mathewhe/aqua_rat huggingface dataset:
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 40% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
(A)  5%
(B)  10%
(C)  25%
(D)  15%
(E)  30%
Rationale: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.
Neither is zero.
Hence 100 = 60 + 40 + 35 - n (Exactly 2 products) - 2*10
100 = 115 - n (Exactly 2 products) => n (Exactly 2 products) = 15.
Answer: D
Answer: (D)  15%
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 28
(B) 26
(C) 20
(D) 87
(E) 24
Rationale: M = 15
S = 5
DS = 15 + 5
=20
Answer: C
Answer: (C) 20
Question: A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss?
(A) 9% loss
(B) 400
(C) 4000
(D) 324
(E) 8% LOSS
Rationale: (30*30)/100 = 9%loss
ANSWER:A
Answer: (A) 9% loss
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
(A) 50
(B) 40
(C) 25
(D) 15
(E) 10
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
ANSWER:C
Answer: (C) 25
Question: What ratio must a shopkeeper mix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.19 ?
(A) 10 : 7
(B) 9 : 8
(C) 2 : 1
(D) 13 : 11
(E) 14 : 8
Rationale: Correct option: (C)
Use rule of alligation, to determine the ratio
The required ratio of Soybean and Peas = 6 : 3 =2 : 1
Answer: (C) 2 : 1
Question: A 90 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 25
(B) 20
(C) 47
(D) 36
(E) 30
Rationale: 1: 2/5 = 5: 2
2/7 * 90 =25
Answer:A
Answer: (A) 25
Question: A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number X is
(A) 74
(B) X=75
(C) X=175
(D) X=680
(E) 690
Rationale: I solved this question by plugging in numbers from the answer choices.
A.) 74
Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5.
B.) 75
I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7.
15-7 = 8 so I know the correct answer isB
Answer: (B) X=75
Question: 1370 , X, 1070 , -180, -6430
(A) 1320
(B) 6530
(C) 6630
(D) 6730
(E) 6830
Rationale: 1370-50*(5^0)=1320
1320-50*(5^1)=1070
1070-50*(5^2)=-180
-180-50*(5^3)=-6430
ANSWER:A.
Answer: (A) 1320
Question: Coins are to be put into 9 pockets so that each pocket contains at least one coin. At most 5 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?
(A) 7
(B) 13
(C) 16
(D) 19
(E) 28
Rationale: Since at most 5 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;
Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);
Total: 1+1+1+1+1+2+3+4+5=19
Answer: D
Answer: (D) 19
Question: John is the owner of a company and for Thanksgiving he wants to give a Turkey to each employee to celebrate the holiday. Each turkey cost him $25. If he has 85 employees, how much would John need to spend?
(A) $2,125
(B) $1,320
(C) $2,000
(D) $1,580
(E) $2,000.75
Rationale: Answer is (A). If John wants to give each of his employees a turkey to help celebrate the Thanksgiving holiday and each one costs him $25 multiplied by the number of employees (85), he would have to pay a total of $2,125.
Answer: (A) $2,125
Question: In how many ways letters of the word DATA be arranged?
(A) 6
(B) 18
(C) 12
(D) 6
(E) 2
Rationale: DATA has 4 letters, out of which A repeated 2 times. Hence total ways = 4! / 2!=12 ways
C
Answer: (C) 12
Question: Two pipes a and b can fill a tank in 12 hours and 15 hours respectively.if both pipe open together in tank,then how much time it take to fill the tank?
(A) 15
(B) 18
(C) 20/3
(D) 19/4
(E) 25/4
Rationale: in 1 hour pipe a fill=1/12
in 1 hour pipe b fill=1/15
pipe(a+b) in 1 hour=[1/12+1/15]=3/20
total time taken to fill the tank=20/3 hour
answer C
Answer: (C) 20/3
Question: What distance will be covered by a bus moving at 72 kmph in 30 seconds?
(A) 877 m
(B) 600 m
(C) 167 m
(D) 176 m
(E) 546 m
Rationale: Explanation:
72 kmph = 72 * 5/18 = 20 mps
D = Speed * time = 20 * 30 = 600 m.
Answer: B
Answer: (B) 600 m
Question: Which of the following is equal to the value of 2^3 + 2^3 + 3^3 + 3^3 + 3^3 ?
(A) 2^3 + 3^3
(B) 2^7 + 3^4
(C) 2^8 + 3^4
(D) 2^4 + 3^4
(E) 2^4 + 3^6
Rationale: 2^3 + 2^3 + 3^3 + 3^3 + 3^3
= 2 (2^3) + 3 (3^3)
= 2^1 (2^3) + 3^1 (3^3)
= 2^(1+3) + 3^(1+3)
= 2^4 + 3^4
Ans: D
Answer: (D) 2^4 + 3^4
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
(A) 190 sec
(B) 200 sec
(C) 210 sec
(D) 220 sec
(E) 250 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.
ANSWER A
Answer: (A) 190 sec
Question: ‘A’ and ‘B’ started a business in partnership investing Rs 20000/- and Rs 15000/- respectively. After six months ‘C’ jointed them with Rs 20000/-. What will beB’s share in the total profit of Rs 25000/- earned at the end of two years from the starting of the business?
(A) 6500
(B) 7500
(C) 8500
(D) 9000
(E) 9500
Rationale: A:B:C =(20000*24) : (15000*24) : (20000*18)
= 4 : 3 : 3
B's Share = (3*25000)/(4+3+3)=7500Rs
ANSWER:B
Answer: (B) 7500
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 877m
(B) 189m
(C) 350m
(D) 216m
(E) 978m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39
= 50/3
3(x + 300) = 1950 è x
= 350m.
Answer: C
Answer: (C) 350m
Question: Anand and Deepak started a business investing Rs. 5,500 and Rs. 19,000 respectively. Out of a total profit of Rs. 20,800, Deepak's share is?
(A) Rs. 9400
(B) Rs. 16130.6
(C) Rs. 8400
(D) Rs. 3400
(E) Rs. 8440
Rationale: Ratio of their shares = 5500 : 19000 = 11 : 38
Deepak's share = 20800 * 38/49= Rs. 16130.6
Answer:B
Answer: (B) Rs. 16130.6
Question: A man can row with a speed of 12 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 33
(B) 77
(C) 20
(D) 99
(E) 17
Rationale: M = 12
S = 5
DS = 12 + 5 = 17
Answer: E
Answer: (E) 17
Question: A train leaves New York City at 7.15 Am and arrives in Buffalo at 2.47 that afternoon. What total length of time does the trip take?
(A) 7 h 92 min.
(B) 7 h 32 min.
(C) 7 h 12 min.
(D) 8 h 32 min.
(E) 5 h 32 min.
Rationale: Explanation:
2.47 PM = 14.47
Total time = 14.47 – 7.15 = 7 hrs 32 min
Answer:B
Answer: (B) 7 h 32 min.
Question: A no.when divided by 158 gives a remainder 50, what remainder will be obtainedby dividingthe same no.16?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 158 + 50 = 208/16 = 13 (Remainder)
D
Answer: (D) 13
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
(A) 16 sec
(B) 18 sec
(C) 19 sec
(D) 10 sec
(E) 17 sec
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10 = 10 sec.
Answer: D
Answer: (D) 10 sec
Question: If selling price of 12 pens is equal to the cost price of 18 pens, find the profit percent.
(A) 50%
(B) 58%
(C) 59%
(D) 51%
(E) 55%
Rationale: Explanation:
Selling price of 12 pens = cost price of 18 pens
Therefore, the profit is 6 pens and cost price is 12 pens.
% profit = profit/cost price * 100
= 6/12 * 100
= 50%
ANSWER: A
Answer: (A) 50%
Question: The probability that a convenience store has no iced tea is 60%. If Karl is stopping by 3 convenience stores on his way to work, what is the probability thatat least oneof the stores will not have a can of iced tea?
(A) 1/8
(B) 1/4
(C) 1/2
(D) 3/4
(E) 7/9
Rationale: p=1-3/5^3(all stores have iced tea)=7/9
E
Answer: (E) 7/9
Question: If a and b are the roots of the equation x2 - 9x + 9 = 0, then the value of a2 + b2 is:
(A) 63
(B) 24
(C) 17
(D) 6
(E) 5
Rationale: Sol.(b) The sum of roots = a+ b = 9
Product of roots = ab = 9
Now, a2 + b2 = (a + b)2 - 2ab = 81 - 18 = 63
Answer A
Answer: (A) 63
Question: A businessman earns $26800 in December, thus decreasing his average annual (January to December) earnings by $1200. His average annual earnings would be
Source: CMAT Preparation
(A) $29000
(B) $33500
(C) $40000
(D) $41000
(E) $42300
Rationale: (x - 26,800)/11 - x/12 = 1,200
x = 480,000
x/12 = 40,000
Answer: C.
Answer: (C) $40000
Question: An insect leaps 72 centimeters in 1.5 seconds. What is its speed?
(A) 90 centimeters per second
(B) 10.8 centimeters per second
(C) 1.08 meters per second
(D) 4.8 centimeters per second
(E) 0.48 meters per second
Rationale: 72 / 1.5 = 48 cm/s = 0.48 m/s
The answer is E.
Answer: (E) 0.48 meters per second
Question: A room contains 200 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
(A) 0
(B) 05
(C) 10
(D) 15
(E) 20
Rationale: Say group of x people left the room.
# of women in the room was 0.15*200=30;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(160-x);
So, 30-0.3x= 0.1(200-x) --> x=10.
Answer: C.
Answer: (C) 10
Question: A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 45% are drinking beer, 40% are drinking mixed drinks, and 15% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?
(A) 1/2
(B) 4/7
(C) 10/17
(D) 7/24
(E) 7/10
Rationale: Suppose there are 100 students
Group A : 40% = 40 students
45% drink beer = 18
40% mixed = 16
15% both = 6
Group B 60% = 60
30% beer= 18
30% mixed = 18
20% both= 12
now we need both ( beer + mixed = both)
probability = total beer drinker = 18+18 =36 and both = 20
thus 18/36 = 1/2
Hence A
Answer: (A) 1/2
Question: Which of these following integers is the square of an integer?
(A) 20821304103
(B) 20571304329
(C) 20467304228
(D) 20453304487
(E) 20814304592
Rationale: The unit digit of any perfect square can not be 2, 3, 7, or 8.
The answer is B.
Answer: (B) 20571304329
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
(A) 24 years
(B) 33 years
(C) 14 years
(D) 18 years
(E) 9 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
answer :C
Answer: (C) 14 years
Question: Martha takes a road trip from point A to point B. She drives x percent of the distance at 50 miles per hour and the remainder at 40 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?
(A)  110
(B)  20,000
(C)  1,100
(D)  3,000
(E)  30,000
Rationale: total distance = d
total time taken = x/(100*50) + (100-x)/(100*40)
speed = distance / time
gives numerator = 20000
Answer : B
Answer: (B)  20,000
Question: An amount of Rs.10,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
(A) 2500
(B) 2697
(C) 2697
(D) 5000
(E) 6971
Rationale: Explanation:
We have, P = 2Q & S = 4R
Further Q = R & P + Q + R + S = 10,000
Thus we get, 2Q + Q + Q + 4Q = 10,000
8Q = 10,000 or Q = Rs. 1250
Thus, R = Rs. 1250, P = 2500 & S = Rs. 5000
Hence, the required difference = (S – P) = (5000 – 2500) = Rs. 2500
ANSWER:A
Answer: (A) 2500
Question: What is the speed of the stream if a canoe rows upstream at 4km/hr and downstream at 12km/hr
(A) 1 kmph
(B) 4 kmph
(C) 3 kmph
(D) 2 kmph
(E) 1.9 kmph
Rationale: Sol.
Speed of stream = 1/2(12 - 4) kmph = 4 kmph.
Answer B
Answer: (B) 4 kmph
Question: A cylinder is inserted in a sphere d/h = 2/3. Find the surface area of the cylinder ?
(A) 23.12
(B) 24.12
(C) 25.12
(D) 26.12
(E) 27.12
Rationale: take r=1, h=3
=2*3.14*r*r+2*3.14*r*h
=2*3.14*r(r+h)
=2*3.14*1(1+3)
=2*3.14(4)
=25.12
ANSWER:C
Answer: (C) 25.12
Question: Jerry and Beth each drove from Smallville to Crown City by different routes. Jerry drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than Jerry to complete the trip. How many miles per hour was Beth's average speed on this trip?
(A)  24
(B)  30
(C)  48
(D)  54
(E)  75
Rationale: Speed = Distance/Time
Distance for Jerry = Speed * Time = 40 * 1/2 = 20 miles
Distance for Beth = Distance for Jerry +5 = 20+5 = 25 miles
Time taken by Beth = Time taken by Jerry + (1/3 hour) = 1/2+1/3 = 5/6
Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour
Hence, B is the answer.
Answer: (B)  30
Question: The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly five elements each?
(A) 120
(B) 126
(C) 130
(D) 140
(E) 144
Rationale: nC2 = 36
=> n*(n-1)/2 = 36 by middle term factor and n cannot be -ve
=> n = 9
nC3 = 9C5 = 9!/5!(9-5)!= 9*8*7*6*5!/5!*4*3*2*1= 126
So, Answer is B
.
Answer: (B) 126
Question: m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 15) both lie on the line defined by the equation x = (y/5) - (2/5), what is the value of p?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x = (y/5) - (2/5), and so y = 5x + 2. The slope is 5.
(n+15-n) / (m+p-m) = 5
p = 3
The answer is C.
Answer: (C) 3
Question: Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 240 marks in the second test and failed by 57 marks in that test. Find the pass mark in the first test?
(A) 768
(B) 243
(C) 246
(D) 264
(E) 224
Rationale: Let the maximum mark in each test be M.
The candidate failed by 57 marks in the second test.
pass mark in the second test = 240 + 57 = 297
45/100 M = 297
Pass mark in the first test = 40/100 M = 40/45 * 297 = 264.
Answer:D
Answer: (D) 264
Question: A scuba diver descends at a rate of 32 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 6400feet below the sea level..how long will he take to reach the ship?
(A) 200 minutes
(B) 240 minutes
(C) 220 minutes
(D) 210 minutes
(E) 77 minutes
Rationale: Time taken to reach = 6400/32= 200 minutes
ANSWER:A
Answer: (A) 200 minutes
Question: A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $320,000, 80% of which was in the first mortgage, what is her approximate monthly interest payment?
(A) $1,333
(B) $1,733
(C) $3,466
(D) $13,333
(E) $20,796
Rationale: Making the numbers a little easy looking:
Monthly payment = 320,000*(80/100*4/100+20/100*9/100)/12
= 3200/12*(3.2+1.8)
= 16000/12=1333
ANSWER:A
Answer: (A) $1,333
Question: Find the next number in this Sequence and solve this thinking riddle.
6 14 36 98 ?
(A) 120
(B) 200
(C) 398
(D) 276
(E) 490
Rationale: D
276
6 = 11 + 21 + 31
14 = 12 + 22 + 32
36 = 13 + 23 + 33
98 = 14 + 24 + 34
276 = 15 + 25 + 35
Answer: (D) 276
Question: A and B can complete a work in 15days and 10day. They started doing the work together but after 2days B had to leave and A alone completed the remaining work. The whole work was completed in?
(A) 10days
(B) 12days
(C) 15days
(D) 8days
(E) 16days
Rationale: A+B 1day work = 1/15 + 1/10 = 1/6
Work done by A and B in 2days = 1/6 * 2 = 1/3
Remaining work = 1-1/3 = 2/3
Now 1/15 work is done by A in 1day
2/3 work will be done by A in 15*2/3 = 10days
Total time taken = 10+2 = 12days
Answer is B
Answer: (B) 12days
Question: In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 320 points, how many points is the third question worth?
(A) 39
(B) 24
(C) 22
(D) 20
(E) 18
Rationale: x
x+4
x+8
x+12
x+16
x+20
x+24
x+28
x+32
x+36
10x+180=320
10x=140
x=14
3rd question = x+8 = 14+8 = 22
Answer C
Answer: (C) 22
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
(A) 23.56
(B) 23.59
(C) 23.55
(D) 23.53
(E) 23.57
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
Answer:E
Answer: (E) 23.57
Question: A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate?
(A) Rs.256.20
(B) Rs.256.08
(C) Rs.256.02
(D) Rs.256.34
(E) Rs.256.25
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.500
(P)(8)(5)/100 = 500
P = 1250
C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years
=2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}
= 2500/400(441 - 400)
= 25/4(41) = 1025/4 = Rs.256.25
Answer: E
Answer: (E) Rs.256.25
Question: Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
(A) 16 hours
(B) 18 hours
(C) 20 hours
(D) 24 hours
(E) 26 hours
Rationale: speed of upstream=9-1.5=7.5kmph
speed of down stream=9+1.5=10.5kmph
total time=(105/7.5)+(105/10.5)=24hrs
ANSWER:D
Answer: (D) 24 hours
Question: A lamp is put on one corner of a square plot of side 50m. It's light reaches 21m. Find the area of that plot that is lit by that lamp?
(A) 248
(B) 312.5
(C) 346.5
(D) 392.5
(E) 424
Rationale: Area covered by lamp = Pi*r^2/4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1/4 part lit is of the plot)
where r= 21 m = length of part lit
So area = (22/7)*21*21/4 = 346.5 sq m
answer :C
Answer: (C) 346.5
Question: 4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 3 professor, how many ways can this committee be formed?
(A) 36
(B) 60
(C) 72
(D) 80
(E) 100
Rationale: you count up combinations twice.
4*9*8... and let me name 6 with students A,B,C,..,F
after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same.
I don't think that's the only mistake.
36 is a factor of = 2^2*3^2
72 is a factor of = 2^3*3^2.
These are very different numbers and you cannot divide 72 with something to get to 36. ans A
Answer: (A) 36
Question: A travel agent offers a vacation plan which costs 'a' dollars for the first day, and a/5 for each additional day. How much does a vacation of b days cost, where b > 1.
(A) (ab+4a)/2
(B) (ab+8a)/5
(C) (ab+4a)/5
(D) (ab+4a)/3
(E) (ab+a)/5
Rationale: Cost = a + (b-1)*a/5 = (5a + (b - 1)*a)/5 = (ab+4a)/5
Answer is C
Answer: (C) (ab+4a)/5
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
(A) 3.6
(B) 7.2
(C) 8.4
(D) 10
(E) 8
Rationale: Speed = 600/(5 x 60)	m/sec.
= 2 m/sec.
Converting m/sec to km/hr
= (2 x	(18/5)) km/hr
= 7.2 km/hr.
Answer : B
Answer: (B) 7.2
Question: In one can of mixed nuts, 50% is peanuts. In another can of mixed nuts that is one-half the size of the first one, 40% is peanuts. If both cans are emptied into the same bowl, what percentage of the mixed nuts in the bowl is peanuts?
(A) 46 2/3%
(B) 20%
(C) 25%
(D) 33 1/3%
(E) 35%
Rationale: Can 1: size 1; 50% nuts
Can 2: size 0.5 and 40% nuts
(1x0.5+0.5x0.4)/1.5=46 2/3
A
Answer: (A) 46 2/3%
Question: A set of 12 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
(A) 32
(B) 37
(C) 40
(D) 43
(E) 50
Rationale: The correct answer is D.
A set of 15 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
Given 15 different integers, lets say
n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, n11, n12, n13, n14, n15
Also given median is 25 i.e. n8 = 22
n1, n2, n3, n4, n5, n6, n7, 25, n9, n10, n11, n12, n13, n14, n15
As each integer is different we need to find the maximum values for all those numbers before the median.
the maximum value n7 can have is one less then the median i.e. 24, similarly n6 will be one less than 24 i.e. 23 ... using this process the values for all number before the median would be..
18, 19, 20, 21, 22, 23, 24, 25, n9, n10, n11, n12, n13, n14, n15
Also given the range is 25 i.e. n15 - n1 (18) = 25
The maximum value n15 can have is 22 + n1 (18) = 40
C
Answer: (C) 40
Question: The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 230
(B) 225
(C) 245
(D) 238
(E) 236
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30 = 25/2 ==> 2(150 + X) = 750 ==> X = 225 m.
Answer: Option B
Answer: (B) 225
Question: Evaluate 24.39 + 562.093 + 35.96
(A) 631.344
(B) 622.443
(C) 623.434
(D) 632.423
(E) 632.443
Rationale: 24.39 + 562.093 + 35.96 = 622.443
Option B
Answer: (B) 622.443
Question: In a race where 15 cars are running, the chance that car X will win is 1/4, that Y will win is 1/8 and that Z will win is 1/12. Assuming that a dead heat is impossible, find the chance that one of them will win.
(A) 1/140
(B) 1/180
(C) 11/24
(D) 10/15
(E) 57/120
Rationale: Required probability = P(X) + P(Y) + P(Z) (all the events are mutually exclusive).
= 1/4 + 1/8 + 1/12
= 11/24
ANSWER:C
Answer: (C) 11/24
Question: Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are:
(A) 7, 6
(B) 5, 1
(C) 6, 3
(D) 8, 7
(E) None of these
Rationale: Explanation :
Let A and B be such sets, i.e., n (A) = m, n (B) = n
So, n (P(A)) = 2m and n (P(B)) = 2n
Thus n (P(A)) – n (P(B)) = 56, i.e. 2m – 2n = 56
⇒ 2n (2m-n - 1) = 23 x 7
⇒ n = 3 , 2m-n – 1 = 7
⇒ m = 6
Answer : C
Answer: (C) 6, 3
Question: Eleven bags are bought for Rs.1000 and sold at 10 for Rs.1300. What is the gain or loss in percentage?
(A) 10%
(B) 21%
(C) 25%
(D) 23%
(E) None of these
Rationale: Explanation:
As selling price is Rs.1300 for 10 bags, each bag is sold at Rs.130.
Hence, the profit is Rs.100 after selling 10 bags plus the selling price of 1 bag = 100 + 130 = Rs.230.
%profit = 230/1000 *100
= 23%
ANSWER D
Answer: (D) 23%
Question: A password of a computer used six digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
(A) 1/64
(B) 1/16
(C) 1/8
(D) 2/5
(E) 1/2
Rationale: We have six digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10 * 5/10 * 5/10 * 5/10 * 5/10=1/64 (A)
Answer: (A) 1/64