mathewhe/aqua_rat huggingface dataset:
Question: If 1/(n – 2) = 1/(n + 2) + 1/(n – 1), which of the following is a possible value of n?
(A) -3
(B) 0
(C) 3
(D) -4
(E) 4
Rationale: Multiply by (n-2)*(n+2)*(n-1) throughout to get:
(n+2)*(n-1) = (n-2)*(n-1) + (n+2)(n-2)
Of the given options, only n=0 satisfies this.
Answer : B
Answer: (B) 0
Question: Katie owned ten times as many cats as she did dogs. If she adopted 4 more dogs, the ratio of cats to dogs would be 1 to 1. How many dogs and cats does Katie have total after adopting the 4 more dogs.
(A) There is not enough information to solve the problem.
(B) 10
(C) 33
(D) 99
(E) None of the Above
Rationale: By checking the answer choices:
Since we have an initial ratio of 10:1, the total count should be divisible by 11.
A. There is enough information to solve this problem, therefore A is not the correct choice.
B. Out, Since not divisible by 11.
C. 33/11=3, Cats = 30, Dogs = 3, Since 30-4 is not equal to 3+4, this is not the answer.
D. 99/11=9, Cats = 90, Dogs = 9, Since 90-4 is not equal to 9+4 this as well can not be the answer.
E. Since none of the choices above are correct, E is the answer.
E is the correct answer.
Answer: (E) None of the Above
Question: If A:B = 1/4: 1/3 B:C = 1/4:1/3 then A:B:C?
(A) 9:12:6
(B) 9:2:16
(C) 9:12:16
(D) 9:12:14
(E) 19:12:16
Rationale: A:B = 1/4:1/3 = 3:4
B:C = 1/4:1/3 = 3:4
--------------------
A:B:C = 9:12:16
ANSWER:C
Answer: (C) 9:12:16
Question: A and B together have $ 1210. If of A's amount is equal to of B's amount, how much amount does B have?
(A) $400
(B) $489
(C) $484
(D) $365
(E) %342
Rationale: (4/15)A=(2/5)B
=>A=((2/5)*(15/4))B
=>A=(3/2)B
=>A/B=3/2
A:B=3:2
B's share=rs.(1210*(2/5))=$484
Option C
Answer: (C) $484
Question: There are two numbers. If 30% of the first number is added to the second number, then the second number increases to its five-fourth. What is the ratio of the first number to the second number?
(A) 3 : 25
(B) 25 : 8
(C) 8 : 5
(D) 5 : 6
(E) 7 : 2
Rationale: Let the two numbers be x and y.
(3/10) * x + y = (5/4) * y
(3/10) * x = (1/4) * y
x/y = 10/12 = 5/6
The answer is D.
Answer: (D) 5 : 6
Question: The area of a rectangle is 24 cm2. The width is two less than the length. What is the length and width of the rectangle?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Solution
Let x be the length and let x - 2 be the width
Area = lenth × width = x × ( x - 2) = 24
x × ( x - 2) = 24
x2 + -2x = 24
x2 + -2x - 24 = 0
Since -24 = 4 × -6 and 4 + -6 = -2, we get:
(x + 4) × ( x + -6) = 0
This leads to two equations to solve:
x + 4 = 0 and x + -6 = 0
x + 4 = 0 gives x = -4. Reject this value since a dimension cannot be negative
x + -6 = 0 gives x = 6
Therefore, length = 6 and width = x - 2 = 6 - 2 = 4
Answer B
Answer: (B) 4
Question: The area of a rectangular field is 144 m2. If the length had been 6 metres more, the area would have been 54 m2 more. The original length of the field is
(A) 22 metres
(B) 18 metres
(C) 16 metres
(D) 24 metres
(E) None of these
Rationale: Let the length and breadth of the original rectangular field be x m and y m respectively.
Area of the original field = x × y = 144 m2
∴ x = 144⁄y .....(i)
If the length had been 6 m more, then area will be
(x + 6) y = 144 + 54
⇒ (x + 6)y = 198… (ii)
Putting the value of x from eq (i) in eq (ii), we get
(144⁄y + 6)y = 198
⇒ 144 + 6y = 198
⇒ 6y = 54 ⇒ y = 9m
Putting the value of y in eq (i) we get x = 16 m
Answer C
Answer: (C) 16 metres
Question: If Rs.440 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
(A) s.575
(B) s.595
(C) s.590
(D) s.580
(E) s.585
Rationale: 80 = (440*4*R)/100
R = 5.68%
I = (440*6*5.68)/100 = 150
440 + 150 = 590
ANSWER:C
Answer: (C) s.590
Question: The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.8000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is
(A) 20
(B) 21
(C) 22
(D) 7
(E) 24
Rationale: Solution
Let the toatl number of workers be x.
Then 8000x=(8000 x 7) + 6000 (x -7)
x= 7.
Answer D
Answer: (D) 7
Question: If both 5^2 and 3^3 are factors of n x (2^5) x (6) x (7^3), what is the smallest possible positive value of n?
(A) 75
(B) 125
(C) 145
(D) 175
(E) 225
Rationale: (2^5) x (6) x (7^3) has one appearance of 3 (in the 6) and no appearances of 5.
Thus n must include at least 3^2 * 5^2 = 9 * 25 = 225
The answer is E.
Answer: (E) 225
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 7 yrs
(B) 10 yrs
(C) 18 yrs
(D) 20 yrs
(E) 25 yrs
Rationale: Explanation:
9 * 2 = 18 years
ANSWER C
Answer: (C) 18 yrs
Question: There are three foam generators in the factory, each of the first two can generate 10 liters of foam in one hour and the third can generate 16 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?
(A) 120.
(B) 121
(C) 146.
(D) 154.
(E) 166.
Rationale: Let the foam generators capacity be -
A = 10 lit/hr
B = 10 lit/hr
C = 16 lit/hr
Total foam generation in 1 hour will be 36 lit ( 10 + 10 + 16 ) ; since in 1 and 1/2 hr they will generate 36 + 18 => 54 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 10 lit/hr
C = 16 lit/hr
Total foam generation in 2 hour will be 52 litres {2 (10+16)}
The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...
Foam generated by B will be 3/2 * 10 => 15 litres
So, total foam generated will be 121 Litres ( 54 + 52 + 15 ) ; hence answer will be (B)
Answer: (B) 121
Question: If the length of an edge of cube M is five times the length of an edge of cube N, what is the ratio of the volume of cube N to the volume of cube M?
(A) 1/125
(B) 1/25
(C) 1/5
(D) 1/16
(E) 1/32
Rationale: The length of cube N = 1;
The length of cube M = 5;
The ratio of the volume of cube N to the volume of cube M = 1^3/5^3 = 1/125
Answer : A
Answer: (A) 1/125
Question: Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
(A) 10
(B) 12
(C) 15
(D) 20
(E) 25
Rationale: Explanation:
Speed of the first train =120/10 m/sec = 12 m/sec.
Speed of the second train =120/15 m/sec = 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Therefore Required time =(120+120)/20 sec = 12 sec.
ANSWER IS B
Answer: (B) 12
Question: Of 30 applicants for a job, 12 had at least 4 years' experience, 19 had degrees, and 6 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?
(A)  14
(B)  13
(C)  9
(D)  7
(E)  5
Rationale: set A : people with more than 4 years exp
set B : people with degree
AUB = total - (less than 4 exp and no degree)
AUB = 30-6=24
AUB = A + B - AiB
AiB = 19+12-24
=7
Answer D
Answer: (D)  7
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
(A) 16
(B) 19
(C) 15
(D) 22
(E) 10
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4
=> x = .
Answer: D
Answer: (D) 22
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 38 with him, what was the average amount with the group before his joining the group?
(A) s.17
(B) s.12
(C) s.15
(D) s.22
(E) s.12
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 38. So, the amount with remaining 6 people = 140 - 38 = Rs. 102
The average amount with them = 102/6 = Rs.17.
Answer:A
Answer: (A) s.17
Question: If 1*548 is divisible by 3, which of the following digits can replace *?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Solution
1 + x + 5 + 4 + 8 = (18 + x).
Clearly, when x=0, then sum of digits divisible by 3.
Answer D
Answer: (D) 3
Question: A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability T that the sum of the two integers will equal 9 ?
(A)  0.15
(B)  0.20
(C)  0.25
(D)  0.30
(E)  0.33
Rationale: Rearrange the first set:
A = {5,4,3,2}
B = {4,5,6,7, 8}
As you can see numbers in each column (the numbers of the same color) give the sum of 9. So there are 4 such pares possible, total # of pairs is 4*5=20. T=favorable/total=4/20=0.2.
Answer: B.
Or: we can select ANY number from set A (4/4=1) but in this case we must select its matching pair from set B (the number of the same color) and since there are only one matching pair of this particular number in B then the probability of this is 1/5. So, overall: T=1*1/5.
Answer: B.
Answer: (B)  0.20
Question: 3*15 + 3*16 + 3*19 + 11 = ?
(A) 125
(B) 126
(C) 130
(D) 148
(E) 161
Rationale: 3*15 + 3*16 + 3*19 + 11 = 45 + 48 + 57 + 11 = 161
The answer is E.
Answer: (E) 161
Question: A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 10 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans?
(A) 54%
(B) 70%
(C) 75%
(D) 85%
(E) 95%
Rationale: find the product of the two increases: (1.4) * (1.1), which is 1.54 and a 54% increase.
A
Answer: (A) 54%
Question: The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
(A) 288
(B) 240
(C) 267
(D) 299
(E) 162
Rationale: 4a = 68 => a = 17
172 – 82 = 152
1/2 * 16 * 30 = 240
Answer:B
Answer: (B) 240
Question: In what time will a train 100 meters long cross an electric pole, if its speed is 180 km/hr
(A) 5 seconds
(B) 4.5 seconds
(C) 3 seconds
(D) 2 seconds
(E) None of these
Rationale: Explanation:
First convert speed into m/sec
Speed = 180*(5/18) = 50 m/sec
Time = Distance/speed
= 100/50 = 2 seconds
Answer: D
Answer: (D) 2 seconds
Question: In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike?
(A) 45.5 kg
(B) 50.5 kg
(C) 55.5 kg
(D) 66.5 kg
(E) 72.5 kg
Rationale: Let Mike's weight be X kg.
According to Mike, 65 < X < 72.
According to Mike's brother, 60 < X < 70.
According to Mike's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg
D
Answer: (D) 66.5 kg
Question: Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 37 pages per hour. If Tom starts reading a novel at 4:00, and Jan begins reading an identical copy of the same book at 4:56, at what time will they be reading the same page?
(A) 7:26
(B) 7:56
(C) 8:26
(D) 8:56
(E) 9:26
Rationale: Since Tom reads an average of 1 page every 2 minutes, Tom will read 28 pages in the first 56 minutes. Jan can catch Tom at a rate of 7 pages per hour, so it will take 4 hours to catch Tom.
The answer is D.
Answer: (D) 8:56
Question: There are 50 students in a class. If 10 % are absent on a particular day, find the number of students present in the class.
(A) 43
(B) 36
(C) 28
(D) 45
(E) 11
Rationale: Number of students absent on a particular day = 10 % of 50
i.e., 10/100 × 50 = 5
Therefore, the number of students present = 50 - 5 = 45 students.
Answer:D
Answer: (D) 45
Question: How many rectangles can be formed out of a chess board ?
(A) 204
(B) 1230
(C) 1740
(D) 1296
(E) none of these
Rationale: A chess board consists 9 parallel lines x 9 parallel lines.
For a rectangle we need to select 2 parallel lines and the other two parallel lines that are perpendicular to the first set.
Hence, 9C2 x 9C2 = 1296 rectangles
ANSWER:D
Answer: (D) 1296
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
(A) 399
(B) 238
(C) 200
(D) 288
(E) 291
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500 .Answer: C
Answer: (C) 200
Question: How many quarters are equal to 4 dollars?
(A) 16
(B) 8
(C) 12
(D) 9
(E) 7
Rationale: 4*4 = 16 quarters
Answer : A
Answer: (A) 16
Question: Look at this series: 36, 34, 30, 28, 24, ... What number should come next?
(A) 20
(B) 24
(C) 22
(D) 26
(E) 30
Rationale: alternating no subtraction series first 2 is subtracted and then 4 and 2 so on
22 is the next one
ANSWER C
Answer: (C) 22
Question: Bradley owns b video game cartridges. If Bradley’s total is one-third the total owned by Andrew and seven times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) (16/3)b
(B) (17/4)b
(C) (13/4)b
(D) (19/12)b
(E) (29/7)b
Rationale: Step 1: Categorize the problem
This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.
Step 2: Think like the test maker
What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlie’s totals in relation to Bradley’s total rather than giving you Bradley’s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlie’s values in relation to Bradley’s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.
Step 3: Solve the problem
b = Bradley’s total
3b = Andrew’s total
(1/7)b = Charlie’s total
Add each total
b + 3b+ (1/7)b = 4b + (1/7)b = (29/7)b
Therefore,choose E.
Answer: (E) (29/7)b
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 5 kmph
(B) 1kmph
(C) 7 kmph
(D) 9 kmph
(E) 11 kmph
Rationale: Explanation:
DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: B
Answer: (B) 1kmph
Question: What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12% p.a.?
(A) 10123.298
(B) 10123.22
(C) 10123.2
(D) 10123.21
(E) 10123.54
Rationale: Amount = [25000 * (1 + 12/100)3]
= 25000 * 28/25 * 28/25 * 28/25 = Rs. 35123.20
C.I. = (35123.20 - 25000) = Rs. 10123.20
Answer: C
Answer: (C) 10123.2
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 11.30 a.m. ?
(A) 7
(B) 5
(C) 9
(D) 17
(E) 12
Rationale: D
17
Relative speed = 2 + 3 = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 17 times before 11.30 a.m.
Answer: (D) 17
Question: A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 8 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?
(A) (a) 24/5
(B) (b) 5
(C) (c) 26/5
(D) (d) 27/5
(E) (e) 16/3
Rationale: from the uphill we can find out the distance = 4*2 = 8
average speed = total distance/total time
= 16/ (2+ (8/8)) = 16/3
Answer is E.
Answer: (E) (e) 16/3
Question: A jar contains 10 marbles consisting of an equal number of red, green, and blue marbles. Three marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the Three marbles have been removed?
(A) 1/40
(B) 1/165
(C) 1/81
(D) 1/30
(E) 1/20
Rationale: Jar contains {3-red, 3-green, 3-blue} marbles. We are asked to find the probability that after removing 3 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue.
Sample space = 10C3 = 120.
Probability of choosing 3 red = 3C3/10C3 = 1/120.
Probability of choosing 3 green = 3C3/10C3 = 1/120.
Probability of choosing 3 blue = 3C3/10C3 = 1/120.
Required probability = 1+1+1/120 = 3/120 = 1/40. Ans (A).
Answer: (A) 1/40
Question: A,B,C together can earn $600 per day. while A and C together earn $400 and B and C together can earn $300. The daily earnings of C?
(A) $100
(B) $200
(C) $250
(D) $300
(E) $500
Rationale: B's daily earnings = 600-400 = $200
A's daily earnings = 600-300 = $300
C's daily earnings = 600-200-300 = $100
Answer is A
Answer: (A) $100
Question: A profit of Rs. 800 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
(A) s. 260
(B) s. 160
(C) s. 360
(D) s. 50
(E) s. 90
Rationale: A profit of Rs. 800 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.
so profits are 480 and 320.
difference in profit share = 480-320=160
ANSWER:B
Answer: (B) s. 160
Question: If each side of a square is increased by 25%, find the percentage change in its area.
(A) 46.25%
(B) 56.25%
(C) 56%
(D) 50.25%
(E) 36.25%
Rationale: Let each side of the square be a. Then, area = a2.
New side =(125a/100) =(5a/4). New area = (5a/4) 2=(25a2)/16.
Increase in area = ((25 a2)/16)-a2=(9a2)/16.
Increase% = [((9a2)/16)*(1/a2)*100] % = 56.25%.
ANSWER B 56.25%
Answer: (B) 56.25%
Question: What day of the week was 7th January 1601
(A) Sunday
(B) Tuesday
(C) Monday
(D) Thursday
(E) Saturday
Rationale: Explanation:
7th Jan 1601 = (1600 years + 7th Jan 1601)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)
7th Jan 1601 = 7 odd day
Total number of odd days = (0 + 7) = 7 = 0
0 odd days = Sunday
Hence 7th January 1601 is Sunday.
Answer: Option A
Answer: (A) Sunday
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State ?
(A) 2438
(B) 8000
(C) 2379
(D) 2988
(E) 2791
Rationale: Explanation:
Let the number of candidates appeared from each state be x.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
Answer: B) 8000
Answer: (B) 8000
Question: A bag contains 20 red jellybeans and 20 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability that all 3 jellybeans removed from the bag are blue?
(A) 9/100
(B) 2/19
(C) 1/8
(D) 3/20
(E) 3/10
Rationale: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability = 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 3/20
Answer: option D
Answer: (D) 3/20
Question: If a, b, and c are distinct positive prime numbers, then (a^3)(b)(c) has how many different positive factors greater than 1?
(A) a. 3
(B) b. 9
(C) c. 12
(D) d. 15
(E) e. 27
Rationale: Let Number is (a^3)(b)(c) = (1^3)(2)(3) = 6
We can write 6 as product of two numbers in following ways
1*6
2*3
2 cases = 2*2 i.e. 4 factors (including 1)
Factors greater than 1 = 3
Answer: Option A
Answer: (A) a. 3
Question: A trader sold an item at a loss of 18%. if he had increased the price by $25 he would have made a gain of 5%. what is the cost price of the item?
(A) $414.78
(B) $424.78
(C) $534.78
(D) $434.78
(E) $435.78
Rationale: Let C.P. be $x
Then 105% of x - 82% of x = 100
23% of x = 100
23/100 *X = 100
23x = 10000
x = 434.78
Answer is D
Answer: (D) $434.78
Question: There are 12 pieces of radioactive metal W that look identical. 11 of the pieces give the same radiation count when measured, the 12th piece is a counterfeit and gives a different radiation level, which may be more or less than the other 11. We are given a radiation scale, which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different, which set has the higher level of radiation. What is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: First of all if you are down to just 3 pieces and you know that if the offending piece is less or more active, then it takes exactly 1 measurement to find out the offending piece. So you know you have to reduce the problem to three.
Now when you are down to either A or B after measurement 1, you need the next measurement to (a) reduce the problem set to 3 and (b) to know whether anser is more or less. Now you cannot compare a group of 4 to 4, as in the best case it will only reduce the problem to 4 elements which is not good enough.
If you have to choose a set of 3 to compare, you cannot pick any 3 on the same side from the same set (A or B) because if you do this, a quick check will show you that in every choice there is a case where you can only get down to 4 elements. Eg. If you weighed {1,2,3} v/s {5,9,10} and they were equal you're problem would only reduce to {4,6,7,8}
The easiest way to solve this then is to compare 3 to 3, and make sure each side has elements from both AB such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only. Which is why the sets {1,5,9} and {2,6,7} OR {A,B,C}{A,B,B}. The extra element from C is just taken to make the problem symmetric so to say, we have 8 elements and we make it 9, to compose 3 sets of 3 each.=B
Answer: (B) 3
Question: Of 70 players on a football team, 28 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
(A) 56
(B) 59
(C) 63
(D) 71
(E) 92
Rationale: Total = 70
Thrower = 28
Rest = 70 - 28 = 42
Left Handed = 42/3 = 14
Right handed = 28
If all Thrower are right handed then total right handed is 28 + 28 = 56
so A. 56 is the right answer
Answer: (A) 56