mathewhe/aqua_rat huggingface dataset:
Question: A 15 by 20 rectangle is inscribed in circle. What is the circumference of the circle?
(A) 5π
(B) 10π
(C) 15π
(D) 20π
(E) 25π
Rationale: The diagonal of the rectangle will be the diameter of the circle.
and perimeter= 2*pi*r
Ans: E
Answer: (E) 25π
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
(A) 20088
(B) 20000
(C) 67892
(D) 28826
(E) 25781
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
Answer: B
Answer: (B) 20000
Question: 5358 x 54 = ?
(A) 272258
(B) 272358
(C) 289332
(D) 274258
(E) 274358
Rationale: 5358 x 51	= 5358 x (50 + 4)
= 5358 x 50 + 5358 x 4
= 267900 + 21432
= 289332.
C)
Answer: (C) 289332
Question: At what angle the hands of a clock are inclined at 15 minutes past 5?
(A) 65°
(B) 67.8°
(C) 67.5°
(D) 69.5°
(E) 67.2°
Rationale: Hence the angle
=30(5-15/5)+15/2
=30(5-3)+7.5
=30 X 2 + 7.5+=67.5 °
Answer C
Answer: (C) 67.5°
Question: There are some goats in James farm. If they don't die for any reason James can make new farm in 6 years with baby goat and older goats. But goats die for many reason, if no baby goats are born the farm will be empty in 12 years. If new babies are born and older die in same time , how many time needed for make a new farm?
(A) 10
(B) 15
(C) 5
(D) 12
(E) 20
Rationale: Goats die in every year = 1/12
Goats born in every year = 1/6
Total growth in every year = 1/6 - 1/12 = 1/12
So James can make a new farm in = 12 years
ANSWER:D
Answer: (D) 12
Question: The population of a town increases 10% and 20% respectively in two consecutive years. After the growth the present population of the town is 1320. Then what is the population of the town 2 years ago?
(A) 1100
(B) 1001
(C) 1010
(D) 1000
(E) 1002
Rationale: Explanation:
Formula: (After =100 denominator
Ago = 100 numerator)
1320 * 100/110 * 100/120 = 1000
Answer: Option D
Answer: (D) 1000
Question: The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 80 minutes after it was poured was how many degrees Fahrenheit?
(A) 45
(B) 56
(C) 60.4
(D) 85
(E) 90
Rationale: Answer: B
The temperature of coffee 10 minutes after it was poured (120 F) will help in solving the constant “a”.
120 = 120(2 ^ 10a) + 60
2 ^ -1 = 2 ^ 10a
a = -1/10
The temperature of coffee 80 minutes after it was poured is:
F = 120 ( 2 ^ -80/10) + 60
F = 120 * 1/ 256 + 60
F = 15/32 + 60
F = 1935/32=60.4
C
Answer: (C) 60.4
Question: If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by how much % should he reduce the quantity of gasoline that he buys?
(A) 10%
(B) 12.5%
(C) 8%
(D) 12%
(E) 6.66%
Rationale: Explanatory Answer
Let the price of 1 litre of gasoline be $x and let Ron initially buy 'y' litres of gasoline.
Therefore, he would have spent $xy on gasoline.
When the price of gasoline increases by 25%, the new price per litre of gasoline is 1.25x.
Ron intends to increase the amount he spends on gasoline by 15%.
i.e., he is willing to spend xy + 15% of xy = 1.15xy
Let the new quantity of gasoline that he can get be 'q'.
Then, 1.25x * q = 1.15xy
Or q = 1.15xy/1.25x = 0.92y.
As the new quantity that he can buy is 0.92y, he gets 0.08y lesser than what he used to get earlier.
Or a reduction of 8%.
The correct choice is (C)
Answer: (C) 8%
Question: A certain number of men can do a work in 54days. If there were 6 men more it could be finished in 6 days less. How many men were there in the beginning?
(A) 50
(B) 48
(C) 70
(D) 40
(E) 50
Rationale: Explanation:
m(54) = (m+6)(48)
9m-8m=48
M=48
Answer: Option B
Answer: (B) 48
Question: A retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price q of the machine?
(A) 	81
(B) 	100
(C) 	120
(D) 	135
(E) 	160
Rationale: Since the wholesale price was $90 and the profit was 20% of the wholesale price ([.2][90] = $18), the retail price would have to be above $108, but not that much greater than that.
Let's start by TESTing Answer C: $120....
If.....
Retail Price q= $120
10% discount off = $120 - (.1)(120) = 120 - 12 = 108
20% profit on wholesale price = 90 + (.2)(90) = 90 + 18 = 108
These two numbers MATCH, so this MUST be the answer!
Final Answer:
[Reveal]Spoiler:
C
Answer: (C) 	120
Question: In 40 litres of a mixture the ratio of milk to water is 7:1. In order to make the ratio of milk to water as
3:1, the quantity of water that should be added to the mixture will be
(A) 523 litre
(B) 413 litre
(C) 623 litre
(D) 6 litre
(E) None of these
Rationale: Explanation :
By the rule of alligation, we have
Concentration of water
in pure water : 1 Concentration of water
in mixture : 1/8
Concentration of water in the final mixture
1/4
1/4 - 1/8 = 1/8 1 - 1/4 = 3/4
Quantity of water : Quantity of mixture = 1/8 : 3/4 = 1 : 6
Given that quantity of mixture = 40 litre
=>Quantity of water : 40 = 1 : 6
⇒Quantity of water = 40×16=623 litre
Answer : Option C
Answer: (C) 623 litre
Question: A computer program generates a sequence of numbers a1, a2, a3, ... such that a1=1, a2=2, and ak=a(k-1)*5 - 3 for 2 < k < n. If n = 10, find a5.
(A) 115
(B) 137
(C) 141
(D) 151
(E) 157
Rationale: a1=1
a2=2
a3=2*5-3=7
a4=7*5-3=35-3=32
a5=32*5-3=160-3=157
157
Answer: (E) 157
Question: Of the 8 distinguishable wires that lead into an apartment, 2 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Given:
Total number of wires = 5
Number of cable wires = 2
Number of telephone wires = 3
To find:
Number of combination which has at least one cable wires
Solution:
No of ways of selecting'at least'1 cable wire means, we can select more than one as well. The minimum we can select is one and the maximum we can select, given the constraints that 3 wires need to be selected in total and there are 2 cable wires, is 2
Since it is a combination of wires, the arrangement is not important
Approach 1:
Number of ways of selecting at least one cable wire in a selection of 3 wires from 5 wires =Selection 1(Number of ways of selecting one cable wire and two telephone wires )+Selection 2(Number of ways of selecting two cable wires and 1 telephone wire)
Selection 1
Number of ways of selecting one cable wire = 2C1 = 2
Number of ways of selecting 2 telephone wires = 3C2 = 3
Total = 2C1 * 3C2 = 6 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 2
Number of ways of selecting one cable wire = 2C2 = 1
Number of ways of selecting 2 telephone wires = 3C1 = 3
Total = 2C2 * 3C1 = 3 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 1 + Selection 2 = 9 ways of selecting 3 wires out of 5 such that at least one is a cable wire
Approach 2
Number of ways of selecting 3 wires out of 5 such that at least one is a cable wire =Selection X(Total number of ways of selecting 3 wires from the 5) -Selection Y(total ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires)
Total number of ways of selecting 3 wires out of 5 = 5C2 = 10
Number ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires = 3C3 ( 3 telephone wires and we are selecting all the three at once) = 1
Selection X - Selection Y = 8
Answer is Option C
Answer: (C) 8
Question: 16 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?
(A) 5
(B) 2
(C) 8
(D) 4
(E) 16
Rationale: 1. We need to find out the time taken by 7 workers after day 1.
2. total no.of wokers * total time taken = time taken by 1 worker
3. Time taken by 1 worker = 16*8 = 128 days
4. But on day 1 sixteen workers had already worked finishing 1/8 of the job. So 7 workers have to finish only 7/8 of the job.
5. Total time taken by 7 workers can be got from formula used at (2). i.e., 7* total time taken = 128. Total time taken by 7 workers to finish the complete job is 128/7 = 18.286 days.
6. Time taken by 7 workers to finish 7/8 of the job is 7/8 * 18.286 = 16 days.
The answer is choice E
Answer: (E) 16
Question: a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (8/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
(A)  3/8
(B)  1/2
(C)  11/16
(D)  5/7
(E)  3/4
Rationale: The answer isC: 11/16.
The key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean. For example, the mean and median of a set consisting of x, x+1, x+2, ... ,y will always be (x+y)/2.
For set S, consisting of numbers (a, a+1,...,b), the median is given to be 3/4*b:
(a+b)/2 = (3/4)*b
a = b/2
For set Q, consisting of numbers (b, b+1,...,c), the median is given to be 8/8*c:
(b+c)/2 = (8/8)*c
b = (1)*c
For set R, consisting of numbers (a, a+1,...c), the median needs to be found:
a = b/2 = (1*c)/2 = (1/2)*c
Median = (a + c)/2 = (1/2*c + c)/2 = (3/2)*c/2 = (3/4)*c (ANSWER E)
Answer: (E)  3/4
Question: The present population of a town is 200. Population increase rate is 10% p.a. Find the population of town after 1 years?
(A) 100
(B) 120
(C) 200
(D) 220
(E) 250
Rationale: P = 200
R = 10%
Required population of town = P*(1 + R/100)^T
= 200*(1 + 10/100)
= 200*(11/10)
= 220(approximately)
Answer is D
Answer: (D) 220
Question: In an examination, a student scores 3 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 120 questions and secures 180 marks, the number of questions he attempts correctly, is:
(A) 45
(B) 90
(C) 80
(D) 75
(E) 70
Rationale: Let the number of correct answers be x.
Number of incorrect answers = (120 â€“ x).
3x â€“ (120 â€“ x) = 180 or 4x = 300 or x = 75
ANSWER:D
Answer: (D) 75
Question: The average of five numbers is 45. If one number is excluded, the average becomes 38. The excluded number is?
(A) 8
(B) 73
(C) 58
(D) 35
(E) 96
Rationale: Excluded number
= (45 * 5) - (38 * 4)
= 225 - 152 = 73
Answer:B
Answer: (B) 73
Question: Average of 11 results is 59. If the average of first five results is 55 and average of last five results is 60 Then find the sixth result?
(A) 71
(B) 85
(C) 86
(D) 74
(E) 69
Rationale: Option 'D'
Answer: (D) 74
Question: 1/2 divived by 1/2 of 1/2 whole divided by 1/2 +1/2 of 1/2
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 1/2 divided by 1/2 of 1/2 :
1/2 of 1/2 = 1/2*1/2 = 0.25
1/2 divided by .25 = 2
1/2+1/2 of 1/2:
1/2+1/2 = 1
1 of 1/2 = 0.5
1/2 divived by 1/2 of 1/2 ) whole divided by 1/2 +1/2 of 1/2
2/0.5 = 4
ANSWER:B
Answer: (B) 4
Question: If S is the sum of reciprocals of a list of consecutive integers from 44 to 55, inclusive, S is approximately equal to
(A) 0.1
(B) 0.2
(C) 0.3
(D) 0.4
(E) 0.5
Rationale: We need to find the approximate value of 1/44 + 1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53. Now, the sum of these 10 terms will be very close to 10 times 1/50, which is 0.02*10=0.2.
Answer: B.
Answer: (B) 0.2
Question: Calculate the total gain or loss of a shop owner who sold two items for Rs. 1200 each, if he made a profit of 15% from the first item and a loss of 15% from the second item.
(A) 24.5
(B) 14.5
(C) 2.25
(D) 5.5
(E) 2.5
Rationale: (15*15)/100 = 2.25%
Answer: C
Answer: (C) 2.25
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.900, what is the reduced price for kg?
(A) s.40
(B) s.46
(C) s.49
(D) s.45
(E) s.42
Rationale: 900*(25/100) = 225 ---- 5
? ---- 1
=> Rs.45
Answer: D
Answer: (D) s.45
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 21.0 sec
(B) 12.1 sec
(C) 13.9 sec
(D) 43.9 sec
(E) 37.9 sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B
Answer: (B) 12.1 sec
Question: An investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?
(A) 3
(B) 4
(C) 6
(D) 9
(E) 12
Rationale: Assume initial amount is x
Annual Interest is 34.1% so after 1 year the amount will become x * (100+34.1)/100 => x*4/3
now we need to find n for x * (4/3)^n = 3x ;or in other words n = 4
ANSWER:B
Answer: (B) 4
Question: Average of first five multiples of 8 is
(A) 9
(B) 11
(C) 24
(D) 15
(E) 16
Rationale: Explanation:
Average=8(1+2+3+4+5)/5=24
Answer: Option C
Answer: (C) 24
Question: Three balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?
(A) 60
(B) 90
(C) 120
(D) 150
(E) 180
Rationale: Since the balls are all of different colors, let's permute them and then decide how many balls we put in each box.
For example, arrange in a row the balls, then decide: two balls go into the first box, next two in the second box, and the last ball goes to the third box.
Since in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes.
For the 2,2,1 type arrangements, we have [5!/(2!2!1!)]*3 = 90 possibilities. Inside a box, it doesn't matter the order of the balls.
For the 3,1,1 type arrangements, we have [5!/(3!1!1!)]*3 = 60 possibilities.
Total of 40 + 20 = 60 possibilities.
Answer A.
Answer: (A) 60
Question: An anti- aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shots are 0.4, 0.3, 0.2 and 0.1 respectively.
What is the probability that the plane is hit when all the four shots are fired?
(A) 0.6872
(B) 0.4379
(C) 0.6976
(D) 0.1274
(E) None of these
Rationale: Solution:
Required probability:
=(0.4Ã—0.7Ã—0.8Ã—0.9)+(0.6Ã—0.3Ã—0.8Ã—0.9)+(0.6Ã—0.7Ã—0.2Ã—0.9)+(0.6Ã—0.7Ã—0.8Ã—0.1)+(0.4Ã—0.3Ã—0.8Ã—0.9)+(0.4Ã—0.7Ã—0.2Ã—0.9)+(0.4Ã—0.7Ã—0.8Ã—0.1)+(0.6Ã—0.3Ã—0.2Ã—0.9)+(0.6Ã—0.3Ã—0.8Ã—0.1)+(0.6Ã—0.7Ã—0.2Ã—0.1)+(0.4Ã—0.3Ã—0.2Ã—0.9)+(0.6Ã—0.3Ã—0.2Ã—0.1)+(0.4Ã—0.3Ã—0.8Ã—0.1)+(0.4Ã—0.7Ã—0.2Ã—0.1)+(0.4Ã—0.3Ã—0.2Ã—0.1)
=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002
=0.6976
ANSWER IS C
Answer: (C) 0.6976
Question: A company recently conducted a survey and found that 30,000 of its customers live in rural areas. If the number of customers who live in urban areas is 130 percent greater than the number of customers who live in rural areas, how many customers live in urban areas?
(A) 65,000
(B) 67,000
(C) 69,000
(D) 71,000
(E) 73,000
Rationale: The number of customers in urban areas is 30,000+1.3*30,000=69,000.
The answer is C.
Answer: (C) 69,000
Question: At the opening of a trading day at a certain stock exchange, the price per share of stock K was $6. If the price per share of stock K was $8 at the closing of the day, what was the percent increase in the price per share of stock K for that day?
(A) 1.4%
(B) 5.9%
(C) 11.1%
(D) 12.5%
(E) 33.33%
Rationale: Opening = 6
Closing = 8
Rise in price = 2
So, percent increase = 2/6*100 =33.33%
Answer : E
Answer: (E) 33.33%
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
(A) 2
(B) 3
(C) 5
(D) 81
(E) 6
Rationale: :
1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
1/4 + 9/20 = 14/20
1 h ---- 1/20
? ----- 14/20
14 hours ==> 5 PM.Answer: D
Answer: (D) 81
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation h of the mean, what percent of the distribution is less than m+h?
(A)  16%
(B)  32%
(C)  48%
(D)  84%
(E)  92%
Rationale: 16%
________________________________________________ m+h
34%
________________________________________________ m
34%
________________________________________________ m-h
16%
since 68% lies one standard deviation from mean m, => 50% of 68% lies on either side as it is symmetric about m.
thus 16% lie below m-h and 16% lie above m+h
now below m+h = 16+34+34 = 84%
hence D
Answer: (D)  84%
Question: Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married ?
(A) 23 years
(B) 25 years
(C) 33 years
(D) 35 years
(E) 45 years
Rationale: Ayush's present age = 10 years.
His mother's present age = (10 + 20) years = 30 years.
Ayush's father's present age = (30 + 5) years = 35 years.
Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years.
Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.
ANSWER:A
Answer: (A) 23 years
Question: The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
(A) 9 : 29
(B) 9 : 23
(C) 9 : 24
(D) 9 : 25
(E) 9 : 21
Rationale: a13 : a23 = 27 : 125
a1 : a2 = 3 : 5
6 a12 : 6 a22
a12 : a22 = 9 : 25
Answer: C
Answer: (C) 9 : 24
Question: A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/8 of th area of the garden. What is the radius of the circular garden?
(A) 1
(B) 2
(C) 4
(D) 8
(E) 16
Rationale: as per the question-- width is negligible
now,
let L be the length of the fence =2pir
L=1/8(pir^2)
pir^2=16pir
r=16
Answer : E
Answer: (E) 16
Question: 107 x 107 + 93 x 93 =?
(A) 19578
(B) 19418
(C) 20098
(D) 21908
(E) None of them
Rationale: =(107)^2+(93)^2
=(100+7)^2+(100-7)^2
=2 x [(100)^2+7^2]
=2[10000+49]
=2 x 10049 = 20098
Answer is C
Answer: (C) 20098
Question: What quantity of water should taken out to concentrate 18 liters of 40% acidic liquid to 60% acidic liquid?
(A) 5liters
(B) 10liters
(C) 15liters
(D) 8liters
(E) 6liters
Rationale: Required answer is = 18(60-40)/60 = 6 liters
Answer is E
Answer: (E) 6liters
Question: To furnish a room in a model home an interior decorator is to select 3 chairs and 3 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 6 chairs in the warehouse and if 80 different combinations are possible, how many tables are there in the warehouse?
(A) A)4
(B) B)8
(C) C)10
(D) D)15
(E) E)30
Rationale: Total number of ways to choose 3 chairs from 6= 6C3=20
Total number of combination=80
That means we need get 4 combinations from the selection of tables....
Screening through the answers.... 4C3=4..... 4*20=80
Answer is 6... A
Answer: (A) A)4
Question: A and B began business with Rs.6000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
(A) 240
(B) 288
(C) 277
(D) 357
(E) 361
Rationale: (6*8 + 5*4):(4*8 + 5*4)
17:13
17/30 * 630 = 357
Answer: D
Answer: (D) 357
Question: If x and y are non-zero integers, and 25x^4 – 4y^4 = 5x^2 + 2y^2, which of the following could be the value of x2 in terms of y?
(A) 2y^2+1/6
(B) 2y^2/5
(C) 2y^2
(D) 2y^2+1/5
(E) 2y
Rationale: 25x^4 – 4y^4 = 5x^2 + 2y^2
(5x^2 + 2y^2) (5x^2 - 2y^2) = 5x^2 + 2y^2
5x^2 - 2y^2 = 1
5x^2 = 2y^2+1
x^2 = 2y^2+1/5
Answer : D
Answer: (D) 2y^2+1/5
Question: If four coins are tossed, the probability of getting two heads and two tails is?
(A) 3/8
(B) 3/5
(C) 3/9
(D) 3/3
(E) 3/1
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24
= 3/8
Answer: A
Answer: (A) 3/8
Question: A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 45 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: A- B = 120 Miles
B - C = 60 Miles
Avg Speed = 45 Miles
Time taken for A-B 3t and B-C be t
avg speed = (120+60) / Total time
45 = 180/4t
t = 60
B-C = 60 mph
Answer E
Answer: (E) 60
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5
(B) 2.3
(C) 2.4
(D) 2.1
(E) 2.6
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: A
Answer: (A) 2.5
Question: x and y are positive integers. If xy + x is even, then which of the following must be even?
(A) x
(B) y
(C) x + y
(D) y+1
(E) x^2 − y
Rationale: Given that xy + x is even, which means x(y+1) is even.
Product of two nos. will be even only if both the nos. are odd.
Hence x is odd, y+1 is also even.
y+1 is even. Answer will be D.
Answer: (D) y+1
Question: A certain club has 8 members, including Harry. One of the 8 members is to be chosen at random to be the president, one of the remaining 7 members is to be chosen at random to be the secretary, and one of the remaining 6 members is to be chosen at random to be the treasurer. What is the probability that Harry will either be the secretary or the member chosen to be the treasurer?
(A) 1/4
(B) 2/4
(C) 3/4
(D) 1
(E) 5/4
Rationale: Each member out of 8, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/8 and the probability that Harry will be selected to be the treasurer is also 1/8. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/8+1/8=2/8.
Answer: A.
Answer: (A) 1/4
Question: The grade point average of one third of the classroom is 45; the grade point average of the rest is 60. What is the grade point average of the whole class?
(A) 54
(B) 55
(C) 60
(D) 65
(E) 70
Rationale: Let n=total students in class
total points for 1/3 class=45n/3=15n
total points for 2/3 class=60*2n/3=40n
total points for whole class=15n+40n=55n
63n total class points/n total students=55 grade point average for total class
Answer : B
Answer: (B) 55
Question: Pipe A and pipe B fill water into a tank of capacity 5000 litres, at a rate of 200 l/min and 50 l/min. Pipe C drains at a rate of 25 l/min. Pipe A is open for 1 min and closed, then pipe B is open for 2 min and closed. Further the pipe c is opened and drained for another 2 min. This process is repeated until the tank is filled. How long will it take to fill the tank?
(A) 120
(B) 100
(C) 140
(D) 80
(E) 90
Rationale: tank capacity: 5000 L,
1st- 200 l/min for 1 min, volume filled: 200 L
2nd- 100 l/min for 2 min, volume filled: 100 L
3rd (water draining) : 25 l/min*2 : 50 L
total : (200+100)-50 =250 L filled for 1 cycle
number of 250 in 5000 L tank :1000/250 = 20
time taken to fill: 20* total time= 20*5 = 100 (option B)
Answer: (B) 100
Question: The ratio between the present age 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) 8:7
(B) 7:8
(C) 8:6
(D) 6:7
(E) 6:8
Rationale: Let p and q's age is 6x and 7 x years respectively .7x-6x=4
x=4
Required ratio =(6x+4):(7x+4)
=28:32
=7:8
option A is answer
Answer: (A) 8:7