mathewhe/aqua_rat huggingface dataset:
Question: In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 80% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that a beginner Trigonometry student is selected?
(A) 40%
(B) 44%
(C) 48%
(D) 52%
(E) 56%
Rationale: Let x be the number of students in calculus.
Then the number of students in trigonometry is 1.5x
The number of students on beginner calculus is 0.8x
The number of students in beginner trigonometry is 4/5*(2.5x) - 0.8x = 1.2x
The percentage in beginner trigonometry is 1.2x / 2.5x = 48%
The answer is C.
Answer: (C) 48%
Question: If each term in the sum E=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: Min value of 'n' can be 10 i.e 4*22+6*12=E => 22+22+22+22+2+2+2+2+2+2 = 100
Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options
(20-1) + 22/2 = 30 digits ( not in options)
(30-1) + 22/2 = 40 digits
Hence C.
Answer: (C) 40
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
(A) 0.5907
(B) 0.5904
(C) 0.5902
(D) 0.5901
(E) 0.59023
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904.Answer: B
Answer: (B) 0.5904
Question: The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 62 kg. What is the correct weight?
(A) 58kgs
(B) 58.85kgs
(C) 58.7kgs
(D) 59kgs
(E) 59.85kgs
Rationale: Actual total weight is (20X 58.4 - 56 + 62) = 1174 Kgs
Actual average weight is 1174/20 = 58.7kgs
C
Answer: (C) 58.7kgs
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 170, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
(A) 30
(B) 33
(C) 55
(D) 77
(E) 88
Rationale: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 170 => .1x + 3/4x = 170 => x = 200
200 - 170 = pure gala = 30.
Answer A
Answer: (A) 30
Question: If 5 less than x is 4 greater than y, then a number z that is 3 greater than x reduced by y is equal to
(A) 4
(B) 12
(C) 14
(D) y + 9
(E) y + 14
Rationale: 12 it is....nice one....
B
Answer: (B) 12
Question: How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 2 years
(B) 3 years
(C) 1 year
(D) 4 years
(E) 5 years
Rationale: Explanation:
P = Rs.900
SI = Rs.81
T = ?
R = 4.5%
T= (100×SI)/PR
= (100×81)/(900×4.5) = 2 years
Answer: Option A
Answer: (A) 2 years
Question: How many positive, 3-digit integers contain at least one 7?
(A) 171
(B) 200
(C) 243
(D) 252
(E) 271
Rationale: Contains only one 7:
7XX: 1*9*9 = 81
X7X: 8*1*9 = 72
XX7: 8*9*1 = 72
Contains two 7s:
77X: 1*1*9=9
X77: 8*1*1 = 8
Contains three 7s:
777: 1
Total 243
ANS:C
Answer: (C) 243
Question: How many positive integers D between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?
(A) 3
(B) 16
(C) 75
(D) 24
(E) 26
Rationale: 1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens.
2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers).
3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers.
4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left!
6) Answer choice E.
Answer: (E) 26
Question: Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?
(A) 29
(B) 30
(C) 31
(D) 35
(E) 38
Rationale: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation
larger number – smaller number = 7
which is equivalent to
Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.
C
Answer: (C) 31
Question: A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate?
(A) Rs.256.75
(B) Rs.256.28
(C) Rs.256.29
(D) Rs.256.21
(E) Rs.256.25
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.500
(P)(8)(5)/100 = 500
P = 1250
C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years
=2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}
= 2500/400(441 - 400)
= 25/4(41) = 1025/4
=Rs.256.25
Answer:E
Answer: (E) Rs.256.25
Question: what no should be subtracted from 92555 to make it a perfect square ?
(A) 128
(B) 158
(C) 178
(D) 139
(E) 140
Rationale: root 92555= 304.228
and
304^2=92416
92555-92416=139 should be subtracted from 92555 to make it a perfect square
ANSWER:D
Answer: (D) 139
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms Lucy pick?
(A) 2 kilograms
(B) 4 kilograms
(C) 6 kilograms
(D) 8 kilograms
(E) 10 kilograms
Rationale: Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2, respectively. So
x+2x+x+2=26
4x=24
x=6
Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.
correct answer D
Answer: (D) 8 kilograms
Question: Which of the following is the Highest Common Factor of 27, 81 and 54?
(A) 8
(B) 9
(C) 6
(D) 14
(E) 12
Rationale: the Highest Common Factor is 9Ans is :B
Answer: (B) 9
Question: A man, a woman and a boy can complete a job in 3,4 and 12 days respectively.
How many boys must assist 1 man and 1 woman to complete the job in ¼ of a day?
(A) 1day
(B) 4days
(C) 19days
(D) 41days
(E) 52days
Rationale: (1 man + 1 woman)'s 1 days work = 1/3+1/4=7/12
Work done by 1 man and 1 women n 1/4 day=((7/12)*(1/4))=7/48
Remaining work= 1- 7/48= 41/48
Work done by 1 boy in ¼ day= ((1/12)*(1/4)) =1/48
Therefore, Number of boys required= ((41/48)*48)= 41 days
ANSWER D 41days
Answer: (D) 41days
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.86
(B) 2.88
(C) 2.80
(D) 2.87
(E) 2.82
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: (B) 2.88
Question: A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 8)%. In terms of x, how many species of bacteria will the group be able to model?
(A) x*x – 5x
(B) (x)(105 – x)
(C) (x)*(108 - x)
(D) (100)(95 – x)
(E) (x-5)/100
Rationale: Initial: (x/100)*10000 = 100x (bacterial species)
After reduce BY (x - 8)%, the percentage of bacterial species = 1 - (x - 8)% = 1 - (x - 8)/100 = (108 - x)/100
Note: Difference betweenreduce to[means: the remain] andreduce by[means: the remain = 1 -reduce by]
So, the number of bacterial species after reducing: 100x*(108 - x)/100 = (x)*(108 - x)
Ans is C.
Answer: (C) (x)*(108 - x)
Question: A train is 250 meter long is running at a speed of 36 km/hour. In what time will it pass a station of 200 meter length?
(A) 28 seconds
(B) 27 seconds
(C) 45 seconds
(D) 26 seconds
(E) 18 seconds
Rationale: Speed = 36 Km/hr = 36*(5/18) m/sec = 10 m/sec
Total distance = 250+200 = 450 meter
Time = Distance/speed
= 450 * (10) = 45 seconds
Answer: C
Answer: (C) 45 seconds
Question: John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 1 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?
(A)  4y
(B)  5y
(C)  6y
(D)  8y
(E)  19y
Rationale: Let $x be the advance that both receive = 2x
Amount earned per hour by John and Mary = x/10 and x/9
Mary gives $y to John to make the wages earned equal
Hence John wage per hr = (x+y)10 which is now equal to Mary's wage (x-y)/9
Solve (x+y)10 = (x-y)/9
9x + 9y = 10x -10y
x = 19y
Ans. E
Answer: (E)  19y
Question: Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?
(A) 81.6
(B) 81.5
(C) 81.1
(D) 81.9
(E) 81.2
Rationale: SI = 40 + 40
CI = 40 + 40 + 1.6
= 81.6
Answer: A
Answer: (A) 81.6
Question: Excluding stoppages, the speed of a train is 48 kmph and including stoppages it is 32 kmph. Of how many minutes does the train stop per hour?
(A) A)40
(B) B)30
(C) C)20
(D) D)10
(E) E)5
Rationale: Explanation:
T = 16/48 * 60 = 20
Answer: Option C
Answer: (C) C)20
Question: The edge of a cube is 4a cm. Find its surface?
(A) 104a2 cm2
(B) 64a2 cm2
(C) 96a2 cm2
(D) 84a2 cm2
(E) 56a2 cm2
Rationale: 6a2 = 6 * 4a * 4a = 96a2
Answer:C
Answer: (C) 96a2 cm2
Question: A and B are playing mathematical puzzles. A asks B "which whole numbers, greater than one, can divide all the nine three digit numbers 111,222,333,444,555,666, 777,888 and 999?"
B immediately gave the desired answer. It was :-
(A) 3, 37 and 119
(B) 3 AND 37 and 111
(C) 9, 37 and 111
(D) 3, 9 and 37
(E) None
Rationale: Explanation :
Each of the number can be written as a multiple of 111. And,
The factors of 111 are 3 and 37.
Thus, the desired answer is 3, 37 and 111.
Answer : B
Answer: (B) 3 AND 37 and 111
Question: A certain city with a population of 84,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
(A) a) 10,700
(B) b) 10,800
(C) c) 7,000
(D) d) 11,000
(E) e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 84k
x = 7,000
Answer : C
Answer: (C) c) 7,000
Question: A lady gives a dinner party to 5 guests to be selected from nine friends. The number of ways of forming the party of 5, given that two of the friends will not attend the party together is
(A) 56
(B) 126
(C) 91
(D) 94
(E) None of these
Rationale: Number of ways of selecting 5 guests from nine friends = 9C5
Out of these, 7C3 ways are those in which two of the friends occur together [3 more persons to be selected out of remaining 7]
∴ Number of ways, in which two of the friends will not attend the party together = 9C5 – 7C3 = 91.
Answer C
Answer: (C) 91
Question: The number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 27 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse?
(A) 27
(B) 33
(C) 54
(D) 81
(E) 162
Rationale: Explanations
1) This tells us that the number of boxes is evenly divisible by both 6 and 27; in other words, it’s a common multiple of 6 and 27. The question says: what’s the smallest value it could have? In other words, what’s the LCM of 6 and 27? (This question is one example of a real-world set-up where the question is actually asking for the LCM.)
Step (a): 6 = 2*3 27 = 3*3*3
Step (b): 6 = 2*3 27 = 3*3*3 GCF = 3
Step (c): 6 = 3*2 27 = 3*9
Step (d) LCM = 3*2*9 = 54
Thus, 54 is the LCM of 6 and 27.
Answer: C.
Answer: (C) 54
Question: A bag contains 3 red, 6 yellow and 8 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?
(A) 2/7
(B) 3/5
(C) 3/11
(D) 18/85
(E) 7/16
Rationale: Total number of balls = 3+6+8 = 17
n(S) = 17C3 = 680
n(E) = 3C1 * 6C1 * 8C1 = 144
Probability = 144/680 = 18/85
Answer is D
Answer: (D) 18/85
Question: What is the factorial of 5?
(A) 1
(B) 60
(C) 120
(D) 130
(E) 180
Rationale: C
120
120 (5 X 4 X 3 X 2 X 1).
Answer: (C) 120
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $63 more. What was his original selling price?
(A) $850
(B) $990
(C) $1050
(D) $1180
(E) $1340
Rationale: Let P be the original purchase price of the product.
Bill originally sold the product for 1.1*P.
In the second scenario, the purchase price is 0.9*P.
A 30% profit means the selling price would be 1.3*0.9*P = 1.17*P
Thus, according to the information in the question, 1.17P - 1.1P = 63
0.07 = 63
P = 900
The original selling price was 900*1.1 = 990.
The correct answer is B.
Answer: (B) $990
Question: The workforce of Company X is 60% female. The company hired 28 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers?
(A) 160
(B) 220
(C) 336
(D) 360
(E) 420
Rationale: Let's xx be total quantity of employees
0.6x=females before adding men
0.55(x+28)=females after adding men
as quantity of women doesn't change we can make an equation:
0.6x=0.55(x+28)
0.05x=15.4
x=308 - this is quantity of employees before adding 28 men
So after adding it will be 336
Answer is C
Answer: (C) 336
Question: Bruce and Bhishma are running on a circular track of length 600m. Speed of Bruce is 30 m/s and that of Bhishma is 20 m/s .They start fro the same point at the same time in the same direction. When will they meet again for the first time?
(A) 30 sec
(B) 40 sec
(C) 50 sec
(D) 60 sec
(E) 70 sec
Rationale: Actually Arjun has to make a lead of 600 m, because when Arjun will be 600m ahead of Bhishma, they will be together again as a person when completes the total length it starts retracing he same path and thus Arjun and Bhishma can be together again.
Since , they make a difference of 10 m in 1 second. so, he will create 600m difference in 60 second.
D
Answer: (D) 60 sec
Question: x is the smallest integer greater than 1000 that is not prime and that has only one factor in common with 30!. What is x?
(A) 1009
(B) 1021
(C) 1147
(D) 1273
(E) 50! + 1
Rationale: Next, x and 30! have only one factor in common means that this factor must be 1 (any two integers have 1 as a common factor). Thus no other factor of 30! is a factor of x. So, the least prime of x can be 31 (30! has all primes less than 30).
x cannot be 31*31 = 961 because it's less than 1,000.
The next prime is 37: 31*37 = 1147 > 1,000.
Answer: C
Answer: (C) 1147
Question: A, B and C enter into a partnership by investing $11000, $15000 and $23000 respectively. At the end of 8 months, B receives $1540 as his share. Find the share of A.
(A) $811
(B) $922
(C) $1033
(D) $1144
(E) $1255
Rationale: The ratio of capital of A, B and C = 11000 : 15000 : 23000 = 11 : 15 : 23
A's share = (11/15)*1560 = $1144
The answer is D.
Answer: (D) $1144
Question: A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(A) 34
(B) 35
(C) 37
(D) 38
(E) 40
Rationale: Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of aa by dd be 'x'
Therefore, we can write the relation as a/d = x and the remainder is 24.
i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.
We know that a=dx+24. Therefore, 2a = 2dx + 48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.
C
Answer: (C) 37
Question: What is the area of a square field whose diagonal of length 30 m?
(A) 300 sq m
(B) 250 sq m
(C) 200 sq m
(D) 400 sq m
(E) 800 sq m
Rationale: d2/2 = (30 * 30)/2 = 300
ANSWER:A
Answer: (A) 300 sq m
Question: A,B,C invested the capitals in a business. If the investment of A, B, C are Rs. 40,000, Rs.50,000, Rs.10000 respectively and the profit got by B is Rs.7500, find the profit of others.
(A) 6000, 1500
(B) 5000, 2500
(C) 6500, 1000
(D) 5500, 2000
(E) 5250, 2250
Rationale: A==40,000
B==50,000
C==10,000
so, ration are 4:5:1
5x = 7500 ie) x=1500
A's profit=4x =6000
C's profit =x=1500
ANSWER:A
Answer: (A) 6000, 1500
Question: The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is ?
(A) 87
(B) 95
(C) 99
(D) 100
(E) 103
Rationale: The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.
From above, the total score of the 5 largest scores = 600 - 275 = 325.
Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:
a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.
Answer: C.
Answer: (C) 99
Question: The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is?
(A) 1200
(B) 1500
(C) 1700
(D) 1349
(E) 1389
Rationale: LCM = 1400
1400 - 6 = 1394
ANSWER D
Answer: (D) 1349
Question: If x and y are positive integers such that y is a multiple of 5 and 3x + 6y = 300, then x must be a multiple of which of the following?
(A) 3.
(B) 6.
(C) 7.
(D) 8.
(E) 10.
Rationale: If y is a multiple of 5, then 6y is also a multiple of 5.
3x = 300 - 6y
300 - 6y is even and it is a multiple of 5.
Thus x must also be even and a multiple of 5.
Therefore x must be a multiple of 10.
The answer is E.
Answer: (E) 10.
Question: If a - b = 3 and a(power 2) + b(power 2) = 21, find the value of ab.
(A) 5
(B) 8
(C) 4
(D) 6
(E) 3
Rationale: 2ab = (a(power 2) + b(power 2) - (a - b)(power 2)
= 21 - 9 = 12
ab = 6.
Answer is D.
Answer: (D) 6
Question: A lady builds 9cm length, 12cm width, and 3cm height box using 3cubic cm cubes. What is the minimum number of cubes required to build the box?
(A) 107
(B) 108
(C) 109
(D) 110
(E) 111
Rationale: Number of cubes required = Volume of box/Volume of cube
= 9*12*3/3
=108 cubes
ANSWER:B
Answer: (B) 108
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 47 years. What will be the age of the B ten years hence?
(A) 22
(B) 77
(C) 94
(D) 96
(E) 51
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 47 => b + c = 94 --- (2)
From (1) and (2), we cannot find b.
Answer: C
Answer: (C) 94
Question: One out of every 300 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
(A) 2,000
(B) 30000
(C) 10,000
(D) 50,000
(E) 52,000
Rationale: 20 broken glasses indicates that 10*10= 100 defected bulbs are present.
100 defected bulbs indicates that 100*300= 30,000 light bulbs are present.
B is the answer
Answer: (B) 30000
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 7800 ?
(A) 11
(B) 13
(C) 14
(D) 18
(E) 10
Rationale: Required difference = [3 ½ % of Rs.7800] – [3 1/3 % of Rs.7800]
= [(7/20-(10/3)]% of Rs.7800 =1/6 % of Rs.7800
= Rs. [(1/6)8(1/100)*7800] = Rs. 13.
Answer is B.
Answer: (B) 13
Question: If f(a)=2a+8, what is the value of (f(2a)+f(a)) ?
(A) 6a+16
(B) 8a-7
(C) 6a+18
(D) 6a+12
(E) 3a+5
Rationale: f(a)=2a+8
f(2a)= 4a+8
(f(2a)+f(a)) = 4a+8+2a+8 = 6a+16
Answer is A
Answer: (A) 6a+16
Question: A cistern 10 m long and 6 m wide contains water up to a breadth of 1 m 35 cm. Find the total area of the wet surface.
(A) 100 m sqaure
(B) 103 m sqaure
(C) 152 m sqaure
(D) 164 m sqaure
(E) None of these
Rationale: Explanation:
Area of the wet surface =
2[lb+bh+hl] - lb = 2 [bh+hl] + lb
= 2[(6*1.35+10*1.35)]+10*6 = 103 m square
Option B
Answer: (B) 103 m sqaure
Question: A boat having a length 3 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
(A) 100 kg
(B) 120 kg
(C) 89 Kg
(D) 90 Kg
(E) 110 Kg
Rationale: Volume of water displaced	= (3 x 3 x 0.01) m3
= 0.09 m3.
Mass of man = Volume of water displaced x Density of water
= (0.09 x 1000) kg
= 90 kg.
Answer: D
Answer: (D) 90 Kg
Question: Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many Q minutes it takes John to reach the station?
(A) 5 min
(B) 6 min
(C) 7 and 1/2 min
(D) 8 min
(E) 10 min
Rationale: Since the question states “after 15 minutes”, we can say Tom traveled 15/4km for 15 minutes as he can travel 15km per hour. Hence, using the same logic, we can say John traveled 10/4km as he travels 10km per hour. So, John has to travel (15/4)-(10/4)km=5/4km more. Since John’s speed is 10km/hour, which means 1km/6minutes. As he has to travel 5/4km more, it is going to take him 6(5/4) minutes. Hence,Q= 6(5/4)=15/2 minutes. The correct answer is C.
Answer: (C) 7 and 1/2 min
Question: The diameter of the driving wheel of a bus is 120 m. How many revolution, per minute must the wheel make in order to keep a speed of 60 kmph approximately
(A) 245
(B) 257
(C) 262
(D) 265
(E) 275
Rationale: Explanation:
Distance to be covered in 1 min. = (60 X 1000)/(60) m = 1000 m.
Circumference of the wheel = (2 x (22/7) x 0.60) m = 3.77 m.
Number of revolutions per min. =(1000/3.77) = 265
Answer: Option D
Answer: (D) 265
Question: How many different positive integers exist between 10^6 and 10^7, the sum of whose digits is equal to 2?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 18
Rationale: Total cases => 1000000=> 6 cases for 1 being present at any of the 6 zero
and last case 2000000
hence & cases
ANSWER:C
Answer: (C) 7
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
(A) 11 hours
(B) 16 hours
(C) 12 hours
(D) 13 hours
(E) 17 hours
Rationale: A's 1 hour's work =1/4;
(B + C)'s 1 hour's work = 1/3;
(A + C)'s 1 hour's work = 1/2.
(A + B + C)'s 1 hour's work = ( 1/4 + 1/3 )	= 7/12.
B's 1 hour's work = ( 7/12 - 1/2 ) = 1/12.
Therefore B alone will take 12 hours to do the work.
CORRECT OPTION : "C"
Answer: (C) 12 hours
Question: What is the average of 12, 13, 14, 51, 52, 53, 1,11.5, 1,1.20, and 11.25?
(A)  21.06
(B)  23
(C)  26
(D) 23.69
(E)  22.56
Rationale: Add 12, 13, 14, 51, 52, 53, 1,11.5, 1,12, and 11.25
Grouping numbers together may quicken the addition
sum = 231.75
231.75/11 =21.06
A
Answer: (A)  21.06