mathewhe/aqua_rat huggingface dataset:
Question: In a dairy farm, 45 cows eat 45 bags of husk in 45 days. In how many days one cow will eat one bag of husk ?
(A) 34 days
(B) 45 days
(C) 46 days
(D) 50 days
(E) None of these
Rationale: Explanation:
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
[Cows1 45
Bags 45 1]::45:x
=>x∗45∗1=45∗1∗45
=>x=45
Option B
Answer: (B) 45 days
Question: When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?
(A) 13
(B) 31
(C) 49
(D) 57
(E) 67
Rationale: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.
57 = 5 + 7 = 12--> 1 + 2 = 3
Answer: D
Answer: (D) 57
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 190 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10
(B) 99
(C) 77
(D) 55
(E) 65
Rationale: Speed of the boat in still water = (60+190)/2 = 125 kmph. Speed of the stream
= (190-60)/2
= 65 kmph.
Answer: E
Answer: (E) 65
Question: There are two lines in the neighbourhood supermarket. In the first line there are 2 people, one with 10 items in her cart and the other with 14 items. In the second line there are 3 people, one with 11 items, one with 12 items and one with 13 items. What is the probability of randomly picking 2 people (it doesn't matter from which line), whose combined number of items is 23?
(A) 1/10
(B) 1/5
(C) 2/5
(D) 6/25
(E) 16/25
Rationale: First line we have 10 and 14
Second line we have 11,12 and 13.....Total 5 possibilities..
We need to get total 23 , then we can take pairs of ( 10,13) and (11,12)
We have total 5 possibilities...when we take 10 as first choice 13 can be second choice out of remaining 4.
1/5 * 1/4 = 1/20...we take ( 10,13) or ( 13,10)....we get two different cases.. 1/20*2 = 1/10.
Similarly for (11,12)... we get 1/10.
Total 1/10+1/10 = 1/5.
Answer:B
Answer: (B) 1/5
Question: What is the greatest integer that will always evenly divide the sum of two consecutive even integers?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Rationale: Let the three consecutive even integers be 2x , 2x + 2
Sum = 2x + 2x + 2
= 4x+2 = 2(2x+1)
Therefore , 2 will always be a factor .
Answer A
Answer: (A) 2
Question: What will be the compound interest on a sum of Rs.25,000 after 3 years at the rate of 12 p.c.p.a?
(A) Rs.9000.30
(B) Rs. 9720
(C) Rs. 10123.20
(D) Rs. 10483.20
(E) None
Rationale: Solution
Amount	= Rs.(25000x(1+12/100)³
=Rs.(25000x28/25x28/25x28/25)
= Rs. 35123.20.
C.I	=Rs(35123.20-25000)
=Rs.10123.20.
Answer C
Answer: (C) Rs. 10123.20
Question: One bacterium splits into eight bacteria of the next generation. But due to environment, only 50% of one generation can produced the next generation. If the seventh generation number is 4096 million, what is the number in first generation?
(A) 1 million
(B) 2 million
(C) 4 million
(D) 8 million
(E) None of these
Rationale: Solution: Let the number of bacteria in the 1st generation be x, then number of bacteria in 2nd, 3rd, 4th . . . . . Generation would be
8(x/2), 8(4x/2), 8(16x/2) . . . . And so on.
As x, 4x, 16x, 64x . . . . . it is in GP with common ratio 4.
Hence, 7th term of GP,
x(4)6 = 4096
Or, x = 1 or 1 million.
Answer: Option A
Answer: (A) 1 million
Question: add 16% of 36 and 13% of 45.
(A) 9.5
(B) 8.5
(C) 7.2
(D) 7
(E) 8
Rationale: 16% of 36 + 13% of 45
36*16/100+45*13/100
5.8+1.4=7.2
answer C
Answer: (C) 7.2
Question: Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 200 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
(A) 250
(B) 300
(C) 350
(D) 400
(E) 500
Rationale: Nice problem. +1.
First timetogetherthey run half of the circumference.
Second timetogetherthey run full circumference.
First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.
Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 200 meters, thus the circumference is 200 + 200 = 400 meters.
Answer: D.
Answer: (D) 400
Question: In an election between two candidates first candidate got 60% of votes polled and second Candidate got 280 votes. The total number of votes polled was?
(A) 700 votes
(B) 800 votes
(C) 900 votes
(D) 980 votes
(E) 990 votes
Rationale: Total = 100 %,
First person got 60%
second person got remaining 40 % of votes.
than 40 % = 280
40% = 40×7 = 280
100% =100×7 =700 votes
A
Answer: (A) 700 votes
Question: A boatman can row 3 km against the stream in 20 minutes and return in 12 minutes. Find the rate of current ?
(A) 7/2 kmph
(B) 8/2 kmph
(C) 5/2 kmph
(D) 1/2 kmph
(E) 3 kmph
Rationale: Explanation:
Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.
Speed in downstream = 3 x 60/12 = 15 km/hr
Rate of current = (15-9)/2 = 3 km/hr.
Answer: E
Answer: (E) 3 kmph
Question: How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?
(A) 576
(B) 520
(C) 504
(D) 432
(E) 348
Rationale: A number not to be a multiple of 10 should not have the units digit of 0.
XXX
9 options for the first digit (from 1 to 9 inclusive).
8 options for the third digit (from 1 to 9 inclusive minus the one we used for the first digit).
8 options for the second digit (from 0 to 9 inclusive minus 2 digits we used for the first and the third digits)
9*8*8=576.
Answer: A.
Answer: (A) 576
Question: Find the value of 72519 x 9999 = m?
(A) 434365675
(B) 464687665
(C) 643432672
(D) 725117481
(E) 790023245
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 62.5. When one student dropped the class, the average of the remaining scores increased to 63.0. What is the quiz score of the student who dropped the class?
(A) a) 10
(B) b) 25
(C) c) 40
(D) d) 55
(E) e) 70
Rationale: Total Score of 16 students is 16*62.50 = 1000
Total Score of 15 students is 15*63 = 945
So, the score of the person who left is 55 ( 1000 - 945 )
Answer will be (D)
Answer: (D) d) 55
Question: Jones invested a certain sum of money in a simple interest bond whose value grew to $500 at the end of 3 years and to $ 800 at the end of another 4 years. What was the rate of interest in which he invested his sum?
(A) 12%
(B) 12.5%
(C) 16.67%
(D) 16.25%
(E) 18.18%
Rationale: Lets assume the Principal Amount (initial amount invested) to be P
rate of interest to beRand time as T. We need to find R
Now After a time of 3years the principal P amounts to $500 and after a time of 7years ( question says after another 7years so 3+4) P becomes $800.
Formulating the above data
Amount (A1) at end of 3years
A1= P(1 + 3R/100) = 500
Amount (A2) at end of 7years
A2 = P(1 + 7R/100) = 800
Dividing A2 by A1 we get
(1 + 7R/100)/(1 + 3R/100) = 8/7
after cross multiplication we are left with 11R =100*2 which gives R = 18.18%
Option: E
Answer: (E) 18.18%
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.238 where as B does not. In what ratio should they divide the second year's profit?
(A) 220:113
(B) 201:200
(C) 210:201
(D) 100:99
(E) 113:77
Rationale: Explanation:
3: 4
A = 3/7*238 = 102
402: 400
201:200
Answer:B
Answer: (B) 201:200
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $40,000?
(A) $38,796.
(B) $40,000
(C) $38,976.
(D) $39,679
(E) $36,796.
Rationale: Value in 1973 = 40000
Value in 1983 = 0.84*40000 = 33600
Value in 1993 = 1.16*33600 = $38976
Correct Option: C
Answer: (C) $38,976.
Question: In an election between two candidates - Lange and Sobel - 70% of the voters voted for Sobel. Of the election`s voters, 60% were male. If 35% of the female voters voted for Lange, what percentage of the male voters voted for Sobel?
(A) 14
(B) 16
(C) 26
(D) 44
(E) 65
Rationale: M F total
L 16 14 30
S 44 70
Tot 60 40 100
35% of 40 = 14 ------Female voters that means 16 male voted for L
so 60-16 = 44
D is correct
Answer: (D) 44
Question: A rectangular lawn 55m by 35m has two roads each 4m wide running in the middle of it. One parallel to the length and the other parallel to breadth. The cost of graveling the roads at 75 paise per sq meter is?
(A) rs.259
(B) rs.252
(C) rs.258
(D) rs.251
(E) rs.252
Rationale: area of cross roads = 55*4 + 35*4 - 4*4
= 344sq m
cost of graveling = 344 * (75/100)
= Rs. 258
Answer: C
Answer: (C) rs.258
Question: What is the probability that, when three twelve-sided dice are rolled, at least one 1 is rolled?
(A) 1/4
(B) 3/144
(C) 1331/1728
(D) 23/144
(E) 397/1728
Rationale: Odds of no 1's: (11/12)^3 = 1331/1728
So the probability of at least one 1 is (1 - 1331/1728) = 397/1728, so the answer is E.
Answer: (E) 397/1728
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 5 m, the volume of the box (in m3) is:
(A) 4940
(B) 5120
(C) 6420
(D) 8960
(E) 7960
Rationale: Clearly, l = (48 - 10)m = 38 m,
b = (36 -10)m = 26 m,
h = 8 m.
Volume of the box = (38 x 26 x 5) m3 = 4940 m3. Answer: Option A
Answer: (A) 4940
Question: Find the odd man out. 1, 4, 9, 17, 25, 36, 49
(A) 1
(B) 9
(C) 17
(D) 49
(E) 36
Rationale: Explanation :
The pattern is 1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2
But, instead of 4^2, 17 is given
Answer : Option C
Answer: (C) 17
Question: A train , having a length of 220 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
(A) 10 sec
(B) 12 sec
(C) 6 sec
(D) 4 sec
(E) 2 sec
Rationale: Explanation:
Distance = 220 m
Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 220/(110/6) = 12 s
Answer: Option B
Answer: (B) 12 sec
Question: In a box, there are 6 red, 2 blue and 3 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
(A) 6/11
(B) 8/21
(C) 3/7
(D) 9/22
(E) 10/21
Rationale: Explanation:
Total number of balls = (6 + 2 + 3) = 11
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 6.
P(E) = 6/11.
Answer: Option A
Answer: (A) 6/11
Question: On an order of 19 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
(A) 0.05%
(B) 0.5%
(C) 1%
(D) 5%
(E) 10%
Rationale: Clearly, the retailer gets 1 dozen out of 20 dozens free.
Equivalent discount = 1/20 * 100 = 5%.
Answer D) 5%
Answer: (D) 5%
Question: Today Mary’s father is four times as old as Mary. Ten years ago, he was 10 times as old. How old is Mary today?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Dad's age = 4M
10*(M-10) = 4M-10
6M = 90
M = 15
The answer is E.
Answer: (E) 15
Question: Vijay says that his weight is between 75kg and 85 kg. But his younger sister disagrees with Vijay and says that his weight is greater than 70kg but less than 80 kg. Vijay’s mother says that his weight cannot be greater than 78 kg. If all the three predictions are correct, what is the average of different probable weights of Vijay?
(A) 75
(B) 80
(C) 78.5
(D) 76.5
(E) None of these
Rationale: Explanation:
Vijay’s opinion: - 75 < Vijay’s age < 85
Sister’s opinion: - 72 < Vijay’s age < 82
Mother’s opinion: - Vijay’s age < 78
As all the above three conditions are true, the values satisfying them are 76 & 77.
Average value = (76 + 77)/ 2 = 76.5
ANSWER D
Answer: (D) 76.5
Question: If three sides of the triangle are 8 , 15 and F respectively then the how many values can F ?
(A) [A] 6
(B) [B] 7
(C) [C] 8
(D) [D]9
(E) [E] infinite number of values
Rationale: Needed: How many Values can F take
Concept: Sum of any two sides of a triangle is greater then the third side.
Case 1: 8+5 > F => F<13
Case 2: 5+F > 8 => F >3
Case 3: 8+F > 5 => F > -3 (Always true since F is one side of a Triangle)
Finally, 3 < F < 13. So, we can have infinite number of sides between 3 and 13.
Answer = E
PS: If question said F can take only integer value, the F = 9. Answer choice D.
Answer: (D) [D]9
Question: A cistern is normally filled in 10 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?
(A) 10 hours
(B) 20 hours
(C) 60 hours
(D) 40 hours
(E) 50 hours
Rationale: If leakage/hour=1/x, then 1/10 -1/x= 1/12, solving 1/x=1/60
So in 60 hours full cistern will be empty.
ANSWER:C
Answer: (C) 60 hours
Question: If xy=4, x/y=81, for positive numbers x and y, y=?
(A) 1/2
(B) 2
(C) 2/9
(D) 3
(E) 1/6
Rationale: Very easy question. 2 variables and 2 easy equations.
xy=4 ---> x=4/y - (i)
x/y=81 ---> replacing (i) here ---> 4/(y^2)=81 ---> y^2=4/81 ---> y=2/9 or -2/9
The question states that x and y are positive integers. Therefore, y=2/9 is the answer.
Answer C.
Answer: (C) 2/9
Question: Ajay bought 15 kg of dal at the rate of Rs 14.50 per kg and 10 kg at the rate of Rs 13 per kg. He mixed the two and sold the mixture at the rate of Rs 15 per kg. What was his total gain in this transaction ?
(A) 27.59
(B) 27.52
(C) 37.5
(D) 27.5
(E) 27.51
Rationale: Cost price of 25 kg = Rs. (15 x 14.50 + 10 x 13) = Rs. 347.50.
Sell price of 25 kg = Rs. (25 x 15) = Rs. 375.
profit = Rs. (375 — 347.50) = Rs. 27.50.
Answer: D) Rs 27.50
Answer: (D) 27.5
Question: There are 28 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
(A) 156
(B) 167
(C) 870
(D) 352
(E) 380
Rationale: The total number of stations = 30
From 30 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 3⁰P₂ ways.
30P₂ = 30 * 29
= 870.
Answer: C
Answer: (C) 870
Question: If Q is an odd number and the median of Q consecutive integers is 125, what is the largest of these integers?
(A) (Q - 1)/2 + 125
(B) Q/2 + 119
(C) Q/2 + 125
(D) (Q + 119)/2
(E) (Q + 125)/2
Rationale: Consider the easiest case, say Q=3, then;
Set = {124, 125, 126};
The largest integer = 126.
Now, plug Q=3 into the answers to see which yields 126. Only answer choice A works.Notice that we don't really need to plug for B, C, or E, since these options do not yield an integer value for any odd value of Q.
Answer: A.
Answer: (A) (Q - 1)/2 + 125
Question: The price of 3 tables and 4 chairs is Rs. 3300. With the same money one can buy 2 tables and 10 chairs. If one wants to buy 1 table and 1 chair, how much does he need to pay?
(A) 1075
(B) 1025
(C) 1000
(D) 1050
(E) 1100
Rationale: et price of a table = t
and price of a chair = c
3t + 4c = 3300 ---(Equation 1)
2t + 10c = 3300
=> t + 5c = 1650 ---(Equation 2)
(Equation 2) × 3 => 3t + 15c = 4950 ---(Equation 3)
(Equation 3) - (Equation 1) => 11c = 1650
=> c = 150
Substituting the value of c in equation 1, we get
3t + (4 × 150) = 3300
=> 3t = 3300 – 600 = 2700
=>t = 2700/3 = 900
Cost of 1 table and 1 chair = c + t = 150 + 900 = 1050
Answer is D.
Answer: (D) 1050
Question: Steve bought a total of 6 packages of pens, and each package contained either 3 or 7 pens. If exactly 4 of the packages Steve bought contained 7 pens, how many pens did Steve buy?
(A) 17
(B) 21
(C) 34
(D) 42
(E) 56
Rationale: Explanation:
If Steve bought 4 packages of 7 pens and 6 packages total, then he must have purchased 2 packages of 3 pens.
4(7) + 2(3) = 28 + 6 = 34
Answer : (C).
Answer: (C) 34
Question: Several litres of acid were drawn offa 54 litre vessel full of acid and an equal amount of water was added. Again the same volume of the mixture was drawn off and replaced by water. As a result, the vessel contained 24 litres of pure acid. How much of the acid was drawn off initially?
(A) 12 lts
(B) 16 lts
(C) 18 lts
(D) 24 lts
(E) 28 lts
Rationale: Suppose X litres of acid was drawn off initially.
Remaining acid in the 54 litre vessel full of acid.
=> (54 - x) litres and water added = x litres.
Now out of the 54 litres of mixture of acid and water x litres of mixture is drawn off.
=> quantity of acid drawn off =(54 - X/54 x X)
litres and quantity of water drawn off = X2/54
Now vessel contains [54 - X - (54 - X/54)X]
Thus, 54 - X - [54 - X/54]X = 24
=> X2 - 108X +1620 = 0
=> X = 80, 18
since 90 > 54 therefore X = 90 is ruled out
hence X = 18
ANSWER:C
Answer: (C) 18 lts
Question: Two pipes A and B can fill a tank in 15 min and 25 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
(A) 14 min 19 sec
(B) 14 min 42 sec
(C) 17 min 20 sec
(D) 14 min 40 sec
(E) 14 min 10 sec
Rationale: :
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/25
1/25 : 8/15 :: 1 ; x
x = 8/15 * 1 * 25 = 13 1/3 min = 13 min 20 sec.
The tank will be full in (4 min. + 13 min. 20 sec) = 17 min 20 sec.Answer: C
Answer: (C) 17 min 20 sec
Question: 2 cow’s and 10 goats are brought for Rs.1500. If the average price of a goat be Rs.70. What is the average price of a cow.
(A) 420
(B) 400
(C) 430
(D) 410
(E) 450
Rationale: Explanation:
Average price of a goat = Rs.70
total price of 8 goats = 10*70 = Rs.700
But total price of 2 cows and 8 goats = Rs. 1500
Total price of 2 cows is = 1500 - 700
= 800
Average price of a cow = 800/2
= Rs. 400
Answer: B
Answer: (B) 400
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
(A) 287 cm2
(B) 287 cm2
(C) 285 cm2
(D) 276 cm2
(E) 297 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm2
Answer:C
Answer: (C) 285 cm2
Question: The sum of two numbers is 66. Five times one number is equal to 6 times the other. The bigger of the two numbers is
(A) 10
(B) 12
(C) 14
(D) 36
(E) 60
Rationale: a:b 5:6
a+b=66
5x+6x=66
x=6
then two numbers are 30,36. The bigger number is 36
ANSWER:D
Answer: (D) 36
Question: If the sum of 1st n integers is 55 then what is n?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 9
Rationale: Description :
sum=n(n+1)/2
sum=55
n^2+n=55*2
n^2+n-110=0
(n-10)(n+11)=0
n=10,-11,neglect negative ans
answer =10
Answer D
Answer: (D) 10
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
(A) 360
(B) 60
(C) 300
(D) 180
(E) 240
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is ⁶P₄ = 6 * 5 * 4 * 3 = 360.
ANSWER:A
Answer: (A) 360
Question: Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/2 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity
(A) 1/2
(B) 2/3
(C) 3/4
(D) 4/5
(E) 5/6
Rationale: Because we see H willbring 1/3 of his booksto the new home --> try to pick a number that isdivisible by 3.
Before:
Assume H = 30 books
H = 1/2 M --> M = 60 books
After:
H' = 1/3H = 10 books
M' = 1/2M = 30 books
Total = 40 books
M' = 40 = 5/6*60
Ratio: 5/6
Ans: E
Answer: (E) 5/6
Question: If loga/b + logb/a = log (a + b), then:
(A) a + b = 1
(B) a - b = 1
(C) a = b
(D) a2 - b2 = 1
(E) none of these
Rationale: loga/b+ logb/a	= log (a + b)
log (a + b) = log((a/b)x(b/a))= log 1.
So, a + b = 1.
ANSWER:A
Answer: (A) a + b = 1
Question: Which of the following fractions is greater than 1/6?
(A) 1. 12/50
(B) 2. 3/11
(C) 3. 2/9
(D) 4. 4/17
(E) 5. 6/24
Rationale: 1. 12/50
12.5/50 = 1/4 thus 12/50 < 1/4
2. 3/11
3/12 = 1/4 thus 3/11 > 1/4
3. 2/9
2/8 = 1/4 thus 2/9 < 1/4
4. 4/17
4/16 = 1/4 thus 4/17 < 1/4
5. 6/24
6/24 = 1/4
E
Answer: (E) 5. 6/24
Question: There are 20 balls in a box: 11 balls are green, 6 are blue and 3 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a green ball is selected at random from the box?
(A) 1/13
(B) 10/18
(C) 3/13
(D) 5/13
(E) 6/13
Rationale: If 1 green and 1 blue ball are taken from the box, then there are 10 green, 5 blue and 3 white balls, a total of 18 balls. If one ball is selected at random, the probability that it is green is given by 10 / 18
Answer :B
Answer: (B) 10/18
Question: Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $10,000 and the marginal cost is $250, and the total cost is $16,000, what is the value of n?
(A)  10
(B)  24
(C)  60
(D)  70
(E)  85
Rationale: Total cost for n products = fixed cost for n products + n*marginal cost --> $16,000 = $10,000 + n * $250 --> n = 24.
Answer: B.
Answer: (B)  24
Question: In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is $560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is $1,290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?
(A) $130
(B) $220
(C) $190
(D) $200
(E) $150
Rationale: Let x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat.
4x + 4y + 2z = 560 :
9x + 9y + 6z = 1,290
3x + 3y + 2z = 430 : divide all terms of equation C by 3
x + y = 130 : subtract equation D from equation B
3(x + y) + 2z = 430 : equation D with factored terms.
3*130 + 2z = 430
z = 20 : solve for z
x + y + z = 130 + 20 = $150
correct answer E
Answer: (E) $150
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
(A) 07.30 p.m.
(B) 09.30 p.m.
(C) 08.30 p.m.
(D) 10.30 p.m.
(E) 11.30 p.m.
Rationale: D
10.30 p.m.
D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer: (D) 10.30 p.m.
Question: Solution X is 80% chemical A and 20% chemical B by volume. Solution Y is 50% chemical A and 50% chemical B by volume. If a mixture of X and Y is 68% chemical A, what percent of the mixture is Solution X?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%
Rationale: The volume of the mixture be X+Y.
0.8X +0.5Y=0.68(X+Y)
0.12X=0.18Y
X=3Y/2
X/(X+Y)=(3Y/2) / (5Y/2)=3/5=40%.
The answer is E.
Answer: (E) 40%
Question: If x^2=2x+2, then x^3 = ?
(A) 3x+2
(B) 4x-2
(C) 2x+1
(D) 2x-3
(E) 6x+4
Rationale: x^2 = 2x+2
x^3 = x*x^2 = x*(2x+2) = 2x^2 + 2x = 2(2x+2)+2x = 6x+4
The answer is E.
Answer: (E) 6x+4
Question: Sakshi can do a piece of work in 20 days .Tanya is 25% more efficient than Sakshi. the number of days taken by tanya to do the same piece of work is?
(A) 25days
(B) 45days
(C) 24days
(D) 16days
(E) 36days
Rationale: The ratio of times taken by Sakshi and Tanya=125:100=5:4.
suppose Tanya takes x days to do the work.
5:4::20:x
x=(4*20)/5
x=16 days
Tanya can do work in 16 days
Answer(D)
Answer: (D) 16days
Question: What is the sum of the different positive prime factors of 620?
(A) 17
(B) 24
(C) 38
(D) 47
(E) 62
Rationale: The prime factorization of 620
= 62 * 10
= 2*31 * 2*5
The sum of the different positive prime factors = 2+5+31 = 38
The answer is C.
Answer: (C) 38
Question: A right triangle is inscribed in a circle. The legs of the triangle have lengths 6 and 8. What is the diameter of the circle?
(A) 8
(B) 8π
(C) 9√3
(D) 10
(E) 12
Rationale: Property of a right triangle inscribed in a circle is that when an angle is made from diameter of the circle, it is a right triangle. Or if a right triangle is made inscribed in a circle, its its longest side is the diameter of the circle.
Hence diameter= (6^2+8^2)^1/2= 10
D is the answer
Answer: (D) 10
Question: 1000 men have provisions for 21 days. If 800 more men join them, for how many days will the provisions last now?
(A) 12.9
(B) 12.5
(C) 12.6
(D) 11.6
(E) 12.1
Rationale: 1000*21 = 1800*x
x = 11.6
Answer: D
Answer: (D) 11.6