mathewhe/aqua_rat huggingface dataset:
Question: The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 576 feet squared, what is the difference between the length and the width of the roof?
(A) 38.
(B) 40.
(C) 36.
(D) 44.
(E) 46.
Rationale: Let the width= x
x*4x=576
x^2= 144
x= 12
Length= 4*12= 48
difference= 48-12= 36
C is the answer
Answer: (C) 36.
Question: A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 3 students left over. What is the sum of the two smallest possible values of n?
(A) 54
(B) 58
(C) 62
(D) 66
(E) 70
Rationale: n = 4k+1 = 7j+3
Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+3.
1, 5, 9, 13, 17 = 7(2)+ 3
The next such number is 17 + 4*7 = 45.
17+45 = 62
The answer is C.
Answer: (C) 62
Question: Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in five times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 45 minutes, then how many minutes does it take pump X alone to fill the tank?
(A) 27
(B) 30
(C) 33
(D) 36
(E) 39
Rationale: Let V be the volume of the tank.
Let R be the rate per minute that pump X fills the tank.
Let T be the time it takes pump X to fill the tank.
The rate at which pump Y empties the tank is V/45 per minute.
(R - V/45)*5T=V=RT.
(R-V/45)*5=R
4R=V/9.
R=V/36.
It takes pump X 36 minutes to fill the tank.
The answer is D.
Answer: (D) 36
Question: In what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 6 sec
(B) 7 sec
(C) 3 sec
(D) 9 sec
(E) 2 sec
Rationale: T = 30/36 * 18/5
= 3 sec
Answer:C
Answer: (C) 3 sec
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.25,000 earned at the end of 2years from the startingof the business?
(A) Rs. 5,000
(B) Rs. 5,500
(C) Rs. 5,700
(D) Rs. 6,500
(E) Rs. 7,500
Rationale: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 25000 x	3/10	= Rs. 7,500.
E
Answer: (E) Rs. 7,500
Question: Share Rs.5400 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?
(A) 1800
(B) 980
(C) 1200
(D) 1240
(E) 1400
Rationale: Amount received by sanjay.
4 / 12 X 5400 = 1800= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 1800.
A
Answer: (A) 1800
Question: For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 70 terms?
(A) 3/5
(B) 7/15
(C) 35/36
(D) 70/71
(E) 140/141
Rationale: a1 = 1 - 1/2
a2 = 1/2 - 1/3
a3 = 1/3 - 1/4
etc...
a70 = 1/70 - 1/71
The sum of these terms is 1-1/71 = 70/71
The answer is D.
Answer: (D) 70/71
Question: The diagonal of a rhombus are 80 m and 120m. Its area is:
(A) 4500
(B) 4000
(C) 4800
(D) 4600
(E) 4320
Rationale: Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 80 Ã— 120) Cm(power)2
= 80Ã— 60= 4800 Cm(power)2
Answer is C.
Answer: (C) 4800
Question: The average age of a group of persons going for picnic is years. Seventeen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
(A) 5
(B) 10
(C) 17
(D) 23
(E) 50
Rationale: Solution
Let the initial number of persons be x. Then
16x + 17 x 15 = 15.5(x+20)
= 0.5x = 8.5
x = 17.
Answer C
Answer: (C) 17
Question: A box contains 14 mangoes out of which 6 are spoilt. If six mangoes are chosen at random, find the probability that A number is selected at random from first fifty natural numbers. What is the chance that it is a multiple of either 5 or 12?
(A) 15/25
(B) 2/25
(C) 14/25
(D) 7/25
(E) 7/50
Rationale: The probability that the number is a multiple of 5 is 10/50. (Since 5*10 = 50).
Similarly the probability that the number is a multiple of 12 is 4/50. {Since 14*4 =
48).
Neither 5 nor 12 has common multiple from 1 to 50. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 5 or 12 is (10+4)/50 = 7/25.
ANSWER:D
Answer: (D) 7/25
Question: David has $1,800 at the beginning of his trip, after spending money, he still has exactly $800 less than he spent on the trip. How much money does John still have?
(A) $200
(B) $500
(C) $600
(D) $800
(E) $1,200
Rationale: Suppose total money spent = x
Not spend (Money he still has)= x-800
x+x-800 = 1800
x= 1300
Money not spend= 1300-800= 500
Answer : B
Answer: (B) $500
Question: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits F can does Grace have available during her trip?
(A)  2,520
(B)  1,260
(C)  620
(D)  360
(E)  120
Rationale: The idea is to multiply the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination forumla (don't know how to use math symbols here).
This gives you F=5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.
Answer: (B)  1,260
Question: The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 3 or 4 as its largest number?
(A) 3/4
(B) 3/8
(C) 3/16
(D) 5/16
(E) 3/32
Rationale: The set S has 2^5 = 32 subsets.
The number 5 is in half of these subsets.
Of the remaining 16 subsets, 4 is an element in 8 of them.
Thus 4 is the largest number in 8 subsets of S.
Of the remaining 8 subsets, 3 is an element in 4 of them.
Thus 3 is the largest number in 4 subsets of S.
The probability that 3 or 4 is the largest number is 12/32 = 3/8.
The answer is C.
Answer: (B) 3/8
Question: There are 60 slots around a circle,numbered 1 to 60. A man starts from the first slot and jumps to the 5th slot.From there he jumps to the 9th slot and so on. In which slot will he land in his
2200th jump?
(A) 1
(B) 5
(C) 41
(D) 45
(E) 46
Rationale: every 15th jump, he comes back to 1st position
so, 2200/15 = Remainder 10
Hence 10th position is 41st slot
ANSWER:C
Answer: (C) 41
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 10-meter platform and caught it after it had traveled 29.65 meters. How many times did the ball bounce?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Ans: 6
Division of total diatance travelled will be 10+10+5+2.5+1.25+0.6+0.3 ANS B
Answer: (B) 6
Question: If the units digit of n^43 is 7, which of the following could be the value of n?
I. n = 41
II. n = 43
III. n = 47
(A) Only I
(B) Only II
(C) Only III
(D) I and II
(E) II and III
Rationale: I tried in this way.
Given n^43 units digit is 7.
If at all we have to get 7 as units digits only 3 and 7 series has 7
3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81
7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units)
We have n^43 - then divide 43 by 4 = reminder 3.
Then we have for only 7^3 - we have units digit as 7.
Hence 47^43 = 7 (units).
Option A is correct answer , and with 41^43 we always get 1 as units digit and 43^43 - we get units as 3.
Answer: (A) Only I
Question: What is the units digit of the product of the first 50 odd numbers?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: 1*3*5*7 ................... will end up in 5 in the units place
Answer : E
Answer: (E) 5
Question: The sale price of a trolley bag including the sale tax is Rs. 1190. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:
(A) Rs 800
(B) Rs 820
(C) Rs 860
(D) Rs 850
(E) None of these
Rationale: Explanation :
112% of S.P. = 1190
S.P. = Rs.(1190 x 100/112) = Rs.1062.50.
C.P. = Rs (100/125x 1062.50) = Rs 850
Answer : D
Answer: (D) Rs 850
Question: On his first 3 tests, Rajeev received an average score of N points. If on his fourth test, he exceeds his previous average score by 20 points, what is his average score for his first 4 tests?
(A) N
(B) N + 4
(C) N + 5
(D) N + 10
(E) N + 20
Rationale: Total points from first three tests: 3N
Points on fourth test: N + 20
Total points on all four tests: 3N + (N + 20) = 4N + 20
Average score for first four tests: (4N + 20)/4 = N + 5
Answer is C.
Answer: (C) N + 5
Question: which number need to add to 859622 to get a number exactly divisible by 456?
(A) 547879
(B) 354643
(C) 354673
(D) 575673
(E) 859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: (E) 859622
Question: The triangle ABC has sides of the following lengths: AB = 24, BC = 7, and AC = 25.
Let M be the midpoint of AB. What is the length of CM?
(A) 1
(B) root139
(C) 12
(D) root193
(E) 16
Rationale: Since 242 + 72 = 252, triangle ABC is a right triangle. Thus, MBC is also a right
triangle and CM2 = BM2 + BC2 = 122 + 72 = 193.
correct answer D
Answer: (D) root193
Question: Due to flooding, vendors increased the cost of sandbags by 30% to keep customers from buying out all the sandbags. Government officials declared an emergency and would only pay 60% of total price for sandbags. What is the difference between the new cost of the sandbags and the amount government officials paid?
(A) 12.0%
(B) 15.0%
(C) 20.0%
(D) 22.0%
(E) 25.0%
Rationale: Quantity X Rate = Price
1 X 1 = 1
0.60 X 1.30 = 0.780
Decrease in price = (0.22/1) Ã— 100 = 22.0%
Answer = Option D
Answer: (D) 22.0%
Question: The 7th grade French and Spanish classes each have 21 students in them, and there are six students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes?
(A) 24
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: French class + Spanish class = 42 students.
Six students are in both classes so they were counted twice.
The number of students taking just one class is 42 - 2(6) = 30.
The answer is C.
Answer: (C) 30
Question: 2+2+2²+2³ ... +2^6
(A) 2^9
(B) 2^10
(C) 2^16
(D) 2^35
(E) 2^7
Rationale: 2+2=2^2
2^2+2^2=(2^2)*(1+1)=2^3
2^3+2^3=(2^3)*(1+1)=2^4
Answer E
Answer: (E) 2^7
Question: A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
(A) 175/256
(B) 451/365
(C) 312/456
(D) 156/754
(E) 164/784
Rationale: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾
Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256
The probability that he will hit the target at least in one of the four shots=1-81/256
=175/256
Ans:A
Answer: (A) 175/256
Question: x, a, z, and b are single digit positive integers. x = 1/3a. z = ¼3b. (10a + b) – (10x + z) could NOT equal
(A) 31
(B) 32
(C) 46
(D) 64
(E) 68
Rationale: a=3x , b =3z therefore(3x.10+3z) - (10x +z) = (3-1) (10x+z) =2.(10x+Z)
number should be divisible by 2
A
Answer: (A) 31
Question: The area of a triangle is 615 m2. If one of its sides is 123 metre, find the length of the perpendicular dropped on that side from opposite vertex.
(A) 15 metres
(B) 12 metres
(C) 10 metres
(D) 9 metres
(E) None of these
Rationale: In a triangle,
Area = 1⁄2 × length of perpendicular × base
or 615 = 1⁄2 × length of perpendicular × 123
∴ Length of perpendicular = 615×2/123=10m
Answer C
Answer: (C) 10 metres
Question: If the cost price of 50 articles is equal to the selling price of 20 articles, then the gain or loss percent is?
(A) 16
(B) 127
(C) 12
(D) 18
(E) 150
Rationale: Percentage of profit = 30/20 * 100 = 150%
Answer: E
Answer: (E) 150
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
(A) 4
(B) 7
(C) 9
(D) 14
(E) None
Rationale: 1 woman's 1 day's work = 1/70
1 Child's 1 day's work = 1/140
5 Women and 10 children 1 day work = (5/70+10/140)=1/7
So 5 women and 10 children will finish the work in 7 days.
Answer: B
Answer: (B) 7
Question: What is the remainder when 1014*1047*1050*1053 is divided by 33?
(A) 3
(B) 6
(C) 30
(D) 21
(E) 18
Rationale: OA is 'C'.
OE:
take the remainder from each of 1044/33, 1047/33 and so on..
1014/33 gives remainder = 24
1047/33 gives remainder = 24
1050/33 gives remainder = 27
1053/33 gives remainder = 30
the net remainder is the product of above individual remainders. i.e = 24*24*27*30
break them into pairs 24*24/33 gives remainder 15
and 27*30/33 gives remainder 18
so 15*18/33 gives remainder 6.
B
Answer: (B) 6
Question: Alice and Bob will throw three dice each. The score is the sum of points on all three dice. If Alice scores 17 in her attempt what is the probability that Bob will outscore Alice in his attempt?
(A) 1/216
(B) 5/216
(C) 7/216
(D) 1/36
(E) 5/36
Rationale: The total number of ways the dice can land is 6*6*6=216.
Bob must get a score of 18=6+6+6.
There is only 1 way to do this.
P(Bob wins)=1/216
The answer is A.
Answer: (A) 1/216
Question: Nine family members: 5 grandchildren (3 brothers and 2 sisters) and their 4 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?
(A) 120
(B) 480
(C) 1440
(D) 2880
(E) 8640
Rationale: Consider two brothers and two sisters between them as one unit: {BSSB}.
So, now we have 6 units: {G}, {G}, {G}, {G}, {B}, and {BSSB}.
These 6 units can be arranged around a circular table in (6-1)!=5! ways.
Next, analyze {BSSB} unit:
We can choose 2 brothers out of 3 for the unit in C23=3C32=3 ways;
These brothers, within the unit, can be arranged in 2! ways: {B1,S,S,B2}{B1,S,S,B2} or {B2,S,S,B1}{B2,S,S,B1}
The sisters, within the unit, also can be arranged in 2! ways: {B,S1,S2,B}{B,S1,S2,B} or {B,S2,S1,B}{B,S2,S1,B}
Therefore, the final answer is 5!*3*2*2=1440.
Answer: C.
Answer: (C) 1440
Question: When Jessica withdrew $200 from her bank account, her account balance decreased by 2/5. If she deposits an amount equal to 2/3 of the remaining balance, what will be the final balance in her bank account?
(A) 300
(B) 375
(C) 400
(D) 500
(E) 575
Rationale: As per the question 200=2a/5
thus- a which is the total amount =500
The amount thus left =300
She then deposited 2/3 of 300=200
total amount in her account =500
Answer D
Answer: (D) 500
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
(A) 11
(B) 25
(C) 7
(D) 88
(E) 98
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer: B
Answer: (B) 25
Question: The mean of 50 observations is 200. But later he found that there is decrements of 9 from each observations. what is the the updated mean is ?
(A) 165
(B) 185
(C) 190
(D) 191
(E) 199
Rationale: 191
Answer is D
Answer: (D) 191
Question: A man rows his boat 78 km downstream and 50 km upstream, taking 2 hours each time. Find the speed of the stream?
(A) 76 kmph
(B) 6 kmph
(C) 14 kmph
(D) 7 kmph
(E) 4 kmph
Rationale: Speed downstream = d/t = 78/(2)
= 39 kmph
Speed upstream = d/t = 50/(2)
= 25 kmph
The speed of the stream = (39 - 25)/2
= 7 kmph
Answer:D
Answer: (D) 7 kmph
Question: The food in a camp lasts for 34 men for 56 days. If fourteen more men join, how many days will the food last?
(A) 80 days
(B) 30 days
(C) 65 days
(D) 40 days
(E) 42 days
Rationale: one man can consume the same food in 34*56 = 1904 days.
14 more men join, the total number of men = 48
The number of days the food will last = 1904/48
= 40 days.
Answer:D
Answer: (D) 40 days
Question: An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 11. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?
(A) s 1200
(B) s 1500
(C) s 1600
(D) s 1900
(E) s 2400
Rationale: Explanation :
Let P = Faruk, Q = Vasim, R = Ranjith
Let P = 3x, Q = 5x and R = 11x.
Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 3300.
Hence, (R - p) = (3300 - 900) = 2400
Answer : E
Answer: (E) s 2400
Question: What is the CP of Rs 100 stock at 8 discount, with 1/5% brokerage?
(A) 92.9
(B) 96.3
(C) 92.2
(D) 96.7
(E) 92.8
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-8+1/5
92.2
Thus the CP is Rs 92.2.
ANSWER: C
Answer: (C) 92.2
Question: Take number 1000 and then add 20 to it.
Now add 1000 one more time.
Now add 30.
Now add 1000 one more time.
Now add 40.
Now add 1000 one more time.
Now add 10.
What is the total?
(A) 4100
(B) 3870
(C) 5200
(D) 6230
(E) 8340
Rationale: A
4100
some people might guess 5000
Answer: (A) 4100
Question: The edges of three metal cubes are 2 cm, 3 cm, and 4 cm respectively. A new cube is made by melting these three cubes together. What is the edge of the new cube (in centimeters)?
(A) 4.0
(B) 4.2
(C) 4.4
(D) 4.6
(E) 4.8
Rationale: The total volume is 2^3+3^3+4^3=99
The edge of the new cube is the cube root of 99 which is about 4.6 cm.
The answer is D.
Answer: (D) 4.6
Question: Each shelf of a bookcase contains 22 books. If the librarian took out 40 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 18 books, how many shelves does the bookcase have?
(A) A)4
(B) B)5
(C) C)7
(D) D)8
(E) E)9
Rationale: Denoting x the number of the shelves,
we can build an equation: 22x=16(x−1)+18+40
Solving the equation, we get x=7
Answer: C
Answer: (C) C)7
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 28
(C) 27
(D) 17
(E) 21
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25
= 40 sec
Answer: A
Answer: (A) 40
Question: In a river flowing at 2 km/hr, a boat travels 40 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.
(A) 10 hours
(B) 12 hours
(C) 14 hours
(D) 15 hours
(E) None of these
Rationale: Explanation :
speed of the boat = 6 km/hr
Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 40 km
Total time taken = Time taken downstream + Time taken upstream
= (40/8) + (40/4) = 15
D
Answer: (D) 15 hours
Question: If (6)(x^2) has three different prime factors, at most how many different prime factors does x have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x can have at most 3 prime factors, namely the prime factors 2 and 3, plus one other.
If x had more than this number of prime factors, then (6)(x^2) would have more than 3 prime factors.
The answer is C.
Answer: (C) 3
Question: Five years ago Anita was P times as old as Ben was. If Anita is now 14 years old, how old is Ben now in terms of P ?
(A) 9/P + 5
(B) P/9 +5
(C) 17 - P/5
(D) 17/P
(E) 11.5P
Rationale: let's call Ben age five years ago is x
so five years ago Anita was: 14-5 = 9 years old
and five years ago Anita was P times as old as Ben was
=> 9/x = P
=> x = 9/P
=> Now Ben age will be : x+5 = 9/P+5
=> the answer is A
Answer: (A) 9/P + 5
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 197
(B) 280
(C) 189
(D) 278
(E) 268
Rationale: x*(85/100)
= (480 - x)119/100
x = 280
Answer: B
Answer: (B) 280
Question: The salary of a person was reduced by 10%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
(A) 10%
(B) 11 1/9%
(C) 13 2/7%
(D) 15 3/11%
(E) 12 1/3%
Rationale: Let the original salary be $100
New salary = $90
Increase on 90 =10
Increase on 100 = 10/90 * 100 = 11 1/9%
Answer is B
Answer: (B) 11 1/9%
Question: A person traveled from his house to office at 30 kmph; then he was late to his office by 5 minutes. If he increases his speed by 10 kmph he would be early by 15 minutes to his office. What should be his speed so that he reaches his office on time ?
(A) 36 kmph
(B) 32 kmph
(C) 34 kmph
(D) 35 kmph
(E) 36 kmph
Rationale: Expl :
Let the distance between house and office be x km
(x/30) – (x/40) = 20/40; x/120 = 1/3 x = 40 km
Travlling at 40 kmph, he reaches office in 1 hour i.e. 15 minutes early
So required speed = 40/ 5/4 = 40 * 4/5 = 160/5 = 32 kmph
Answer: B
Answer: (B) 32 kmph
Question: The average weight of 3 men A, B and C is 84 kg. Another man D joins the group and the average now becomes 80 kg. If another man E, whose weight is 3 kg more than that of D, replaces A, then average weight of B, C, D and E becomes 79 kg. The weight of A is?
(A) 70 kg
(B) 72 kg
(C) 75 kg
(D) 80 kg
(E) None of these
Rationale: Weight of D = (80 x 4 - 84 x 3) kg = 68 kg
Weight of E = (68 + 3) kg = 71 kg
(B + C + D + E)’s weight = (79 x 4) kg = 316 kg
Therefore, (B + C)’s weight = [316 - (68 + 71)] kg = 177 kg.
Hence, A’s weight = [(84 x 3) - 177] kg = 75 kg.
ANSWER:C
Answer: (C) 75 kg
Question: Set Y consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set Y?
(A) 767
(B) 76
(C) 7
(D) 5
(E) 1
Rationale: Whenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least,group offthe numbers so that you can restrict the potential value of the median).
Here, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working....
Since the group includes 8 values, the median will be the AVERAGE of the 4th and 5th values...
Putting the 7 numbers in order, we have:
-27, -3, -2, 2, 3, 15, 17
This means that the2will either be the 4th term or the 5th term (depending on the value of N).
IF....
N is REALLY BIG, then the 4th and 5th terms will be 2 and 3, so the median will = 2.5
N is REALLY SMALL, then the 4th and 5th terms will be -2 and 2, so the median will = 0
Neither of those answers is among the choices though, so N must be something relativelycloseto 2.....
IF....
N = 0, then the 4th and 5th terms will be 0 and 2, so the median will = 1. That answer IS among the choices, so we're done.
E
Answer: (E) 1
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
(A) Rs.13
(B) Rs.12
(C) Rs.15
(D) Rs.22
(E) Rs.12
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90
The average amount with them = 90/6 = Rs.15.
Answer:C
Answer: (C) Rs.15
Question: If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers?
(A)  3
(B)  4
(C)  5
(D)  9
(E)  12
Rationale: If x=8 and y=6, then x^2-y^2=28 and 28 is divisible only by 4 from the options, thus it must be correct.
Answer: B.
Answer: (B)  4