mathewhe/aqua_rat huggingface dataset:
Question: One man adds 3 liters of water to 12 liters of milk and another 4 liters of water to 10 liters of milk. What is the ratio of the strengths of milk in 2 mixtures?
(A) 11:21
(B) 15:33
(C) 28:25
(D) 3:2
(E) 31:33
Rationale: Strength of milk in the mixture = Quantity of milk/total quantity of mixture
strength of milk in the 1st mixture = 12/15
strength of the milk 2nd mixture = 10/14
The ratio of their strengths = 12/15 : 10/14 = 28:25
Answer is C
Answer: (C) 28:25
Question: What is the units digit of (498) (915) (381) (756) (29)
(A) 0
(B) 1
(C) 2
(D) 5
(E) 6
Rationale: Just multiply the digits in the units place for each term and you will get the answer. It should be 0. you got a 5 as a unit digit and an even number term. so the multiplication of this will definitely yield a 0. Answer has to be 0.
I also tried it using the calculator and the answer is 2.
IMO C.
Answer: (C) 2
Question: In how many ways the letters of the word ENGINEERING can be arranged?
(A) 200002
(B) 262011
(C) 277200
(D) 216181
(E) 280161
Rationale: Total number of ways=(11!)/(3!*3!*2!*2!*1!)
=(11*10*9*8*7*6*5*4*3!)/(3!*3*2*2*2)
=277200 ways
Option C
Answer: (C) 277200
Question: Fence X is twice as long as fence Y, and fence Y is 1 feet shorter than fence Z. If 3 feet were added to each fence, which of the following must be true?
I) X is twice as long as Y.
II) Y is 1 feet shorter than Z.
III) X is longer than Z.
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I and II
Rationale: If X= 6
Y= 3
Z= 4
Then, after adding 3 feet to each:
X= 9
Y=6
Z=7
And the answer would be E, which is wrong.
D
Answer: (D) II and III
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor.
(A) 10
(B) 11
(C) 12
(D) 13
(E) 15
Rationale: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
C
Answer: (C) 12
Question: 120kg of an alloy A is mixed with 180 kg of alloy B. If alloy A has lead and tin in the ratio 2:3 and alloy B has tin and copper in the ratio 3:5, then the amount of tin in the new alloy is?
(A) 100.6kg
(B) 120.3kg
(C) 139.5kg
(D) 140.8kg
(E) 114.5kg
Rationale: Quantity of tin in 120kg of A = 120*3/5 = 72kg
Quantity of tin in 180kg of B = 180*3/8 = 67.5kg
Quantity of tin in the new alloy = 72+67.5 = 139.5kg
Answer is C
Answer: (C) 139.5kg
Question: 180,131,95,70,?
(A) 42
(B) 43
(C) 54
(D) 40
(E) 39
Rationale: 180 - 131 = 49 = 7^2
131 - 95 = 36 = 6^2
95 - 70 = 25 = 5^2
so we can write
70 - x = 16 = 4^2 , where x is the next number
x = 70 - 16 = 54
so the next number will be 54
ANSWER:C
Answer: (C) 54
Question: A plant manager must assign 6 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers?
(A) 24
(B) 27
(C) 33
(D) 45
(E) 54
Rationale: whatever : my take selecting team of 2 out of 10 to assign to the shifts =6C2 = 15 ways.
now 2 out of 10 means total of 3 group possible.
so putting them in shifts = counting methode: first, second, third, alt , alt
= 3*2*1 = 6
here alt and alt are the same: so 6/2 = 3 ways.
total ways of selecting = (selecting 2 out of 6)*arranging those teams in shifts
= 15*3 = 45
Ans: D
Answer: (D) 45
Question: The timing of a college is from 12 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
(A) 52 minutes
(B) 45 minutes
(C) 30 minutes
(D) 48 minutes
(E) 44 minutes
Rationale: Explanation:
Total time a student spends in college = 4 hours 20 minutes = 260 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (260 – 20)/5
= 48 minutes
ANSWER D
Answer: (D) 48 minutes
Question: Albert invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit ?
(A) Rs.8600
(B) Rs.8620
(C) Rs.8840
(D) Rs.8820
(E) None
Rationale: Solution
Amount	=Rs.[8000x(1+5/100)²]
= Rs.
[8000 x 21/20x21/20]
= Rs.8820.
Answer D
Answer: (D) Rs.8820
Question: If p+q=8z, then which of the following represents the average (arithmetic mean) of p, q, and z, in terms of z?
(A)  2z+1
(B)  3z
(C)  5z
(D)  z/3
(E)  3z/2
Rationale: Pick any number like P=12, Q=12 and Z= 3 so that P+Q=8Z, now then the arithmetic mean will be (12+12+3)/3=9. Now, just look at the answers and put the value of Z there.
(A) 2.3+1=7, no.
(B) 3.3=9, it can be the answer, lets check us the other options
(C) 5.3=15, no
(D) 3/3=1 no
(E) (3.3)/2=9/2, no
so the answer will be B..
Answer: (B)  3z
Question: How much space, in cubic units, is left vacant when maximum number of 6x6x6 cubes are fitted in a rectangular box measuring 12x18x14 ?
(A) 428
(B) 429
(C) 430
(D) 431
(E) 432
Rationale: No of cubes that can be accommodated in box = (12*18*14)/(6*6*6)
12*16 in numerator can be perfectly divided by 6*6 in denominator.
side with length 14 can't be perfectly divided by 6 and hence is the limiting factor. Closet multiple of 6 less that 14 is 12. so vacant area in cube =
=18*12*(14-12)
=18*12*2
=432
Ans - E
Answer: (E) 432
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
(A) Rs. 1(2/9)
(B) Rs. 2(2/9)
(C) Rs. 2(2/7)
(D) Rs. 3(2/5)
(E) Rs. 3(1/9)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: (B) Rs. 2(2/9)
Question: A bag contain 4 red , 6 yellow, 5 green balls, 3 balls are drawn randomly . What is the probability that the balls drawn contain exactly two green balls ?
(A) 5/11
(B) 4/11
(C) 6/11
(D) 7/11
(E) 8/11
Rationale: 2 green balls can be selected from 5 green balls and the remaining one ball select from
(15-5) = 10 balls in 8C1 ways
n(E) 5C2 X 8C1
=10 X 8 =80
So, P(E) = 80/220 =4/11
Answer is B
Answer: (B) 4/11
Question: A team of 6 cooks is chosen from 6 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?
(A) 140
(B) 320
(C) 275
(D) 700
(E) 840
Rationale: Only possible combinations are a team of 2M, 4 W or 3M,3W.
Possible ways to make a team of 2M,4W = 6C2 * 5C4 =15*5 =75
Possible ways to make a team of 3M,3W = 6C3* 5C3 = 20*10 = 200
Total possible ways = 75+200 = 275
Ans C it is.
Answer: (C) 275
Question: What percent of the different arrangements of the letters of the word ABACUS are those in which the vowels appear together?
(A) 10%
(B) 20%
(C) 40%
(D) 50%
(E) 60%
Rationale: The total number of different arrangements are 6!/2=360. We divide here by 2, since we have two same letters A.
Letters A, A, and U are vowels. Put them together and consider as one object. So, we have 4 different objects (AAU) B C S. The number of different arrangements of them are 4!=24. And we have 3 possibilities to arrange vowels: AAU, AUA, UAA. Therefore, we have 24*3=72 different arrangements.
Hence, 72/360*100%=20%.
The correct answer is B.
Answer: (B) 20%
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
(A) A)3:4
(B) B)3:5
(C) of these
(D) inadequate
(E) C)4:3
Rationale: Let P's age and Q's age be 6x and 7x years respectively.
Then, 7x - 6x = 4 => x = 4
Required ratio = (6x + 4) : (7x + 4)
28 : 32 = 7:8
ANSWER:C
Answer: (C) of these
Question: Three pounds of 05 grass seed contain 3 percent herbicide. A different type of grass seed, 20, which contains 20 percent herbicide, will be mixed with three pounds of 05 grass seed. How much grass seed of type 20 should be added to the three pounds of 05 grass seed so that the mixture contains 15 percent herbicide?
(A) 3
(B) 7.2
(C) 4.5
(D) 6
(E) 9
Rationale: 05 grass seed contains 5% herbicide and its amount is 3 pound
20 grass seed contains 20% herbicide and its amount is x
when these two types of grass seeds are mixed, their average becomes 15%
thus we have
3(3)+x(20)/(x+3) = 15
9+20x=15x +45
5x=36
or x=7.2
B
Answer: (B) 7.2
Question: What will be the reminder when (67^67+67) is divided by 68?
(A) 1
(B) 63
(C) 66
(D) 67
(E) None of these
Rationale: (x^n+1) will be divisible by (x+1) only when n is odd;
(67^67+1) will be divisible by (67+1);
(67^67+1)+66 when divided by 68 will give 66 as remainder.
Correct Option : C
Answer: (C) 66
Question: There are 20 poles with a constant distance between each pole. A car takes 24 second to reach the 12th pole. How much will it take to reach the last pole.
(A) 41.4543
(B) 41.4545
(C) 41.45128
(D) 41.41288
(E) 41.41222
Rationale: Assuming the car starts at the first pole.
To reach the 12th pole, the car need to travel 11 poles (the first pole doesn't count, as the car is already there).
11 poles 24 seconds
1 pole (24/11) seconds
To reach the last (20th) pole, the car needs to travel 19 poles.
19 pole 19 x (24/11) seconds
= 41.4545 seconds
Answer:B
Answer: (B) 41.4545
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
(A) 3/8
(B) 3/2
(C) 3/5
(D) 3/9
(E) 4/2
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y)
= 23 ==> 27 x + 17 y = 23 x + 23 y
==> 4 x = 6 y
==> x/y = 3/2.
Answer:B
Answer: (B) 3/2
Question: A person got Rs.60 more when he invested a certain sum at compound interest instead of simple interest for two years at 15% p.a. Find the sum?
(A) 7500
(B) 2666
(C) 2877
(D) 2667
(E) 2671
Rationale: P = (d * 1002) / R2
=> (60 * 100 * 100) / 15 * 15 = Rs.2666
Answer:B
Answer: (B) 2666
Question: Q's mother is sister of P and daughter of M. S is daughter of P and sister of T.How is M related to T?
(A) Grandfather
(B) Grandmother
(C) Father
(D) Either Grandmother or Grandfather
(E) Grandf4her
Rationale: Explanation:
Q's mother is sister of P & daughter of M.[sex of P and M are not clear]
S is daughter of P and sister of T. [sex of P and T is not clear]
M's children : Q's mother and P
P's children :S[female] and T
\fn_cm \therefore M is either Grandmother or Grandfather of T
Answer: D
Answer: (D) Either Grandmother or Grandfather
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
The total amount of Fuel paid by the company during the given period is approximately what percent of the total amount of salary paid during this period?
(A) A)0.5%
(B) B)1%
(C) C)1.25%
(D) D)3%
(E) E)4%
Rationale: Required percentage
=	(288 + 342 + 324 + 336 + 420)
=	[	17	x 100	]	%
1710
~= 1%.
Answer : B
Answer: (B) B)1%
Question: he distance from town A to town B is five miles. C is six miles from B. Which of the following could be the maximum distance from A to C?
(A) 11
(B) 77
(C) 51
(D) 16
(E) 12
Rationale: Explanation:
Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11
Answer:A
Answer: (A) 11
Question: Margaret is 13 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages
(A) 10yrs
(B) 20yrs
(C) 30yrs
(D) 40yrs
(E) 25yrs
Rationale: Let, age of son x=12
Margaret is 13 years more than twice the age of his son, y = 13+2(x)
=13+2(12)
=13+24
=37yrs
Difference = 37 - 12
=25yrs
ANSWER:E
Answer: (E) 25yrs
Question: The price of an item is discounted 7 percent on day 1 of a sale. On day 2, the item is discounted another 7 percent, and on day 3, it is discounted an additional 10 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
(A) 83.7%
(B) 85.2%
(C) 86.8%
(D) 78.8%
(E) 69.4%
Rationale: Let initial price be 100
Price in day 1 after 7% discount = 93
Price in day 2 after 7% discount = 86.49
Price in day 3 after 10% discount = 77.84
So, Price in day 3 as percentage of the sale price on day 1 will be = 77.84/93*100 => 83.7%
Answer will definitely be (A)
Answer: (A) 83.7%
Question: Out of the total 390 students studying in a college of Arts and Science, boys and girls are in the ratio of 7 : 6 respectively and the number of students studying Arts and Science are in the ratio of 3 : 7 respectively. The boys and girls studying Arts are in the ratio of 4 : 5 respectively. How many boys are studying science?
(A) 52
(B) 65
(C) 115
(D) 158
(E) 168
Rationale: Given, boys and girls are in the ratio of 7 : 6,
So, Number of boys = 7/13 x 390 = 210
Number of girls = 390 - 210 = 180
Students studying Arts and Science are in the ratio of 3 : 7,
Number of students studying Arts = 3/10 x 390 = 117
Number of students studying Science = 390 - 117 = 273
Also boys and girls studying Arts are in the ratio of 4 : 5,
Number of boys studying arts = 4/9 x 117 = 52
Number of boys studying science = 210 - 52 = 158
ANSWER:D
Answer: (D) 158
Question: In 2 bags, there are to be put together 5 red and 12 white balls, neither bag being empty. How must the balls be divided so as to give a person who draws 1 ball from either bag- the greatest chance of drawing a red ball ?
(A) 1/8
(B) 2/8
(C) 3/8
(D) 4/8
(E) 5/8
Rationale: greatest chance.
1/2*1 +1/2*4/16=5/8
ANSWER:E
Answer: (E) 5/8
Question: The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 5 ?
(A) 96
(B) 106
(C) 128
(D) 137
(E) 122
Rationale: Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 * 20 = 640
Now increase in avg = 4 runs. So, new avg = 32+5 = 37 runs
Total runs = new avg x new no. of innings = 37 * 21 = 777
Runs made in the 11th inning = 777-640 = 137
ANSWER:D
Answer: (D) 137
Question: A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 9 is
(A) 3
(B) 7
(C) 21
(D) 189
(E) 267
Rationale: In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be D
Answer: (D) 189
Question: Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 100 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
(A) a. 0.96
(B) b. 0.096
(C) c. 0.0096
(D) d. 0.00096
(E) e. 0.000096
Rationale: Let total Production be 10000 units....
A produces 4000 units and 36 units are defective
B produces 6000 units and 60 units are defective
So, Out of total 10,000 units 96 units are defective...
So the required probability = 96/10000 => 0.0096
Answer will be (C)
Answer: (C) c. 0.0096
Question: There are 3 people and 3 chairs. In how many different ways people can occupy the chairs?
(A) 6
(B) 15
(C) 24
(D) 36
(E) 120
Rationale: number of ways =3! = 6
Answer is A
Answer: (A) 6
Question: If a positive integer n is divisible by both 3 and 7, then n must also be divisible by which of the following?
I. 21
II. 10
III. 63
(A) None
(B) I only
(C) II only
(D) I and II
(E) II and III
Rationale: A multiple of 3 and 7 is also a multiple of 21, but not necessarily a multiple of 10 or 63.
The answer is B.
Answer: (B) I only
Question: A train passes a station platform in 40 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 177 m
(B) 300 m
(C) 240 m
(D) 187 m
(E) 186 m
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 40 = 15
x + 300 = 600
x = 300 m.
Answer: B
Answer: (B) 300 m
Question: Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 8 different shirts, 10 different pairs of jeans, and 8 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?
(A) 30
(B) 90
(C) 640
(D) 480
(E) 960
Rationale: Total # of outfits = 8 * 10 * 8 = 960
Answer - C
Answer: (C) 640
Question: X can finish a work in 30 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
(A) 3
(B) 10
(C) 6
(D) 8
(E) 9
Rationale: Work done by X in 1 day = 1/30
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/30) = 10
B
Answer: (B) 10
Question: There are different 6 circles. What is the number of the greatest possible points with which the circles intersect?
(A) 90
(B) 100
(C) 110
(D) 180
(E) 30
Rationale: Maximum points of intersection between n different circles = n*(n - 1) = 6*5 = 30
Answer: E
Answer: (E) 30
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.15,000 earned at the end of 2years from the startingof the business?
(A) s. 5,000
(B) s. 4,500
(C) s. 5,700
(D) s. 6,500
(E) s. 7,500
Rationale: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 15000 x	3/10	= Rs. 4,500.
B
Answer: (B) s. 4,500
Question: If the weight of 10 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ?
(A) 7.2 kg.
(B) 10.8 kg.
(C) 14.04 kg.
(D) 18.0 kg
(E) None
Rationale: Answer
∵Weight of 10 m long rod = 23.4 kg
∴ Weight of 1 m long rod = 23.4 / 10 kg
∴ Weight of 6 m long rod = 23.4 x 6 / 10
= 14.04 kg
Option: C
Answer: (C) 14.04 kg.
Question: Two trains are moving in the same direction at 54 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
(A) 135
(B) 277
(C) 187
(D) 257
(E) 271
Rationale: Relative speed = (54 - 36) * 5/18 = 5 mps.
Distance covered in 27 sec = 27 * 5 = 135 m.
The length of the faster train = 135 m.
Answer: A
Answer: (A) 135
Question: Solution for 3.15+.014+.458
(A) 3.622
(B) 3.911
(C) 4.938
(D) 2.986
(E) 2.999
Rationale: 3.15+.014+.458=0
0=0-3.15-0.014-0.458
0=-3.622
answer :A
Answer: (A) 3.622
Question: If by selling twelve note-books, the seller earns profit equal to the selling price of two note-books, what is his percentage profit?
(A) 20%
(B) 25%
(C) 2163%
(D) Data inadequate
(E) None of these
Rationale: Percentage profit= 2/12−2×100=20%
Answer A
Answer: (A) 20%
Question: If x^2=x+2, then x^3 = ?
(A) 3x+2
(B) 3x-2
(C) 2x+1
(D) 2x-3
(E) 3x+4
Rationale: x^2 = x+2
x^3 = x*x^2 = x*(x+2) = x^2 + 2x = (x+2)+2x = 3x+2
The answer is A.
Answer: (A) 3x+2
Question: Find the odd man out. 5,7,9,12,13
(A) 52
(B) 12
(C) 11
(D) 14
(E) 10
Rationale: Explanation :
5+2=7
7+2=9
9+2=11
11+2=13
Hence, it is clear that 11 should have come instead of 12
Answer : Option C
Answer: (C) 11
Question: Eva’s grade was in the 80th percentile out of 80 grades in her class. In another class of 70 students there were 30 grades higher than Eva’s. If nobody had Eva’s grade, then Eva was what percentile of the two classes combined?
(A) 84
(B) 80
(C) 74
(D) 69
(E) 65
Rationale: Being in 80% percentile out of 80 grades means Eva was 65th (from the least grade) in the class (as long as nobody had Eva's grades), she outscored 64.
In another class her grade would rank her 41 (from the least grade out of 71, 70+Eva), 40 had the grades lower than Eva.
So in combined classes she outscored 64+40=104. There are 150 students 104/150=0.69
Answer: D (69%)
Generally being in x% means that x% has the grades less than you.
Eva in 80% --> she outscored 890% of of 80=64 (Eva is 65th).
Of the 70 grades from another class, 30 were higher than Eva's, and the rest were lower --> rest is 40, hence Eva outscored 40.
So out of total 80+70=150, Eva outscored 64+40=104. Hence she is in 104/150=69%.
Answer: E
Answer: (E) 65
Question: It will take 16 days for Mary to complete a certain task alone. She worked for 8 days before she was joined by her sister. both of them completed the remaining task in 2 and half days. if her sister had joined her when she started the task, how many days would it have taken?
(A) 6
(B) 8
(C) 2
(D) 5
(E) 4
Rationale: Explanation:
Mary and her sister complete half work in 2.5 days
=> they can complete whole work in 5 days
Answer: Option D
Answer: (D) 5
Question: The radius of a cylindrical vessel is 7cm and height is 1cm. Find the whole surface of the cylinder?
(A) 352
(B) 771
(C) 440
(D) 767
(E) 1981
Rationale: r = 7 h = 1
2πr(h + r) = 2 * 22/7 * 7(8) = 352
Answer:A
Answer: (A) 352
Question: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 12 ?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Denote |x - 3| as y: y^2 + y = 12 --> y = -4 or y = 3. Discard the first solution since y = |x - 3|, so it's an absolute value and thus cannot be negative.
y = |x - 3| = 3 --> x = 6 or x = -1. The sum = 5.
Answer: A.
Answer: (A) 5
Question: In the formula of converting temperature from Celsius to Fahrenheit F=9/5C+32, How many integer values(not fractional) of F will be there that lies between 100 to 200 for integer values of C.
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: for c=40 ,F=((9/5) *40)+32=104
c=45 ,f=(9*9)+32=113
c=50 ,f=(9*10)+32=122
c=55 ,f=(9*11)+32=131
c=60 ,f=(9*12)+32=140
c=65 ,f=(9*13)+32=149
c=70 ,f=(9*14)+32=158
c=75 ,f=(9*15)+32=167
c=80 ,f=(9*16)+32=176
c=85 ,f=(9*17)+32=185
c=90 ,f=(9*18)+32=194
so ans is 11.
ANSWER:C
Answer: (C) 11
Question: A businessman earns $25800 in December, thus decreasing his average annual (January to December) earnings by $1000. His average annual earnings would be
Source: CMAT Preparation
(A) $29000
(B) $36800
(C) $40200
(D) $41000
(E) $42300
Rationale: (x - 25,800)/11 - x/12 = 1,000
x = 441,600
x/12 = 36,800
Answer: B
Answer: (B) $36800
Question: Which of the following data sets has the second smallest standard deviation?
(A)  {1, 2, 3, 4, 5}
(B)  {2, 3, 3, 3, 4}
(C)  {2, 2, 2, 4, 5}
(D)  {0, 2, 3, 4, 6}
(E)  {-1, 1, 3, 5, 7}
Rationale: since we are asked to compare 'standard deviation', we should look out for similarity between all the sets..
The SIMILARITY is - the SUM of all sets is equal =15..
and hence average = 15/5 = 3...
Now we have 5 different sets which have AVG as 3, so we will look for the spread of the other elements of set around the AVERAGE..
clearly E has a range of 7-(-1) or 8, and has the highest standard deviation..
Next is D, which has a range of 6-0 or 6..
and has smallest standard of deviation.
and (C) {2, 2, 2, 4, 5} has second smallest standard of deviation.
ans C
Answer: (C)  {2, 2, 2, 4, 5}
Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
(A) 20 hours
(B) 25 hours
(C) 35 hours
(D) Cannot be determined
(E) None of these
Rationale: If c takes x hrs, B takes 2x hrs and A takes 4x hrs,
then
1/x +1/2x = 1/4x = 1/5
7/4x = 1/5
x= 7*5/4 hrs = 35/4 hrs
So A alone will take 4*35/4 = 35 hrs
ANSWER:C
Answer: (C) 35 hours
Question: A die is rolled twice. What is the probability of getting a sum equal to 9?
(A) 2/9
(B) 5/7
(C) 1/7
(D) 1/9
(E) 3/7
Rationale: Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 × 6 = 36
E = Getting a sum of 9 when the two dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}
Hence, n(E) = 4
P(E) = n(E)/n(S)
=4/36
=1/9
Answer : Option D
Answer: (D) 1/9
Question: What is the least number which when divided by 8, 12, 15 and 20 leaves in each case a remainder of 5
(A) 110
(B) 125
(C) 75
(D) 170
(E) 195
Rationale: LCM of 8, 12, 15 and 20 = 120
Required Number = 120 + 5 = 125
Answer: Option B
Answer: (B) 125