can be arranged in 7! ways, and since the four books can be moved around among themselves with each combination giving us a new overall combination, we have an additional 4! ways. Therefore, the answer would be 7!*4!, which is C.
Answer: (C) (4!)(7!)
Question: A can do a piece of work in 6 hours; B and C together can do it in 5 hours, while A and C together can do it in 3 hours. How long will B alone take to do it?
(A) 3 6/8 hours
(B) 4 6/8 hours
(C) 2 6/8 hours
(D) 5 5/8 hours
(E) none of the above
Rationale: A's 1 hour's work = 1/6 ;
(B + C)'s 1 hour's work = 1/5 ;
(B + C)'s 1 hour's work = 1/3
(A + B + C)'s 1 hour's work = (1/6 + 1/5) = 11/30
B's 1 hour's work = (11/30 - 1/3) = 8/30
B alone will take 30/8 hours to do the work.
=3 6/8
Answer = A
Answer: (A) 3 6/8 hours
Question: At a certain conference, 78% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance?
(A)  18.0%
(B)  62.0%
(C)  79.2%
(D)  86.67%
(E)  82.0%
Rationale: I do not think that Venn will be helpful here. A table will make more sense. But here is my approach.
78% regestered at least 2 weeks and paid full fee.
10% paid full fee and did not registered at least 2 weeks in advance. Then 90% paid full fee and registered at least 2 weeks before.
90% *X=78% where X is the number of people who registerd 2 weeks in advance and paid full fee. (ANSWER D)
Answer: (D)  86.67%
Question: 1. X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
(A) Rs.14400
(B) Rs.26400
(C) Rs.12000
(D) Rs.12500
(E) Rs.13000
Rationale: Explanation:
Ratio of the investment
=21000:17500=210:175=21000:17500=210:175 =42:35=6:5=42:35=6:5
Share of X in the profit
=26400Ã—611=2400Ã—6=14400
ANSWER IS A
Answer: (A) Rs.14400
Question: 1.12.91 is the first Sunday. Which is the fourth Tuesday of December 91?
(A) 20.12.91
(B) 22.12.91
(C) 24.12.91
(D) 25.12.91
(E) 26.12.91
Rationale: Explanation:
Given that 1.12.91 is the first Sunday
Hence we can assume that 3.12.91 is the first Tuesday
If we add 7 days to 3.12.91, we will get second Tuesday
If we add 14 days to 3.12.91, we will get third Tuesday
If we add 21 days to 3.12.91, we will get fourth Tuesday
=> fourth Tuesday = (3.12.91 + 21 days) = 24.12.91
Answer: Option C
Answer: (C) 24.12.91
Question: In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 3 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?
(A) 27/343
(B) 3/7
(C) 27/125
(D) 279/343
(E) 9/125
Rationale: Let us take 7*5=35 as the total number of customers. So 7*3=21 customers bought a bagel and 5*5=25 customers bought a coffee.
chances that at least 1 customer bought a coffee and a bagel = 1 - chances that no customer bought a coffee and a bagel
chances that no customer bought a coffee and a bagel= 24/35*23/34*22/33=12*23*2/35*17*3=552/1785
chances that at least 1 customer bought a coffee and a bagel= 1 - 552/1785 = 1233/1785 = 279/343
Answer D.
Answer: (D) 279/343
Question: Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?
(A) 19/20
(B) 24/25
(C) 29/30
(D) 34/35
(E) 39/40
Rationale: P(no graduates) = 3C3 / 7C3 = 1/35
P(at least one graduate) = 1- 1/35 = 34/35
The answer is D.
Answer: (D) 34/35