mathewhe/aqua_rat huggingface dataset:
Question: The ratio of the incomes of A and B is 5:4 and the ratio of their expenditure is 3:2. If at the end of the year, each saves $1600 then the income of A is?
(A) $1500
(B) $4000
(C) $2000
(D) $2500
(E) $3200
Rationale: Let the income of A and B be $5x and $4x
Let their expenditures be $3y and $2y
5x-3y = 1600-------1)
4x-2y = 1600-------2)
From 1) and 2)
x = 800
A's income = 5x = 5*800 = $4000
Answer is B
Answer: (B) $4000
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) 18997
(B) 12000
(C) 28992
(D) 13009
(E) 28811
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100)
= 600
X = 12000
Answer: B
Answer: (B) 12000
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
(A) 18
(B) 27
(C) 20
(D) 80
(E) 81
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer: D
Answer: (D) 80
Question: Mr Shivkumar started a business, investing 25000 in 1996. In 1997 he invested an additional amount of 10000 and Mr Rakesh joined him with an amount of 35000. In 1998, Mr Shivkumar invested another additional amount of 10000 and Mr Suresh joined them with an amount of 35000. What will be Rakesh’s share in the profit of 150000 earned at the end of three years from the start of the business in 1996?
(A) 70000
(B) 50000
(C) 45000
(D) 75000
(E) None of these
Rationale: Ratio of their investments = 25,000 × 1 + 35000 × 1 + 45000 × 1 : 35000 × 2 : 35000 × 1 = 3 : 2 : 1.
∴ Rakesh’s share = 2⁄6 × 150000 = 50000
Answer B
Answer: (B) 50000
Question: There are 250 scraps. For each 11 cutting one extra can be obtained. How much maximum is possible, if one cut by one unit?
(A) 271
(B) 272
(C) 273
(D) 274
(E) 275
Rationale: 242 is divisible by 11.s0,22 extra will come.and another 8 remained.so,242+8+22=272
ANSWER:B
Answer: (B) 272
Question: a man have 800kg mango.he found 8% of its mango are rotten.then how much mango is rotten?
(A) 64
(B) 72
(C) 68
(D) 65
(E) 82
Rationale: 8% of 800kg =(800*8)/100.
=64 mangoes
answer A
Answer: (A) 64
Question: In a graduating class, 40 percent of the students are male. In this class, 50 percent of the male students and 40 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
(A) 0.44
(B) 0.5
(C) 0.56
(D) 0.62
(E) 0.68
Rationale: Let x be the total number of students.
The number students who are younger than 25 is 0.5*0.4x+0.6*0.6x = 0.56x
The answer is C.
Answer: (C) 0.56
Question: If 2x=y=6z, what is x-z, in terms of y?
(A) y
(B) 2y
(C) y/2
(D) y/3
(E) y/4
Rationale: 2x=y=6z
x = y/2
and z = y/6
x-z = y/2 - y/6 = y/3
Answer is D
Answer: (D) y/3
Question: which of the following could be the greatest common factor of positive integers 4 and 6 ? I) 8 II) 4 III) 2
(A) I only
(B) II only
(C) II,III only
(D) I, II only
(E) III only
Rationale: 4=2*2
6=2*3
GCF =2
Answer : E
Answer: (E) III only
Question: Ajay pays Rs 8.0 per litre of spirit. He adds water and sells the mixture at Rs 9 per litre, thereby making 40 % profit. The proportion of water to spirit received by the customers is
(A) 45:11
(B) 11:45
(C) 2:45
(D) 45:2
(E) None of these
Rationale: Suppose the quantity of spirit purchased = X lites
Suppose quantity of water mixed = Y litres
Required ratio of the water and the spirit in the mixture = Y:X
C.P. of x litres of spirit = Rs 8.0X
S.P of x litres of spirit = 9(X + Y)
Thus,C.P = S.P x 100/(100 + gain% )
=> 64 = (9X+9Y) x 100/100 + 40
=> 1120X =900X +900Y
=> 220X= 900Y
=> Y/X = 220/900 = 11/45
ANSWER:B
Answer: (B) 11:45
Question: Cole drove from home to work at an average speed of 80 kmh. He then returned home at an average speed of 120 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
(A) 66
(B) 70
(C) 72
(D) 75
(E) 78
Rationale: First round distance travelled (say) = d
Speed = 80 k/h
Time taken, T2 = d/80 hr
Second round distance traveled = d (same distance)
Speed = 120 k/h
Time taken, T2 = d/120 hr
Total time taken = 2 hrs
Therefore , 2 = d/80 + d/120
LCM of 80 and 120 = 240
2= d/80 + d/120
=> 2 = 3d/240 + 2d/240
=> d = 240 * 2/ 5 Km
Therefore, T1= d/80
=> T1 = (240 *2) / (5 x 80)
=> T1 = (6 x 60) / 5 -- in minutes
=> T1 = 72 minutes.
C
Answer: (C) 72
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 5% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
(A) 2:5
(B) 3:5
(C) 4:7
(D) 2:6
(E) 1:4
Rationale: 2% is 3%-points below 5% and 10% is 5%-points above 5%.
The ratio of A:B should be 3:5.
The answer is B.
Answer: (B) 3:5
Question: What will be the cost of building a fence around a square plot with area equal to 36 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 3944
(B) 2287
(C) 2977
(D) 2668
(E) 1392
Rationale: Let the side of the square plot be a ft.
a2 = 36=> a = 6
Length of the fence = Perimeter of the plot = 4a = 24 ft.
Cost of building the fence = 24 * 58 = Rs. 1392.
Answer:E
Answer: (E) 1392
Question: 2 dice are tossed. What is the probability that the total score is a prime no. is?
(A) 3/13
(B) 5/12
(C) 6/13
(D) 7/15
(E) 8/21
Rationale: 5/12
B
Answer: (B) 5/12
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
(A) Rs.18000
(B) Rs.15000
(C) s.17000
(D) Rs.14000
(E) Rs.19000
Rationale: Explanation:
25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: Option D
Answer: (D) Rs.14000
Question: 9 men are equal to as many women as are equal to 7 boys. All of them earn Rs.216 only. Men’s wages are?
(A) 6
(B) 5
(C) 2
(D) 8
(E) 2
Rationale: 9M = xW = 7B
9M + xW + 7B ----- 216 Rs.
9M + 9M + 9M ----- 216 Rs.
27M ------ 216 Rs. => 1M = 8Rs. Answer: D
Answer: (D) 8
Question: The average age of 3 girls is 24 years and their ages are in the proportion 1:2:3. The age of the youngest girl is?
(A) 10 years
(B) 11 years
(C) 12 years
(D) 13 years
(E) 14 years
Rationale: Total age of 3 boys = 24*3 =72
ratio of their ages = 1:2:3
Age of the youngest = 72*1/6 = 12 years
Answer is C
Answer: (C) 12 years
Question: In flip of coin seven times in a row, what is the probability that the result will not be tails at any ?
(A) 1/128
(B) 29/128
(C) 35/128
(D) 1/16
(E) 1/4
Rationale: In a flip of a coin seven times in a row, tails at no time means heads all the time
Heads = at least 7 heads
Atleast 7 heads in 7 flip.
The total outcome of flip is = 2^7 = 128
For any Coins problem write the ask in the shown format.
HHHHHHH
Once you have written in the above mentioned format the answer is pretty straight.
HHHHHHH = [7!]/[7!] = 1
Sum = 1 =
Answer = 1/128
Answer - A
Answer: (A) 1/128
Question: 12 buckets of water fill a tank when the capacity of each bucket is 49 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 7 litres?
(A) 39
(B) 84
(C) 80
(D) 82
(E) 86
Rationale: Capacity of the tank = (12 Ã— 49) litre
Number of buckets required of capacity of each bucket is 17 litre = 12Ã—49/7=12Ã—7=84
Answer is B
Answer: (B) 84
Question: As they say, beggars can't be choosers, in fact begger take what they can get. A begger on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the begger finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?
(A) 14
(B) 18
(C) 15
(D) 10
(E) 13
Rationale: A
14
If the beggar can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14.
Answer: (A) 14
Question: Given that x and y are nonnegative integers, compute the number of pairs (x, y) such that
5x + y = 20.
(A) 2
(B) 3
(C) 5
(D) 9
(E) 8
Rationale: For x = 0,1,2,3,4, there is a valid y, giving the answer 5 .
correct answer C
Answer: (C) 5
Question: A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
(A) 87 days
(B) 48 days
(C) 17 days
(D) 87 days
(E) 12 days
Rationale: B = 1/16 – 1/24
= 1/48
=> 48 days
Answer: B
Answer: (B) 48 days
Question: Of 64 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
(A) 54
(B) 55
(C) 59
(D) 71
(E) 92
Rationale: Total = 64
Thrower = 37
Rest = 64 - 37 = 27
Left Handed = 27/3 = 9
Right handed = 18
If all Thrower are right handed then total right handed is 37 + 18 = 55
so B. 55 is the right answer
Answer: (B) 55
Question: Roger can read a book in k minutes. What part of the book can he read in 9 minutes? (k>8)
(A) 8+k
(B) 8/k
(C) k/8
(D) (k+ 8)/k
(E) (k-8) / k
Rationale: Let's sayk = 24
That is, it takes 24 minutes to read the entire book.
So, in 8 minutes, Roger can read1/3of the book
So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24
A) 8+24=32ELIMINATE
B) 8/24=1/3KEEP
C)24/8 =3ELIMINATE
D) (24+ 8)/24=32/24 = 4/3ELIMINATE
E) (24-8) /24=16/24 = 2/3ELIMINATE
Answer: C
Answer: (C) k/8
Question: What is the dividend. divisor 14, the quotient is 9 and the remainder is 5?
(A) A)130
(B) B)131
(C) C)148
(D) D)158
(E) E)160
Rationale: D = d * Q + R
D = 14 * 9 + 5
D = 126 + 5
D = 131
Answer B
Answer: (B) B)131
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 2 professor, how many ways can this committee be formed?
(A) 36
(B) 64
(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.
64 is a factor of = 2^2*4^2
144 is a factor of = 2^4*3^2.
These are very different numbers and you cannot divide 144 with something to get to 64.
Answer: (B) 64
Question: How many three letter words are formed using the letters of the word LUNCH?
(A) A)15
(B) B)150
(C) C)12
(D) D)120
(E) E)18
Rationale: The number of letters in the given word is fIVE.
The number of three letter words that can be formed using these five letters is 5P4
= 5 * 4 * 3*2 = 120.
Answer:D
Answer: (D) D)120
Question: A person covered one-fourth of the total distance at 15 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
(A) 20 (1/8)kmph
(B) 20 (20/23)kmph
(C) 20 (17/23)kmph
(D) 27 (1/23)kmph
(E) 21 (1/8)kmph
Rationale: Let the total distance be x km
total time taken = (x/4)/15 + (3x/4)/24 = x/60 + x/32 = 23x/480
Average speed = x/(23x/480) = 480/23kmph
= 20 (20/23)kmph.
Answer:B
Answer: (B) 20 (20/23)kmph
Question: Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 70 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
(A) 11 : 6
(B) 12 : 7
(C) 13 : 7
(D) 15 : 6
(E) 13 : 6
Rationale: Sol. Distance travelled by Car A = 65 × 8 = 520 km
Distance travelled by Car B = 70 × 4 = 280 km
Ratio = 520/280 = 13 : 7
C
Answer: (C) 13 : 7
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
(A) 4/5
(B) 4/6
(C) 4/0
(D) 4/2
(E) 4/1
Rationale: x/3 – x/4 = 4/60
x = 4/5 km
Answer: A
Answer: (A) 4/5
Question: On the number line, the number p is twice as many units from -2 as -2 is from 4. If p is less than –2, what is the value of p ?
(A) –14
(B) –10
(C) –6
(D) 10
(E) 14
Rationale: Distance between -2 and 4 = 6
Since number p is twice as many units from -2 as -2 is from 4
, therefore p can be -14 Since , p is less than -2 ,
the value of p = -14
Answer A
Answer: (A) –14
Question: In a bag containing only blue, red and green marbles, all but 15 are blue, all but
13 are red and all but 12 are green. How many are red?
(A) 13
(B) 7
(C) 25
(D) 20
(E) 10
Rationale: All but blue means number of marbles except blue..hence, let x be the red marble,y
be the green marble,z be the blue marble...
x+y=15
y+z=13
x+z=12
solving this eqns, we get x=7 y=8 z=5 hence number of red marbles are 7
ANSWER:B
Answer: (B) 7
Question: A first grade teacher uses ten playing cards, each numbered from 1 to 10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?
(A) 70
(B) 60
(C) 50
(D) 40
(E) 30
Rationale: proble of combination 8C4 = 8!/4!*(8-4)! = 8*7*6*5*4!/4!*4! =70
A
Answer: (A) 70
Question: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 19th terms in the sequence?
(A) 2^18
(B) 3(2^17)
(C) 7(2^16)
(D) 3(2^16)
(E) 11(2^15)
Rationale: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...
so 16th term will be 2^15
17th term 2^16
19th term 2^18
adding all three
we get
2^15+(2^15)*2+(2^15)*8
so answer is 2^15(1+2+8)=>11(2^15)
answer E
Answer: (E) 11(2^15)
Question: In an xy-coordinate plane, a line is defined by y = kx + 1. If (1, b), (a, 4), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?
(A)  1/2
(B)  1
(C)  3/2
(D)  2
(E)  5/2
Rationale: b=k+1...(1)
b+1=ak+1...(2)
4=ak+1...(3)
Taking (2) and (3)
4=b+1
b=3
Taking (1)
3=k+1
k=2
Answer : D
Answer: (D)  2
Question: If the height of a cone is increased by 190% then its volume is increased by?
(A) 100
(B) 777
(C) 998
(D) 190
(E) 2879
Rationale: 100%
Answer:D
Answer: (D) 190
Question: A set of numbers has the property that for any number t in the set,t+3 is in the set. If -2 is in the set, which of the following must also be in the set? I. -3 II. 1 III. 4
(A) I,III only
(B) III only
(C) II only
(D) II,III only
(E) I only
Rationale: question is asking for must be there elements.
According to the question if t is there t+3 must be there.
if -2 is the starting element the sequence is as follows.
S ={-2,1,4,7,10....}
if -2 is not the starting element the sequence is as follows
S = {...-5,-2,1,4,7,10...}
By observing the above two sequences we can say that 1,4 must be there in set S.
Answer : D
Answer: (D) II,III only
Question: If a:b = 2:3 and b:c = 4:3, then find a:b:c
(A) 8:12:9
(B) 2:3:8
(C) 2:3:9
(D) 2:3:12
(E) None of these
Rationale: Explanation:
a:b=2:3
b:c=4:3=(4∗3/4:3∗3/4)
=3:9/4
a:b:c=2:3:9/4
=8:12:9
Option A
Answer: (A) 8:12:9
Question: If the L.C.M of two numbers is 660 and their product is 18480, find the H.C.F of the numbers.
(A) 50
(B) 30
(C) 125
(D) 25
(E) None of these
Rationale: H.C.F = (Product of the numbers) / (Their L.C.M) = 18480/660 = 28.
ANSWER:E
Answer: (E) None of these
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 4
(B) 5
(C) 8
(D) 9
(E) 6
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Answer: (C) 8
Question: The average of 6 no.'s is 5.40. The average of 2 of them is 5.2, while the average of the other 2 is 5.80. What is the average of the remaining 2 no's?
(A) 5.2
(B) 2.6
(C) 3.6
(D) 4.5
(E) 4.6
Rationale: Sum of the remaining two numbers = (5.40 * 6) - [(5.2 * 2) + (5.8 * 2)]
= 32.40 - (10.4+ 11.6) = 32.40 - 22.0 = 10.40.
Required average = (10.4 / 2) = 5.2
Answer : A
Answer: (A) 5.2
Question: The simple Interest on a certain sum of money at the rate of 4% p.a. for 5 years is Rs. 1680. At what rate of interest the same amount of interest can be received on the same sum after 4 years ?
(A) 5%
(B) 6%
(C) 8%
(D) 4%
(E) 7%
Rationale: S.I. = 1680, R = 4% T = 5 years
Principal = (100 *1680)/ (5*4) = 8400
So P = 8400
Rate = (100 *1680)/ (8400 * 4) = 5%
ANSWER:A
Answer: (A) 5%
Question: The average of first 20 prime numbers is?
(A) 9.5
(B) 8.6
(C) 9.3
(D) 9.6
(E) 9.8
Rationale: Explanation:
Average = (2+3+5+7+11+13+17+19/8 = 77/8= 9.6(Approx)
Answer is D
Answer: (D) 9.6
Question: At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:30 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:40 PM, in terms of p, r, and s, do the two trains pass each other?
(A) 0.5 + (p - 0.5s)/(r + s)
(B) (p - 0.5s)/(r + s)
(C) 0.5 + (p - 0.5r)/r
(D) (p - 0.5r)/(r + s)
(E) 0.5 + (p - 0.5r)/(r + s)
Rationale: The distance A is going to cover between 1:00 and 1:30
= .5r
now the distance between the two trains = (p-.5r)
the relative velocity = (r-(-s)) = r+s
From 1:30, time is going to take when they meet = (p-.5r)/(r+s)
so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]
ans is C
Answer: (C) 0.5 + (p - 0.5r)/r
Question: A work crew of 7 Men takes 10 days to complete one-half of a job. If 8 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?
(A) 2
(B) 3
(C) 3 1/3
(D) 4
(E) 4 2/3
Rationale: Suppose 1 man can do work in X days..
so 7 men will do in ..
7/X=1/10*1/2 as half job is done
X=140
now 8 more are added then
15/140=1/2*1/d for remaining half job
d=4 2/3 Number of days
E
Answer: (E) 4 2/3
Question: If the annual interest on a principal is 25%, how many years before the amount is double?
(A) 2
(B) 3
(C) 7
(D) 4
(E) 5
Rationale: P = (P*25*R)/100
R = 4%
Answer: D
Answer: (D) 4
Question: A 10-by-4 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
(A) The volume of the cylinder with height 10 is 40/pi cubic inches greater than the volume of the cylinder with height 6.
(B) The volume of the cylinder with height 4 is 40/pi cubic inches greater than the volume of the cylinder with height 10.
(C) The volume of the cylinder with height 10 is 40pi cubic inches greater than the volume of the cylinder with height 6.
(D) The volume of the cylinder with height 4 is 40pi cubic inches greater than the volume of the cylinder with height 10.
(E) The volume of the cylinder with height 4 is 240/pi cubic inches greater than the volume of the cylinder with height 10.
Rationale: Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 4 and 10 are the circumference of the base and not the radius. B is the right answer.
Answer: (B) The volume of the cylinder with height 4 is 40/pi cubic inches greater than the volume of the cylinder with height 10.
Question: How many positive integers less than 300 are there such that they are multiples of 17 or multiples of 16?
(A) 31
(B) 32
(C) 33
(D) 34
(E) 35
Rationale: 300/17 = 17 (plus remainder) so there are 17 multiples of 17
300/16 = 18 (plus remainder) so there are 18 multiples of 16
We need to subtract 1 because 17*16 is a multiple of both so it was counted twice.
The total is 17+18-1 = 34
The answer is D.
Answer: (D) 34
Question: What is the unit’s digit of 7^8?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 7^1=7
7^2=49
7^3=343
7^4=1(last digit)
7^5=7(last digit) and the cycle repeats after every 4 powers
Therefore, last digit of 7^8=1
Answer A
Answer: (A) 1
Question: A certain experimental mathematics program was tried out in 2 classes in each of 38 elementary schools and involved 44 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
(A) 0 and 13
(B) 0 and 14
(C) 0 and 16
(D) 1 and 9
(E) 2 and 8
Rationale: One may notice that greatest possible values differ in each answer choice in contrast to the least values, which repeat.
To find out the greatest value you should count the total classes (38*2=76), then subtract the total #of teachers since we know from the question that each teacher taught at least one class (76-44=32). Thus we get a number of the available extra-classes for teachers, and all that we need is just to count how many teachers could take 2 more classes, which is 32/2 = 16. So the greatest possible value of the # of teachers who had 3 classes is 16.
Only answer C has this option.
Answer: (C) 0 and 16
Question: A student traveled 25 percent of the distance of the trip alone, continued another 40 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip?
(A) 120
(B) 140
(C) 160
(D) 180
(E) 200
Rationale: Let x be the total length of the trip.
0.25x + 40 miles + 0.5x = x
40 miles = 0.25x
x = 160 miles
The answer is C.
Answer: (C) 160
Question: X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs. 720. With the help of Z they finished it in 5 days. How much is paid to Z?
(A) Rs. 360
(B) Rs. 120
(C) Rs. 240
(D) Rs. 300
(E) None
Rationale: Solution:
In one day X can finish 1/15th of the work.
In one day Y can finish 1/10th of the work.
Let us say that in one day Z can finish 1/Zth of the work.
When all the three work together in one day they can finish 1/15 + 1/10 + 1/Z = 1/5th of the work.
Therefore, 1/Z = 1/30.
Ratio of their efficiencies = 1/15: 1/10: 1/30 = 2: 3: 1.Therefore Z receives 1/6th of the total money.
According to their efficiencies money is divided as 240: 360: 120.
Hence, the share of Z = Rs. 120.
Answer B
Answer: (B) Rs. 120
Question: What is the are of an equilateral triangle of side 8 cm?
(A) 11√3
(B) 12√3
(C) 16√3
(D) 15√3
(E) 18√3
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 8, Area of triangle = √3/4 * 8 * 8
= 16√3 cm2;
Answer:C
Answer: (C) 16√3
Question: In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,8). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?
(A) 1/5
(B) 1/3
(C) 1/2
(D) 2/3
(E) 4/5
Rationale: The area of the right triangle is (1/2)*4*8 = 16.
Only the points (a,b) below the line y=x satisfy a - b > 0.
The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.
P(a - b > 0) = 8/16 = 1/2
The answer is C.
Answer: (C) 1/2
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
(A) 1.44%
(B) 2.45%
(C) 7.44%
(D) 8.44%
(E) 2.44%
Rationale: Explanation:
SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%
Answer: A
Answer: (A) 1.44%
Question: There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R?
(A) 12
(B) 23
(C) 28
(D) 80
(E) 84
Rationale: The number of ways in which one can travel from P to R = 3 × 4 = 12
Answer is A
Answer: (A) 12
Question: If the average (arithmetic mean) of a and b is 40 and the average of b and c is 60, what is the value of c − a?
(A) 25
(B) 40
(C) 90
(D) 140
(E) It cannot be determined from the information given.
Rationale: -(a + b = 80)
b + c=120
c-a=40
B. 40
Answer: (B) 40
Question: Calculate the L.C.M of 2/5, 4/ 7, 3/7, 6/13 is :
(A) 15
(B) 14
(C) 13
(D) 12
(E) 11
Rationale: Required L.C.M =L.C.M. of 2, 4, 3, 6/H.C.F. of 5, 7, 7, 13 =12/1=12
Answer is D
Answer: (D) 12