mathewhe/aqua_rat huggingface dataset:
Question: 3. How many numbers that are not divisible by 6 divide evenly into 264,600?
(A) 9
(B) 36
(C) 51
(D) 63
(E) 72
Rationale: 264600 = 2^3 * 3 * 5^2 * 431
Numbers that will divide 264600 will be made up of multiples of factors of 264600 that do not divide by 6.
Expanding out the factors that are made up of the prime factors I get:
2,4,8,5,25,431
The numbers of multiples of these are: 6C1+6C2+6C3+6C4+6C5+6C6 = 63.
But in addition 1 is also a factor and so is 3 so I would have thought the ans to = 65 but my best guess is:
ANS = D
Answer: (D) 63
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 390 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
(A) 237
(B) 780
(C) 197
(D) 287
(E) 720
Rationale: Explanation:
Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 390) = 2 + 2(extra)
=> 2x - 780 = x => x = 780.
Answer: B
Answer: (B) 780
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.5. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.8. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal?
(A) 0.12
(B) 0.7
(C) 0.28
(D) 0.48
(E) 0.72
Rationale: (1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )
=0.5*0.2+0.4*0.3+0.6*0.8
= 0.10+0.12+0.48
=0.70
B
Answer: (B) 0.7
Question: A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 65 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.)
(A) $15,360
(B) $17,360
(C) $18,000
(D) $21,960
(E) $27,360
Rationale: For every $3 earn above $9360, the recipient loses $1 of benefit.
OR
For every $1 loss in the benefit, the recipient earns $3 above $9360
If earning is; 9360+3x
Benefit = 12000-x
Or the vice versa
If benefit is 12000-x, the earning becomes 9360+3x
He lost 50% of the benefit;
Benefit Received= 12000-0.65*12000 = 12000-7800
x=4200
Earning becomes 9360+3x=9360+3*4200=21960
Ans:D
Answer: (D) $21,960
Question: x/(y/z)
In the expression above, x, y, and z are different numbers and each is one of the numbers 1, 5, or 6. What is the least possible value of the expression?
(A) 6/5
(B) 2/15
(C) 5/6
(D) 3/10
(E) 6/6
Rationale: x/(y/z)
= (x*z)/y
The expression will have the least value when numerator (x*z) is the smallest.
= (1*5)/6
=5/6
Answer C
Answer: (C) 5/6
Question: The ratio of the present ages of a man and his wife is 7 : 6. Which of the following can't be a possible ratio of their ages 40 years ago?
(A) 5: 7
(B) 6: 7
(C) 7:7
(D) 8: 7
(E) 9: 7
Rationale: 7x-40/6x-40 = 8/7
Therefore x=-40
Age cannot be negative.
Answer: D
Answer: (D) 8: 7
Question: Each of the integers from 1 to 15 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?
(A) 9
(B) 12
(C) 11
(D) 10
(E) 3
Rationale: Out of the 15 integers: 8 are odd and 7 are even.
If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case:
1. we will end up picking odd numbers one by one, so we will pick all 8 odd numbers first
2. 9th number will be the first even number
So we need to withdraw at least 9 numbers to make sure that we get one even number and the product of all the integers picked is even.
So, answer will be 9. (A)
Answer: (A) 9
Question: The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages.
(A) 16, 18, 36
(B) 16, 28, 36
(C) 8, 20, 28
(D) 20, 35, 45
(E) None of these
Rationale: Answer: Option B
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80 => x = 4
Their present ages are 16, 28 and 36 years respectively.
Answer: (B) 16, 28, 36
Question: The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is?
(A) 52:56
(B) 52:53
(C) 52:28
(D) 52:19
(E) 52:20
Rationale: Let C.P. of the article be Rs. x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53
=52:53
Answer: B
Answer: (B) 52:53
Question: A van takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 50 Kmph
(B) 60 Kmph
(C) 70 Kmph
(D) 80 Kmph
(E) 90 Kmph
Rationale: Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
B
Answer: (B) 60 Kmph
Question: Which of the following is the product of two integers whose sum is 15?
(A)  -42
(B)  -28
(C)  12
(D)  26
(E)  32
Rationale: I solved this Question like this,
Let the two integers are x,y
x+y=15 (Given)
xy=? (Needed)
instead of solving this algebraically, Test the Answer choices
D. 26
Do the factorization : (1,26)----> There sum is not 15--eliminate
(2.13)---->There sum is 15 Bingo!!!!
So, my answer is D...
As the answer is in D, it took me very less time to answer the question. but i think this method is be simple and efficient.
Answer: (D)  26
Question: In the quiet town ofNothintodothere are 600 inhabitants, 200 are unemployed and 300 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?
(A) 50.
(B) 100.
(C) 150.
(D) 250.
(E) 300.
Rationale: Total = 600
unemployed=200
employed=600-200=400
som=300
unemployed som = 300/2=150
employed som = 150
employed that are not som = 400-150=250
Answer :D
Answer: (D) 250.
Question: The ratio of the adjacent angles of a parallelogram is 8 : 10. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?
(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) 164°
Rationale: The measures of the adjacent angles of a parallelogram add up to be 180°
Given
So, 8x + 10x = 180°
Or, 18x = 180°
Or, x = 10°
Hence the angles of the parallelogram are 80° and 100°
Further it is given
We know sum of all the four angles of a quadrilateral is 360°
So, 5y + 6y + 7y + 12 y = 360°
Or, 5y + 6y + 7y + 12 y = 360°
Or, 30y = 360°
Or, y = 12°
Hence the angles of the quadrilateral are 60° , 72, 84° and 144°
Will be 80° + 84° = 164°
Answer : E
Answer: (E) 164°
Question: 617 x 617 + 583 x 583=?
(A) 720578
(B) 80578
(C) 80698
(D) 81268
(E) None of them
Rationale: =(617)^2 + (583)^2
=(600+17)^2 + (600-17)^2
=2[(600)^2+(17)^2]
=2[360000+289]
=2 x 360289 = 720578
Answer is A
Answer: (A) 720578
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
(A) Rs.9689
(B) Rs.9678
(C) Rs.9688
(D) Rs.9678
(E) Rs.9680
Rationale: A= P{1 + R/100}n
=> 8000{1 + 10/100}2 = Rs.9680
Answer:E
Answer: (E) Rs.9680
Question: 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?
(A) 1:2
(B) 2:1
(C) 2:3
(D) 6:5
(E) 5:6
Rationale: 7M + 6B ------- 5 days
20M + 48B = 35M + 30B
18B = 15M => 5M = 6B
M: B = 6:5
ANSWER D
Answer: (D) 6:5
Question: Both Robert and Alice leave from the same location at 7:00 a.m. driving in the same direction, but in separate cars. Robert drives 50 miles per hour while Alice drives 80 miles per hour. After 5 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car?
(A) 2 p.m.
(B) 3 p.m.
(C) 4 p.m.
(D) 8 p.m.
(E) 9 p.m.
Rationale: 7:00 am so 4 hours later is 11:00 am
In five hours, Robert will have driven 5*50 = 250 miles
In five hours, Alive will have driven 5*80 = 400 miles
So Robert needs 400-250 = 150 miles do catch Alice up.
So at 50 mph, he will need 3 hours
11:00 am + 3 hours = 2:00 pm
ANS : A
Answer: (A) 2 p.m.
Question: In a game, a player can win by getting 3 consecutive tails in four throws of a coin. What is the probability of winning if the player gets a tail on the first throw?
(A) 1/4
(B) 3/4
(C) 1/2
(D) 3/8
(E) 5/8
Rationale: The only way to win is to get a tail on each of the next two throws.
P(two tails)=(1/2)^2=1/4
The answer is A.
Answer: (A) 1/4
Question: Two trains each of which is 100 m long moving in opposite direction to one another cross each other taking 8 seconds. If speed of one train is twice the speed of other
train find the speed of the faster train.
(A) 60 km/hr
(B) 76 km/hr
(C) 98 km/hr
(D) 9 km/hr
(E) 77 km/hr
Rationale: Explanation:
No explanation is available for this question!
ANSWER:A
Answer: (A) 60 km/hr
Question: Into a room you store 38 black bottles and 4 green bottles, and you turn off the light. If you ask to someone look for 2 bottles without turn on the light, what is the probability of both the selected bottles will be green?
(A)  1/574
(B)  2/574
(C)  1/287
(D)  2/287
(E)  3/287
Rationale: There are 4 green bottles in a group of 38 + 4 that is 42. Thus the probability of picking 2 green bottles is: (4/42)(3/41) = 2/287. The correct answer is D.
Answer: (D)  2/287
Question: What is the probability that Company G's advertisement will be one of the first two be shown during the first commercial break?
(A)  1/ 225
(B)  1 / 30
(C)  1 /15
(D)  2 / 15
(E)  4 /15
Rationale: G 1/15 + (14/15) * 1/14 = 2/15 D
Answer: (D)  2 / 15
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B's age = 2x = 10 years.
Answer: Option D
Answer: (D) 10
Question: A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
(A) 24 days
(B) 48 days
(C) 22 days
(D) 77 days
(E) 55 days
Rationale: B = 1/16 – 1/24 = 1/48
=> 48 days
Answer:B
Answer: (B) 48 days
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs.When the smaller wheel has made 21 revolutions,then the number of revolutions made by the larger wheel is :
(A) 4
(B) 9
(C) 12
(D) 49
(E) 59
Rationale: Solution
Let the required number of revolutions made by larger wheel be x.
Then. More cogs, Less revolutions (Indirect Proporation)
∴ 14: 6 :: 21 : x ⇔ 14 × x = 6 × 21 ⇔ x = (6x21/14)=9. Answer B
Answer: (B) 9
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
(A) 10
(B) 18
(C) 20
(D) 25
(E) 30
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
ANSWER B
Answer: (B) 18
Question: If the Average of 10 consecutive integers is 21.5 then the 10th integer is :-
(A) 15
(B) 20
(C) 23
(D) 26
(E) 25
Rationale: The average falls between the 5th and 6th integers,
integer 5 = 21, integer 6 = 22.
Counting up to the tenth integer
we get 26.
ANSWER:D
Answer: (D) 26
Question: A car is bought for Rs.60000/- and sold at a loss of 30% find its selling price?
(A) s.45400/-
(B) s.40000/-
(C) s.48080/-
(D) s.45590/-
(E) s.42000/-
Rationale: 100 % ------> 60000 (100 * 600 = 60000)
70 % ------> 42000 (70 * 600 = 42000)
Selling price = Rs.42000/-
Option 'E'
Answer: (E) s.42000/-
Question: The current in a river is 3 mph. A boat can travel 21 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?
(A) 69 miles
(B) 88 miles
(C) 96 miles
(D) 102.8 miles
(E) 112 miles
Rationale: Upstream Speed = 21-3=18mph
Downstream Speed = 21+3 = 24 mph
D/18 + D/24 = 10 hours
Solving for D we get D=102.8
Answer: D
Answer: (D) 102.8 miles
Question: Solve below question 2x + 1 = -23
(A) -8
(B) -9
(C) -12
(D) -4
(E) 12
Rationale: 1. Subtract 1 from both sides: 2x + 1 - 1 = -23 - 1 2. Simplify both sides: 2x = -24 3. Divide both sides by 2: 4. Simplify both sides: x = -12 C
Answer: (C) -12
Question: From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 11 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: Soln:-
11x=45 --> 10/9*x=45 --> x=45*9/10=1500/37=~41.
Answer: D.
Answer: (D) 41
Question: What is the probability that when a hand of 5 cards is drawn from a well shuffled deck of 52 cards,
it contains all Queens?
(A) 192/3790
(B) 192/379015
(C) 193
(D) Cannot be determined
(E) None
Rationale: nCr = n!/(n-r)!r!
Total number of possible hands = 52C5
52C5 = 2274090
Number of hands with 4 Queens = 4C4 × 48C1
4C4 = 24
48C1 = 48
(other 1 card must be chosen from the rest 48 cards)
Hence P (a hand will have 4 Queens) = (4C4 × 48C1)/52C5 = 192/379015.
Option is B
Answer: (B) 192/379015
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
(A) 7 : 3
(B) 7 : 4
(C) 7 : 5
(D) 7 : 65
(E) 7 : 9
Rationale: Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40
x = 20.
Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.
Answer:A
Answer: (A) 7 : 3
Question: The product of ages of Harshit and Haritika is 240. If Hritika would have been twice her age she will be 4 years elder to Harshit. What is Haritika's age now?
(A) 16 yrs
(B) 24 years
(C) 12 years
(D) 10 years
(E) 15 years
Rationale: x*y=240
2y=x+4
(2y-4)=x
2y^2-4y-240=0
y=12 years
ANSWER:C
Answer: (C) 12 years
Question: A bag consists of 20 marbles, of which 6 are blue, 9 are red, and the remainder are white. If Lisa is to select a marble from the bag at random, what is the probability that the marble will be red or white?
(A) 7/10
(B) 2/4
(C) 1/4
(D) 1/8
(E) 1/16
Rationale: bag consists of 20 marbles, of which 6 are blue, 9 are red
remainder are white. So, white = 20 - 6 - 9 = 5.
probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white
probability that the marble will be red or white = 9/20+5/20 = 14/20 = 7/10
Hence, answer will be A.
Answer: (A) 7/10
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 766 m
(B) 156 m
(C) 245 m
(D) 156 m
(E) 156 m
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2
==> 2(130 + X) = 750 ==> X
= 245 m.
Answer: C
Answer: (C) 245 m
Question: How many integers are there between 35 and 108, inclusive?
(A) 51
(B) 55
(C) 56
(D) 57
(E) 74
Rationale: I guess the easiest way to answer this is -
Say you have two positive integers, x and y where y > x
Then the number of integers between x and y is given by - (y - x) + 1
In this case, it's (108 - 35) + 1 =74. Option E
Answer: (E) 74
Question: On one side of a coin there is the number 0 and on the other side the number 1. What is the probability that the sum of three coin tosses will be 0 if a 1 is the value of the first coin flip?
(A) 0/8.
(B) 1/2.
(C) 1/5.
(D) 3/8.
(E) 1/3.
Rationale: Assume the coin is unbiased.
Possible sums from 3 tosses = 0,1,2,3
O and 3 are possible in only 1 case each. (0,0,0 or 1,1,1)
1 is possible in 3C1 = 3 cases. (1,0,0; 0,1,0 or 0,0,1) or
similarly, 2 is possible in 3C2=3 cases (1,0,1; 1,1,0; 0,1,1)
So answer will be 0/8. Option A.
Its impossible to get a total value of 0 if a 1 has been showed
Answer: (A) 0/8.
Question: In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?
(A) 11
(B) 22
(C) 99
(D) 121
(E) 171
Rationale: Just assume y=11 and C=99
Then C=198 and Y=132
So Y increases by 121
ANSWER:D
Answer: (D) 121
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 20 kg. What is the weight of the new person?
(A) 75
(B) 65
(C) 85
(D) 40
(E) 80
Rationale: Total increase in weight = 8 × 2.5 = 20
If x is the weight of the new person, total increase in weight = x−20
=> 20 = x - 20
=> x = 20 + 20= 40
Answer is D.
Answer: (D) 40
Question: How much interest can a person get on Rs. 8200 at 17.5% p.a. simple interest for a period of two years and six months?
(A) 3587.58
(B) 3587.52
(C) 3587.5
(D) 3587.59
(E) 3582.52
Rationale: I = (8200 * 2.5 * 17.5)/100 = (8200 * 5 * 35)/(100 * 2 * 2) = Rs. 3587.50.Answer: C
Answer: (C) 3587.5
Question: A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $350 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: The smallest amount that the company can spend is the LCM of 350 and 200, which is 1400 for each, which is total 2800.
The number of 1st type of computers which costing $350 = 1400/350 = 4.
The number of 2nd type of computers which costing $200 = 1400/200 = 7.
Total = 4+7 = 11
Answer is C.
Answer: (C) 11
Question: Which of the following equations is NOT equivalent to 4x^2 = a^2 - 9 ?
(A)  4x^2 + 9 = a^2
(B)  4x^2 - a^2 = -9
(C)  4x^2= (a + 3)(a - 3)
(D)  2x = a - 3
(E) x^2 = (a^2-9)/4
Rationale: 4X^2 = a^2 - 9
The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.
Looking at Answer D, we have....
2X = a - 3
While you COULD take the square root of both sides of the original equation, it's important to note that the square root of a^2 - 9 is NOT (a-3).
a^2 - 9 can be factored into (a-3)(a+3), but neither of these parentheses is the square root of a^2 - 9.
You can see the proof when you square either of the two parentheses:
(a-3)^2 = a^2 - 6X + 9
(a+3)^2 = a^2 + 6x + 9
Thus, D is NOT equivalent to the prompt.
Answer: (D)  2x = a - 3
Question: The table shows the number of calls received by each of five operators during each of 5 one-hour periods. For which operator was the standard deviation of the numbers of calls received during these 5 periods the least?
(A) Operator A: 3, 7, 7, 3, 4
(B) Operator B: 4, 5, 5, 6, 5
(C) Operator C: 8, 2, 5, 5, 6
(D) Operator D: 6, 4, 4, 6, 6
(E) Operator E: 3, 4, 5, 8, 7
Rationale: A
it has 2 numbers right at the average, A has none.
Answer: (A) Operator A: 3, 7, 7, 3, 4
Question: 9.6 , 9.8 , 9.9 , 9.9 , 10.0 , 10.1 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.255 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
(A) 90%
(B) 75%
(C) 80%
(D) 85%
(E) 70%
Rationale: Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.255; 10+0.255} = {9.745; 10.255}.
From the 8 listed numbers, 6 are within this range so 6/8=75%.
Answer: B.
Answer: (B) 75%
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?
(A) 10
(B) 5
(C) 8
(D) 6
(E) 11
Rationale: C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25 => x = 5
Hence, B's age = 2x = 10 years.
ANSWER A
Answer: (A) 10
Question: The population of a town is 1,76,400 . If it increases at the rate of 5% per year, what will be its population 2 years hence ? What was it 2 years ago ?
(A) 140000
(B) 180000
(C) 160000
(D) 200000
(E) None of them
Rationale: Population after 2 years = 176400*[1+(5/100)]^2
=[176400*(21/20)*(21/40)]
= 194481.
Population 2 years ago = 176400/[1+(5/100)]^2
=[716400*(20/21)*(20/21)]= 160000.
Answer is C.
Answer: (C) 160000
Question: An aeroplane covers a certain distance at a speed of 150 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
(A) 1300 kmph
(B) 160 kmph
(C) 180 kmph
(D) 1080 kmph
(E) none
Rationale: Explanation: Distance = (150 x 2) = 300 km.
Speed = Distance/Time
Speed = 300/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = 300 x 3/5 km/hr = 180 km/hr.
Answer: Option C
Answer: (C) 180 kmph
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
(A) 7
(B) 8
(C) 6
(D) 5
(E) 1
Rationale: Explanation:
1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
Answer:B
Answer: (B) 8
Question: Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.2 a meter?
(A) 201
(B) 132
(C) 772
(D) 592
(E) 261
Rationale: 2 * 22/7 * 16 = 100.5
100.5 * 2 = Rs.201
Answer: A
Answer: (A) 201
Question: A computer wholesaler sells ten different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display?
(A) 15/56
(B) 3/28
(C) 1/28
(D) 1/15
(E) 1/168
Rationale: Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 8 avilable. so 8C1 is the numerator.
Total no of ways we can choose 3 from 10 is 10c3, which is the denominator.
So, the probability: 8c1/10c3= 1/15 ans is D.
Answer: (D) 1/15
Question: On a Saturday night, each of the rooms at a certain motel was rented for either $50 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $50, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent the motel actually charged for that night ?
(A)  $400
(B)  $800
(C)  $1,000
(D)  $1,600
(E)  $2,400
Rationale: Let total rent the motel charge for all rooms =x
If 10 rooms that were rented for 60 $ had instead been rented for 50 $,
then total difference in prices = 10 $ * 10 = 100 $
Total rent the motel charged would have been reduced by 25 %
.25x = 100
=> x= 400
Answer A
Answer: (A)  $400
Question: In how many ways a committee consisting of 3 men and 2 women can be formed from 9 men and 3 women?
(A) A)252
(B) B)15
(C) C)20
(D) D)18
(E) E)21
Rationale: Required number of ways = 9C3*3C2 = 84*3 = 252
Answer is A
Answer: (A) A)252
Question: In a survey about potential presidential candidates A and B, 32% of the public like A and 50% like B. If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that like neither?
(A) 27.5 %
(B) 35.5 %
(C) 39.5 %
(D) 22%
(E) 67%
Rationale: Let x be the percentage of people who like both.
Then the percentage of people who like only 1 but not both is 2x.
32% + 50% = 2x + 2(x) because the percentage who like both are counted twice.
Then x = 20.5% and 2x = 41%
100% = 20.5% + 41% + Neither
Neither = 39.5%
The answer is C.
Answer: (C) 39.5 %