mathewhe/aqua_rat huggingface dataset:
Question: A number, y is chosen at random from the set of positive integers from 1 to 9. What is the probability that (9/y) > y?
(A)  2/9
(B)  1/9
(C)  1/3
(D)  2/3
(E)  7/9
Rationale: Number x has to be chosen from numbers 1-9
(9/y) > y
=> 9 > y^2
=>y^2 - 9 < 0
y can have 2 values only 1 , 2
Therefore , probability = 2 / 9
Answer A
Answer: (A)  2/9
Question: Find the area of a parallelogram with base 24 cm and height 10 cm?
(A) 240 cm2
(B) 384 cm2
(C) 279 cm2
(D) 200 cm2
(E) 297 cm2
Rationale: Area of a parallelogram
= base * height
= 24 * 10 = 240 cm2
Answer:A
Answer: (A) 240 cm2
Question: What is the 21th digit to the right of the decimal point in the decimal expansion of 1/37?
(A)  0
(B)  2
(C)  4
(D)  7
(E)  9
Rationale: 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (3rd, 6th, 9th, ...) to the right of the decimal point is 7, thus 21st digit to the right of the decimal point is also 7.
Answer: D.
Answer: (D)  7
Question: Let f(x) = ax2 - b|x|, where a and b are constant. Then at x =0, f(x) is
(A) maximized whenever a>0, b>0
(B) maximized whenever a>0, b<0
(C) minimized whenever a>0, b>0
(D) minimized whenever a>0, b<0
(E) None of these
Rationale: Explanation :
When a > 0, b < 0, ax2 and –b |x| are non negative for all x.
i.e. ax2 – b|x| ≥ 0.
∴ ax2 – b |x| is minimum at x = 0 when a > 0, b < 0.
Answer : D
Answer: (D) minimized whenever a>0, b<0
Question: In a certain game, you perform three tasks. You flip a coin, and success would be heads. You roll a single dice, and success would be a point. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
(A) 11/16
(B) 15/32
(C) 23/48
(D) 14/36
(E) 17/56
Rationale: The answer is C
Probability of just one enent will be happining
So, Probability heads=1/2
Probability number point =1/6
Probability picking a spades card =1/4
so, Probability win by getting tails= 1/2*5/6*3/4 = 15/48
Probability win by getting number 6 = 1/2*1/6*3/4 = 3/48
Probability win by picking a spades card =1/2*5/6*1/4=5/48
Probability wining= 15/48+3/48+5/48 =23/48
Answer: (C) 23/48
Question: Ragu purchased a refrigerator and a mobile phone for Rs. 20000 and Rs. 10000 respectively. He sold the refrigerator at a loss of 5 percent and the mobile phone at a profit of 10 percent. Overall he make a.
(A) loss of Rs. 200
(B) loss of Rs. 100
(C) profit of Rs. 100
(D) profit of Rs. 200
(E) No loss No gain
Rationale: Total C.P. = 20000+10000 = 30000
S.P. of refrigerator = 20000/100*95= 19000
S.P. of Mobile = 10000/100*110 = 11000
Total S.P. = 19000 + 11000 = 30000
Tota. C.P. - Total S.P. = 30000 - 30000 = 0
No Loss No gain
Answer : E
Answer: (E) No loss No gain
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
(A) 83.3%
(B) 12%
(C) 18%
(D) 9%
(E) 6%
Rationale: Explanation:
Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.
Correct Option : A
Answer: (A) 83.3%
Question: A man can row a boat at 32 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 96 km downstream?
(A) 12/4
(B) 12/5
(C) 12/6
(D) 12/7
(E) 12/8
Rationale: Speed downstream = 32+8=40 kmph.
Time required to cover 60 km downstream = d/s = 96/40 = 12/5 hours. Answer:B
Answer: (B) 12/5
Question: If all the sides of a right triangle increase in length by 8%, then by what percentage does the area of the triangle increase?
(A) 8%
(B) 16.64%
(C) 24.32%
(D) 32.84%
(E) 36.16%
Rationale: Let B be the base and H be the height of the original triangle.
The original area is (1/2)BH.
The area of the expanded triangle is (1/2)(1.08B)(1.08H) = (1.08)(1.08)(1/2)BH = 1.1664(1/2)BH
The answer is B.
Answer: (B) 16.64%
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45%
(B) 56%
(C) 57%
(D) 70%
(E) 72%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: (C) 57%
Question: A shopkeeper cheats to the extent of 10% while buying and selling, by using false weights. His total gain is.
(A) 22
(B) 21
(C) 8
(D) 9
(E) 81
Rationale: Answer: B) 21%
Answer: (B) 21
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) 4538
(B) 2778
(C) 2608
(D) 4530
(E) 2001
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530
Answer:D
Answer: (D) 4530
Question: 3500 – (1000 ÷ 20.50) is equal to :
(A) 3451.21
(B) 3029.0
(C) 2993.03
(D) 2984.36
(E) None of these
Rationale: Explanation:
Given exp. = 3500 - ((1000 ÷ 2050) * 100)
= 3451.21
ANSWER A
Answer: (A) 3451.21
Question: If two balls are randomly selected from a green urn containing 6 black and 6 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?
(A) A.2/9
(B) B.4/9
(C) C.5/9
(D) D.1/3
(E) E.5/22
Rationale: To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white.
Probability (first ball is white) = 6/12
Probability(second ball is white) = 5/11
Probability (both balls are white) = (6/12)*(5/11) = 5/22
Answer E
Answer: (E) E.5/22
Question: In a system of coding ACCESS is coded CEEGUU, POINTFF as HHKPQRV, LIMERICK as EGKKMNOT and LAMINATE as CCGKNOPV
Waht is likely to be the word of which the code is COTUV?
(A) TRAPS
(B) PARTS
(C) SMART
(D) SMARR
(E) None of the above
Rationale: right answer is EQVWX
SO NONE
ANSWER:E
Answer: (E) None of the above
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) 1 kmph
(B) 9 kmph
(C) 6 kmph
(D) 8 kmph
(E) 2 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: (A) 1 kmph
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
(A) 29%
(B) 25%
(C) 11%
(D) 20%
(E) 15%
Rationale: 800 --- 200
100 --- ? => 25%
Answer: B
Answer: (B) 25%
Question: The banker’s discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is :
(A) 2 months
(B) 4 months
(C) 6 months
(D) 7 months
(E) None
Rationale: Sol.
S.I. on Rs. 1600 = R.D. on Rs. 1680.
∴ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 15%.
∴ Time = [100 * 80 / 1600 * 15] year = 1/3 year = 4 months.
Answer B
Answer: (B) 4 months
Question: Simplfy
b - [b -(a+b) - {b - (b - a+b)} + 3a]
(A) -a
(B) 2a
(C) 4a
(D) 0
(E) 1
Rationale: Explanation:
b-[b-(a+b)-{b-(b-a+b)}+3a]
=b-[b-a-b-{b-(2b-a)}+3a]
=b-[-a-{b-2b+a}+3a]
=b-[-a-{-b+a}+3a]
=b-[-a+b-a+3a]
=b-[-2a+b+3a]
=b-b-a
=-a
Option A
Answer: (A) -a
Question: If a × b = 2a - 3b + ab, then 3 × 5 + 5 × 3 is equal to :
(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: Explanation:
3 × 5 + 5 × 3 = (2 × 3 - 3 × 5 + 3 × 5) + ( 2 × 5 - 3 × 3 + 5 × 3)
= (6 + 10 - 9 + 15) = 22.
Answer: A
Answer: (A) 22
Question: If A,BCD is a four-digit positive integer such that A,BCD is equal to the product of the two-digit number AB and the three digit number ABC, which of the following two-digit numbers cannot be a factor of A,BCD? (Note: the first digit of a number cannot be equal to 0.)
I. AD
II. CD
III. CA
(A) None
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: Ideally, ABC * AB = ABCD should make you think of 1s and 0s. The digits needn't be unique so the first thing that comes to mind is 100*10 = 1000. But since CA and CD are given as two digit numbers, next you should think of 101*10 = 1010 or any such number. This satisfies all conditions so we can analyse using this example.
101 * 10 = 1010
AD = 10 - a factor of 1010
CD = 10 - a factor of 1010
CA = 11 - not a factor of 1010
Now the only thing left to figure is whether it is possible that C1 is a factor of 10C0 for some value of C.
10C0 = 1000 + C0 = 999 + C1
C1 is divisible by C1 but we don't know whether 999 is divisible by C1.
999 = 3^3*37
It has no two digit factor ending in 1 so it will not be divisible by C1.
Answer (C)
Answer: (C) III only
Question: If the cost price of 50 articles is equal to the selling price of 45 articles, then the gain or loss percent is?
(A) 11.11
(B) 65
(C) 78
(D) 33
(E) 25
Rationale: Given that, cost price of 50 article is equal to selling price of 45 articles.
Let cost price of one article = Rs. 1
Selling price of 45 articles = Rs. 50
But Cost price of 45 articles = Rs. 45
Therefore, the trader made profit.\Percentage of profit = 5/45 * 100 = 11.11%
Answer:A
Answer: (A) 11.11
Question: The mass of the sun is approximately 2 × 10^20 kg and the mass of the moon is approximately 8 × 10^12 kg. The mass of the sun is approximately how many times the mass of the moon?
(A) 4.0 × 10^(−18)
(B) 2.5 × 10^17
(C) 2.5 × 10^7
(D) 2.5 × 10^19
(E) 4.0 × 10^42
Rationale: Mass of sun = x * Mass of moon
x = Mass of sun / Mass of moon = (2 × 10^20) / (8 × 10^12) = 2*2^-3*10^8 = 10^8/4 = 2.5*10^7
Ans. C) 2.5 × 10^7
Answer: (C) 2.5 × 10^7
Question: If seven machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job?
(A) 45
(B) 60
(C) 75
(D) 84
(E) 100
Rationale: using the std formula
m1d1h1/w1=m2d2h2/w2
substituting the values we have
7*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2)
14/3=10/3*x
x=7/5 hour
so 84 minutes
ANSWER:D
Answer: (D) 84
Question: 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 160kg then find the average weight of all the 7 rounds?
(A) 91.4 kgs
(B) 88.5 kgs
(C) 86.5 kgs
(D) 67.5 kgs
(E) 88.2 kgs
Rationale: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 160/7 = 91.4kgs
Answer:A
Answer: (A) 91.4 kgs
Question: The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
(A) 1: 5
(B) 1: 6
(C) 1: 9
(D) 1: 3
(E) 1: 2
Rationale: r1: r2 = 1: 3
Πr12: Πr22
r12: r22 = 1: 9
Answer: C
Answer: (C) 1: 9
Question: The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?
(A) A)Rs.4050
(B) B)Rs.4000
(C) C)Rs.4029
(D) D)Rs.4027
(E) E)Rs.4020
Rationale: Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 * 2) = 10200 --- (i)
Q + R = (6250 * 2) = 12500 --- (ii)
P + R = (5200 * 2) = 10400 --- (iii)
Adding (i), (ii) and (iii), we get:
2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv)
Subtracting (ii) from (iv), we get, P = 4050.
P's monthly income = Rs.4050.
Answer: A
Answer: (A) A)Rs.4050
Question: The total weight of nine nougat nuggets is 7 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
(A) 0.18 oz.
(B) 0.5 oz.
(C) 1.8 oz.
(D) 0.77 oz.
(E) 18 oz
Rationale: Average = Total/Number of items
= 7/9 = 0.77.
Hence, D
Answer: (D) 0.77 oz.
Question: If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 6 II. 7 III. 3
(A) II only
(B) I only
(C) I,II only
(D) II,III only
(E) III only
Rationale: We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....
Let's TEST VALUES....
IF we use the 6 consecutive integers: 8,9,10,11,12 and 13, then the sum = 63.
63 is divisible by 3
63 is NOT divisible by 6
63 is NOT divisible by 7
There's only one answer that 'fits' with these facts. Answer : E
Answer: (E) III only
Question: If t>0, which of the following must be true?
(A) 1 < t
(B) 0 < t < 2
(C) -1 < t < 1
(D) -10 < t
(E) 1/100 < t
Rationale: All we know is that t is some positive number. Right away we can see that D must be true: if t is positive then it MUST be true that it's greater than -10. Still let's check each option.
A. 1 < t. We don't know whether the number is greater than 1, it could be a positive number less than or equal to 1. Discard.
B. 0 < t < 2. The same here: we don't know whether the number is less than 2, it could be more than or equal to 2. Discard.
C. -1 < t < 1. The same as A. Discard.
E. 1/100 < t. We don't know whether the number is greater than 1/100, it could be a positive number less than or equal to 1/100. Discard.
Answer: D.
Answer: (D) -10 < t
Question: X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 4. If X invested Rs.40,000. the amount invested by Y is
(A) Rs.45,000
(B) Rs.50,000
(C) Rs.60,000
(D) Rs.80,000
(E) None
Rationale: Solution
Suppose Y invested Rs.y
Then,	40000 /y = 2 / 4
â€¹=â€º y=(40000Ã—4 / 2).
â€¹=â€º y=80000.
Answer D
Answer: (D) Rs.80,000
Question: In an office, totally there are 800 employees and 25% of the total employees are males. 40% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
(A) 120
(B) 160
(C) 132
(D) 130
(E) None of these
Rationale: Number of male employees = 800 * 25/100 = 200
Required number of male employees who are less than 50 years old = 200* (100 - 40)%
= 200* 60/100 = 120.
ANSWER:A
Answer: (A) 120
Question: A man in a train travelling at 20km/hr notices that a train going in the opposite direction passes him in 5 sec.If the length of this train is 140m find its speed .
(A) 30 km/hr
(B) 40 km/hr
(C) 81 km/hr
(D) 60 km/hr
(E) 70 km/hr
Rationale: relative speed of trains = 140/5 mtrs/sec = 140*18/(5*5)= 101 km/hr
speed of 2nd train = 101-20=81 km/hr
ANSWER:C
Answer: (C) 81 km/hr
Question: If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)W of x, x^2, x^3, x^4 and x^5 is equal to which of the following?
(A) 12x
(B) 13x
(C) 14x
(D) 16x
(E) 20x
Rationale: 1 + x^4 + x^3 + x^2 + x = 81
i.e. 1 +x+ x^2+ x^3+ x^4 = 81
x+ x^2+ x^3+ x^4 = 80
x(1 +x+ x^2+ x^3) = 80
x(81-x^4) = 80
81x - x^5 = 80
x^5 = 81x -80
Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x
Average of W{x, x^2, x^3, x^4, x^5} = 81x/5 ~ 16x
AnswerD
Answer: (D) 16x
Question: A man took loan from a bank at the rate of 4 % p.a. S.I. After 10 years he had to pay Rs. 2000 interest only for the period. The principal amount borrowed by him was?
(A) 5000
(B) 4500
(C) 3200
(D) 6000
(E) 1592
Rationale: Principal = (100 * 2000) / (4 * 10)
= Rs.5000
Answer: A
Answer: (A) 5000
Question: A man can row a distance of 6 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 20 km in 10 hours. How much time he would have saved if the direction of tide has not changed?
(A) 2
(B) 8
(C) 1
(D) 6:41
(E) 5
Rationale: Explanation:
He covered 6 km in 1 hour , so he might cover 20 km in 3 hours 19 minutes.
But he took 10 hours.
He would have saved 10 â€“ 3 hours 19 minutes= 6 hours 41 minutes.
Answer: D
Answer: (D) 6:41
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
(A) 12002
(B) 12000
(C) 12028
(D) 12020
(E) 12013
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100)
= 600
X = 12000
Answer: B
Answer: (B) 12000
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 109.12 m.
(B) 104.12 m.
(C) 111.12 m.
(D) 211.12 m.
(E) 132.12 m.
Rationale: C
111.12 m.
A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer: (C) 111.12 m.
Question: List Z consists of 12 consecutive integers. If -4 is the least integer in list Z, what is the range of positive integers in list Z?
(A) 5
(B) 6
(C) 7
(D) 11
(E) 12
Rationale: Since -4 is the least integer in list Z, then 7 is the largest integer in that list. Thus the range of the positive integers in the list is 7-1=6.
Answer: B.
Answer: (B) 6
Question: An automotive test consisted of driving a car the same distance three separate times, first at an average rate of 40 miles per hour, then 50 miles per hour, then 60 miles per hour. If the test took 111 hours to complete, how many miles was the car driven during the entire test?
(A) 5100
(B) 5400
(C) 5500
(D) 5600
(E) 5300
Rationale: x is the segment to be traveled
x/40+x/50+x/60 =111
or 74x/1200 =111
x = 1800miles . total distance =3*1800 = 5400 miles
B
Answer: (B) 5400
Question: The y intercept of a line L is 8. If the slope of L is negative, which of the following could be the x intercept of L.
I. -1
II. 0
III. 6
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Rationale: C) III only
The y-intercept is 8. Therefore we have y=mx+8
It is given that the slope is negative. Therefore the line must go from top left to bottom right.
i.e: the x-intercept has to be positive. That itself rules out III.
If you choose to go with the options directly, here's an approach.
y=mx+8. For the x-intercept, y=0.
i.e. mx+8=0.
We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+8 =0 would never be satisfied.
If x=6, we have 6m+8=0. A value of m=-4/3 would satisfy this equation.(ANSWER C)
Answer: (C) III only
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets into it. The mass of the man is ?
(A) 77 kg
(B) 60 kg
(C) 77 kg
(D) 55 kg
(E) 47 kg
Rationale: In this type of question, first we will calculate the volume of water displaces then will multiply with the density of water.
Volume of water displaced = 3*2*0.01 = 0.06 m cube
Mass of Man = Volume of water displaced * Density of water
= 0.06 * 1000 = 60 kg
Answer: B
Answer: (B) 60 kg
Question: A larger cube has 8 cubic inch as a volume and in the cube there are 8 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 8 smaller cubes and the surface area of the larger cube, in square inch?
(A) 24
(B) 64
(C) 81
(D) 108
(E) 120
Rationale: Volume of larger cube = 8 = 2^3
Side of larger cube = 2
Volume of smaller cube = 1 --> Side of smaller cube = 1
Surface area of larger cube = 6 * 2^2 = 24
Surface area of 27 smaller cubes = 8 * 6 * 1 = 48
Difference = 48 - 24 = 24
Answer: A
Answer: (A) 24
Question: A certain club has 11 members, including Harry. One of the 11 members is to be chosen at random to be the president, one of the remaining 10 members is to be chosen at random to be the secretary, and one of the remaining 9 members is to be chosen at random to be the treasurer. What is the probability that Harry will either be the secretary or the member chosen to be the treasurer?
(A) 1/4
(B) 2/11
(C) 3/11
(D) 5/11
(E) 8/11
Rationale: Each member out of 11, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/11 and the probability that Harry will be selected to be the treasurer is also 1/11. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/11+1/11=2/11.
Answer: B.
Answer: (B) 2/11
Question: In how many ways can the letters of the word "PROBLEC" be rearranged to make 7 letter words such that none of the letters repeat?
(A) 4!
(B) 5!
(C) 7!
(D) 8!
(E) 9!
Rationale: There are seven positions to be filled.
The first position can be filled using any of the 7 letters contained in PROBLEM.
The second position can be filled by the remaining 6 letters as the letters should not repeat.
The third position can be filled by the remaining 5 letters only and so on.
758
Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! Ways.
C
Answer: (C) 7!
Question: Tub A and tub B contain 540 liters of water each. Every minute tub A loses 25 liters of water while tub B loses 15 liters. If in X minutes tub B will contain 6 times as much water as tub A, what is X?
(A) 15
(B) 20
(C) 25
(D) 30
(E) 40
Rationale: The equation is 6(540−25X)=540−15X from where X=20
Answer: B
Answer: (B) 20
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/7
(B) 17 1/6
(C) 17 1/7
(D) 17 1/1
(E) 17 1/2
Rationale: 1/20 + 1/30 - 1/40
= 7/120
120/7
= 17 1/7
Answer: C
Answer: (C) 17 1/7
Question: There are 35 students in a hostel. If the no. of students increases by 11, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) 238
(B) 240
(C) 242
(D) 245
(E) 280
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 11) = x – 1
or, 35x + 42 = 46x – 46
or, x = 8
Thus the original expenditure of the mess = 35 x 8 = Rs. 280
E
Answer: (E) 280
Question: Find the number which is nearest to 3105 and is exactly divisible by 21.
(A) 1208
(B) 3108
(C) 241
(D) 217
(E) 3147
Rationale: Sol. On dividing 3105 by 21, we get 18 as remainder.
Number to be added to 3105 = (21 - 18) - 3.
Hence, required number = 3105 + 3 = 3108.
Option B
Answer: (B) 3108
Question: Raj is working on a set of Data Sufficiency problems for his December GMAT: a geometry problem, an algebra problem, and a data interpretation problem. He has determined that statement 1 of the geometry problem is insufficient on its own, that both statement 1 and 2 of the algebra problem are insufficient on their own, and that statement 2 of the data interpretation problem is insufficient on its own. If the probabilities are expressed as percents Q, approximately how much greater is the probability that all three answers are “C” after Raj figures out that statement 1 of the data interpretation problem is also insufficient on its own?
(A) Q=2.3%
(B) Q=2.8%
(C) Q=3.3%
(D) Q=5.6%
(E) Q=8.3%
Rationale: Step 1: Figure out what we need to know.We have two probabilities that we need to figure out: the one before Raj figures out that statement 1 of the data interpretation problem is also insufficient, and the one after. The answer is the difference between them, in the form of a percent.
Step 2: The first probability.
If statement 1 of the geometry problem is insufficient, then the only valid answer choices are B, C, and E; the probability that it is C is 1/3.
If both statements of the algebra problem are insufficient on their own, then the only remaining valid answers are C and E; the probability that it is C is 1/2
If statement 2 of the data interpretation problem is insufficient, then the remaining answers are A, C, and E, and the probability that C is correct is 1/3.
The probability of all three occurring is the product of the probability fractions: (1/3)*(1/2)*(1/3) = 1/18.
Step 3: The second probability.
Only the third problem has changed; if Raj now knows that statement 1 is also insufficient, the valid answer choices are only C and E, leaving a 1/2 probability that the answer is C.
The probability of all three occurring is still the product of those fractions, but this time they are (1/3)*(1/2)*(1/2) = 1/12.
Step 4: The answer.Note that here, as will sometimes happen on the GMAT, values that you compute “along the way” appear as wrong answer choices. This problem calls for the difference between our two numbers,Q (1/12)-(1/18) = 1/36, which is a 2.77777% chance, rounded to 2.8% —the correct answer is Choice B.
Answer: (B) Q=2.8%