mathewhe/aqua_rat huggingface dataset:
Question: A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements Q of plays can be run, if the same play can’t be run more than once?
(A) 24
(B) 125
(C) 243
(D) 504
(E) 729
Rationale: Number of Q ways to choose the first play: 9
Second play: 8
Third:7
9*8*7= 504.D
Answer: (D) 504
Question: An express traveled at an average speed of 100 km/hr, stopping for 4 min after every 60 km. How long did it take to reach its destination 600 km from the starting point ?
(A) 8 hrs 29 min
(B) 6 hrs 28 min
(C) 2 hrs 28 min
(D) 6 hrs 28 min
(E) 6 hrs 36 min
Rationale: Explanation:
Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/60 - 1 = 9
Total time of stoppages = 4 x 9 = 36 min
Hence, total time taken = 6 hrs 36 min.
Answer: E
Answer: (E) 6 hrs 36 min
Question: A machine, working at a constant rate, manufactures 20 candles in 40 minutes. How many candles does it make in 1 hr 20 min?
(A) 25
(B) 30
(C) 40
(D) 45
(E) 50
Rationale: Change 1 hr 20 min to 80 min. For this, we need to set up a simple proportion of staplers per time 20/40= S/80
The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. Instead, cancel before you multiply. For what we can and can’t cancel in a proportion, seethis post. We can cancel the factor of 10 in the 20 and 40.
2/4 = S/80
1/2 = S/80 ; 1/2*2 = S/80*2
1/1=S/40
Now that the fraction is entirely simplified, we can cross-multiply.
S = 1*40= 40
The machine would be 40 candles in 1 hr 20 min.
Answer: C.
Answer: (C) 40
Question: When 52416 is divided by 312, the quotient is 168. what will be the quotient when 52.416 is divided by 0.168?
(A) 5
(B) 6
(C) 4
(D) 3
(E) 8
Rationale: for the 1st no. there are 2 digits after decimal
for the 2nd no. there are 4 digits after decimal
total no. of decimals = 6
req. no. of digits=(n-1)=(6 -1)=5
ANSWER :A
Answer: (A) 5
Question: The average weight of 5 person's increases by 5.5 kg when a new person comes in place of one of them weighing 68 kg. What might be the weight of the new person?
(A) 60 kg
(B) 95.5 kg
(C) 80 kg
(D) 85 kg
(E) 90 kg
Rationale: Total weight increased = (5 x 5.5) kg = 27.5 kg.
Weight of new person = (68 + 27.5) kg = 95.5 kg
Option B
Answer: (B) 95.5 kg
Question: The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
(A) 1:7
(B) 2:9
(C) 1:9
(D) 3:7
(E) 3:4
Rationale: r1: r2 = 1: 3
Πr12: Πr22
r12: r22 = 1:9
Answer: C
Answer: (C) 1:9
Question: How many zeros does 50! end with?
(A) 20
(B) 24
(C) 25
(D) 12
(E) 32
Rationale: According to above 50! has 50/5+50/25=10+2=12trailing zeros.
Answer: D.
Answer: (D) 12
Question: In a family 4 people eat only vegetarian, 3 people eat only non veg., 2 people eat both veg and non veg.. How many people are in the family?
(A) 4
(B) 3
(C) 10
(D) 2
(E) 9
Rationale: Total number of people in family= veg+non veg+(both veg and non veg)
Total= 4+3+2 = 9
Answer is E
Answer: (E) 9
Question: A train running at a speed of 36 km/h passes an electric pole in 15 seconds. In how many seconds will the whole train pass a 370-meter long platform?
(A) 46
(B) 48
(C) 50
(D) 52
(E) 54
Rationale: Let the length of the train be x meters.
When a train crosses an electric pole, the distance covered is its own length x.
speed = 36 km/h = 36000 m / 3600 s = 10 m/s
x = 15 * 10 = 150 m.
The time taken to pass the platform = (150 +370)/ 10 = 52 seconds
The answer is D.
Answer: (D) 52
Question: If q = 25! + 1, which of the following cannot be a prime factor of q?
I. 11
II. 19
III. 23
(A) I​ only
(B) III only
(C) II and III
(D) I and II
(E) I​, II, and III
Rationale: The numbers 11, 19, and 23 are all factors of 25!
Therefore they can not be factors of 25! + 1.
The answer is E.
Answer: (E) I​, II, and III
Question: A bike covers a certain distance at the speed of 67km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
(A) 89.33 km/h
(B) 85.34 km/h
(C) 87.67 km/h
(D) 90.25 km/h
(E) 90.64 km/h
Rationale: Ans.(A)
Sol. Total distance = 67 × 8 = 536 km
Now speed = 536/6 = 89.33 km/h
Answer: (A) 89.33 km/h
Question: A student committee that must consists of 5 members is to be formed from a pool of 8 candidates. How many different committees are possible
(A) 5
(B) 8
(C) 40
(D) 56
(E) 336
Rationale: the committee must consist of 5 members, not at least 5 members. Hence, all you have to do is 8C5 = 56
Answer (D)
Answer: (D) 56
Question: 4 men&6women finish a job in 8days, while 3men&7women finish it in 10 days. In how many days will 10 women working together finish it ?
(A) 50 days
(B) 40 days
(C) 60 days
(D) 70 days
(E) 90 days
Rationale: Let 1 man's 1 day work = x
and 1 woman's 1 days work = y.
Then, 4x + 6y = 1/8
and 3x+7y = 1/10
solving, we get y = 1/400 [means work done by a woman in 1 day]
10 women 1 day work = 10/400 = 1/40
10 women will finish the work in 40 days
(B)
Answer: (B) 40 days
Question: A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio W of students per class?
(A) W=3
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: Another way to look at the problem...
Since the total is 120, RATIO * CLASSES = R*C = 120.....(i)
we are looking where ratio increases by 1 and # of classes decreases by 10 = (R+1)(C-10) = RC+C-10R-10=120....(ii)
(ii)-(i)....
C=10R+10 = 10(R+1).......
so # of classes has to be multiple of 10
AS RC=120.... 10(R+1)*R = 120...................R(R+1) = 12..
so 12 is a multiple of consecutive numbers ONLY 3 *4 fits in..... and R=3
A
Answer: (A) W=3
Question: If you have 6 black socks, 4 blue socks, 8 brown socks, and 2 red socks in your sock drawer, what is the minimum number of socks that you need to pull out in the dark to be sure you had a matching pair?
(A) five
(B) 7
(C) 8
(D) 9
(E) 2
Rationale: A
5
At least 5, so that at least one color has two socks!
Answer: (A) five
Question: Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?
(A) 75000
(B) 70000
(C) 72000
(D) 78000
(E) 80000
Rationale: Ratio 25000 * 12:60000*8
= 25*12 : 60*18
5*3 : 12*2
5:8
let tot prof = x
then kamal received 10x/100 = x/10 as commission for managing the business
remaining profit = x = x/10 = 9x/10 =>5:8
total amt by kamal = x/10+9x/10*5/13
=>58000
x=130000
kiran shrae = 130000-58000=72000
ANSWER C
Answer: (C) 72000
Question: The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:
(A) 18%
(B) 12%
(C) 15%
(D) 25%
(E) 14%
Rationale: Explanation:
Ans. C. 15%
The true discount on Rs. 2562 due 4 months hence is Rs. 122.
Therefore Present Worth is = 2562 – 122 = 2440.
It means that Rs. 122 is interest on Rs. 2440 for 4 months.
Therefore rate percent is = (122 × 100 × 12)/(2440 × 4) = 15%
Answer: C
Answer: (C) 15%
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
(A) 4:8
(B) 4:2
(C) 4:3
(D) 4:4
(E) 4:1
Rationale: 12:9
= 4:3
Answer:C
Answer: (C) 4:3
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 48 years now, the son's age five years back was?
(A) 18years
(B) 19years
(C) 20years
(D) 21years
(E) 22years
Rationale: Let the son's present age be x years. Then, (48 - x) = x
2x = 48.
x = 24.
Son's age 5 years back (24 - 5) = 19 years.
B)
Answer: (B) 19years
Question: What will be the result of 12/2 + 4/2 -3^5 +8 all this multiplied by 5?
(A) 18
(B) 98
(C) 5
(D) 9
(E) 0
Rationale: The division(e.g. 6/2) is done first and then the sum(e.g. 6+2) and
subtraction (e.g. 2-15), at the end you multiply the expression by 5, and the answer is 5, option C.
Answer: (C) 5
Question: The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?
(A) 71
(B) 44
(C) 66
(D) 16
(E) 18
Rationale: Explanation:
Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years.
Answer: A
Answer: (A) 71
Question: Train X departs from station A at 11 a.m. for station B, which is 180 km so far. Train Y departs from station B at 11 a.m. for station A. Train X travels at an average speed of 70 km/hr and does not stop anywhere until it arrives at station B. Train Y travels at an average speed of 50 km/hr, but has to stop for 15 min at station C, which is 60 km away from station B enroute to station A. Ignoring the lengths of the trains, what is the distance, to the nearest kilometre, from station A to the point where the trains cross each other?
(A) 112 km
(B) 118 km
(C) 120 km
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Total time taken by B to cover 60 km
60/50 hr i.e 6/5 hr.
It stops at station C for 1/4 hr
Now , in (6/5 + 1/4) hr , train X travels 70 x (29/20) = 101.5 km.
This means they do not cross each other by the time train Y finishes it stops at station C.
Let they meet after t hour.
Then, 70t + 50(t- 1/4) = 180.
t = 192.5/120 hr.
Distance from A will be 70 x 192.5/120 km i.e 112 km approximately.
Answer : A
Answer: (A) 112 km
Question: If 0 < p < 1 < q< 3, which of the following must be less than 1?
I.	p/q
II.	pq
III.	q - p
(A) I,II only
(B) I only
(C) II only
(D) III only
(E) II,III only
Rationale: q > 1. So, option II, III is not possible.
So, Option I is correct.
Answer : B
Answer: (B) I only
Question: A train , 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)?
(A) 500
(B) 400
(C) 300
(D) 200
(E) 250
Rationale: Distance = 800+x meter where x is the length of the tunnel
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78×10/36 m/s = 130/6 = 65/3 m/s
Distance/time = speed
(800+x)/60 = 65/3
=> 800+x = 20×65 = 1300
=> x = 1300 - 800 = 500 meter
Answer is A.
Answer: (A) 500
Question: For a bake sale, Simon baked 2n more pies than Theresa. Theresa baked half as many pies as Roger, who baked 1313n pies. No other pies were baked for the sale. What fraction of the total pies for sale did Roger bake?
(A) 1/16
(B) 1/8
(C) 3/16
(D) 3/8
(E) 13/16
Rationale: S : Simon
T : Theresa
R : Roger
Let Theresa baked A.
As per question, we have S = A + 2n
R = 2A = n/3 or A = n/6
Now, Total = A + (A+2n) + 2A = 8n/3
Fraction, (n/3) / (8n/3) = 1/8
ANSWER:B
Answer: (B) 1/8
Question: In assembling a Bluetooth device, a factory uses one of two kinds of modules. One module costs $15 and the other one, that is cheaper, costs $10. The factory holds a $140 worth stock of 13 modules. How many of the modules in the stock are of the cheaper kind?
(A) 20
(B) 25
(C) 30
(D) 11
(E) 35
Rationale: So the number of $10 modules must be 11 so that the leftover 2 modules are of $15 which will give a total value $140. 11*10+2*15 = 110+30=140
Answer : D
Answer: (D) 11
Question: A contractor undertakes to built a walls in 50 days. He employs 30 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time?
(A) 25
(B) 30
(C) 45
(D) 20
(E) None of these
Rationale: 30 men complete 0.4 work in 25 days.
Applying the work rule, m1 × d1 × w2 = m2 × d2 × w1
we have,
30 × 25 × 0.6 = m2 × 25 × 0.4
or m2 = 30×25×0.6/25×0.4 = 45 men
AnswerC
Answer: (C) 45
Question: Every day, the value of a stock rises by exactly two dollars in the morning, and
then falls by exactly one dollar in the afternoon. If the stock's value at the start of the rst
day is $100, on what day will the stock's value rst reach $200?
(A) 50
(B) 99
(C) 100
(D) 101
(E) 200
Rationale: Note that each day the stock is worth $1 more than on the previous day, and that
on the rst day it rises to $102 and then falls to $101. Therefore, on the nth day, the stock's
value rises to n + 101 dollars in the morning and falls to n + 100 dollars in the afternoon.
The solution is therefore the smallest n for which n+101 = 200, or n = 99. In particular,
the stock will be $200 in the middle of day 99, although not at the end of this day.
correct answer B
Answer: (B) 99
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 323
(B) 88
(C) 40
(D) 99
(E) 81
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100 = 40%
Answer: C
Answer: (C) 40
Question: The ratio of two numbers is 5:9. If each number is decreased by 5, the ratio becomes 5:11. Find the numbers.
(A) 30, 19
(B) 21, 37
(C) 15, 34
(D) 15, 27
(E) None of these
Rationale: Explanation:
Let the two numbers be 5x and 9x.
(5x-5)/(9x-5) = 5:11
(5x-5)*11 = (9x-5)*5
55x – 55 = 45x – 25
10x = 30
x = 3
Therefore, the numbers are 15 and 27.
ANSWER: D
Answer: (D) 15, 27
Question: A number is increased by 20 % and then decreased by 20 %. Find the net increase or decrease per cent.
(A) 9%
(B) 8%
(C) 7%
(D) 3%
(E) 4%
Rationale: Let the number be 100.
Increase in the number = 20 % = 20 % of 100
= (20/100 Ã— 100)
= 20
Therefore, increased number = 100 + 20 = 120
This number is decreased by 20 %
Therefore, decrease in number = 20 % of 120
= (20/100 Ã— 120)
= 2400/100
= 24
Therefore, new number = 120 - 24 = 96
Thus, net decreases = 100 - 96 = 4
Hence, net percentage decrease = (4/100 Ã— 100) %
= (400/100) %
= 4 %
Answer:E
Answer: (E) 4%
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 184 votes. Find the total number of valid votes?
(A) 430
(B) 438
(C) 436
(D) 434
(E) 460
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 184 => 4x/10 = 184
=> 4x = 1840 => x = 460.
Answer:E
Answer: (E) 460
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 210 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 41
(C) 68
(D) 88
(E) None
Rationale: EXPLANATION
We have: l = 20 ft and lb = 210 sq. ft.
So, b = 10.5 ft.
Length of fencing = (l + 2b) = (20 + 21) ft = 41 ft.
Answer B
Answer: (B) 41
Question: Two trains A and B are 200 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
(A) 10 s
(B) 6 s
(C) 14 s
(D) 8 s
(E) 12 s
Rationale: DETAILED SOLUTION
Speed of A = 54∗1000/60∗60 = 15 m/s
Speed of B = 36∗1000/60∗60 = 10 m/s
Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s
The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25 = 6s.
What is the time taken for trains to completely cross each other? The length that needs to be crossed = 200 + 150 = 350 m. Time taken = 350/25 = 14 s.
CORRECT ANSWER C.
Answer: (C) 14 s
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?
(A) 2788
(B) 3000
(C) 7282
(D) 2782
(E) 2729
Rationale: 4 --- 2000
5 --- ? => 3000
Answer:B
Answer: (B) 3000
Question: A company D has 15 percent of the employees are secretaries and 10 percent are salespeople. If there are 120 other employees of Company D, how many employees does Company D have?
(A) 200
(B) 160
(C) 180
(D) 152
(E) 250
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 10%
% of of employees other than secretaries and salespeople = 100 - 25 = 75%
But this number is given as 120
so 75% of x = 120
x = 160
Therefore there a total of 160 employees in the company D
Correct answer - B
Answer: (B) 160
Question: Oak trees line both sides of a street for a length of 6/8 of a kilometer. If there is 16 meters of space between the trees, and each tree is 1 meter wide, how many trees are there along the street?
(A) a)	22
(B) b)	23
(C) c)	24
(D) d)	45
(E) e)	46
Rationale: There is a gap of 16 m between every 2 trees , each tree is 1 m wide.
6/8of 1 km = 750 m
Lets assume that x trees are planted So equation is
x*1 +(x-1)*16 = 750
Solve for x and we get x = 45, answer is D
Answer: (D) d)	45
Question: 1397 x 1397 = ?
(A) 1961609
(B) 1851609
(C) 1951619
(D) 1951609
(E) 1851619
Rationale: 1397 x 1397	= (1397)^2
= (1400 - 3)^2
= (1400)^2 + (3)^2 - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.
Answer is D.
Answer: (D) 1951609
Question: Mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 60 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 3 hours, how long after he passed the gas station did Paul catch up with Mary?
(A) 1.5
(B) 1.3
(C) 1.25
(D) 1.6
(E) 2
Rationale: d = rt
M: r = 50mph, t = t + 1/4hr
d = 50 (t + 1/4)
P: r = 60, t = t
d = 60t
since they went the same distance:
50t + 50/4 = 60t
10t = 50/4
t = 1.25 or 1 hr, 15min
C
Answer: (C) 1.25
Question: If the compound interest on a sum of Rs.5000 at the rate of 10% per annum is Rs.1050, then time period is (Interest compounded yearly)
(A) 1 YRS
(B) 21/2 YRS
(C) 3 YRS
(D) 2 YRS
(E) 4 YRS
Rationale: amount=5000+1050=6050
C.I=P(1+R/100)^n
6050=5000(1+10/100)^n
6050/5000=(11/10)^n
121/100=(11/10)^n
(11/10)^2=(11/10)^n
n=2 yrs .
ANSWER:D
Answer: (D) 2 YRS
Question: The cube root of .000216 is:
(A) 0.6
(B) 0.06
(C) 77
(D) 67
(E) 87
Rationale: 0.000216=216/10^6
Cube root of the above=(216/10^6)^1/3=6/100=.06
ANSWER:B
Answer: (B) 0.06
Question: Fom the integer n, if n*n*n is odd, then what is true from below options?
(A) n is odd
(B) n is odd and n*n is even
(C) n is even
(D) n*n is odd
(E) n*n is even
Rationale: n is odd and n*n is even
Option B
Answer: (B) n is odd and n*n is even
Question: The value of (4.7 × 13.26 + 4.7 × 9.43 + 4.7 × 77.31) is :
(A) 0.47
(B) 47
(C) 470
(D) 4700
(E) None of these
Rationale: Solution
Given expression = 4.7 × ( 13.26 + 9.43 + 77.31) = 4.7 × 100 = 470 . Answer C
Answer: (C) 470
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x
(A) 2400
(B) 2600
(C) 2435
(D) 3000
(E) 3158
Rationale: 12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
E
Answer: (E) 3158
Question: A box contains ten bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that exactly two bulbs are good?
(A) 7/21
(B) 10/21
(C) 9/21
(D) 8/21
(E) 5/21
Rationale: Required probability = (5C2 . 5C2)/10C4 = (10 * 10)/210
= 10/21
Answer:B
Answer: (B) 10/21
Question: Evaluate: 1234562- 12*3*2 = ?
(A) 32435453
(B) 1234554
(C) 76768786
(D) 97979797
(E) 75868656
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
1234562 - 12*3*2 = 1234562 - 8 = 1234554
correct answer B
Answer: (B) 1234554
Question: Reena took a loan of $. 1200 with simple interest for as many years as the rate of interest. If she paid $ 972 as interest at the end of the loan period, what was the rate of interest?
(A) 3.6
(B) 6
(C) 18
(D) Cannot be determined
(E) None of these
Rationale: Let rate = R% and time = R years.
Then,1200 x R x R/100= 972
12R2 = 972
R2 = 81
R = 9.
Answer:E
Answer: (E) None of these
Question: What is the area of square field whose side of length 18 m?
(A) 225
(B) 777
(C) 266
(D) 288
(E) 324
Rationale: 18 * 18 = 324 sq m
Answer: E
Answer: (E) 324
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 298 m
(B) 150 m
(C) 208 m
(D) 988 m
(E) 299 m
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9
= 150 m
Answer:B
Answer: (B) 150 m
Question: The perimeter of one face of a cube is 40 cm. Its volume will be:
(A) 125cm3
(B) 400cm3
(C) 250cm3
(D) 1000cm3
(E) None of these
Rationale: Explanation:
Edge of cude = 40/4 = 10 cm
Volume = a*a*a = 10*10*10 = 1000 cm cube
Option D
Answer: (D) 1000cm3
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.7 per sq m?
(A) 4350
(B) 4725
(C) 4328
(D) 4329
(E) 4829
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 7 = Rs.4725
Answer:B
Answer: (B) 4725
Question: The ratio of male to female in a class is 2:3. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one fourth of the males and 3/4th of the females in the class?
(A) a)160 degree
(B) b) 198 degree
(C) c)191 degree
(D) d)192 degree
(E) e)204 degree
Rationale: let the common ratio be x.. so M=2x and F=3x and Total=5x
1/4 of M= 2x/4 and 3/4 of F= 9/4x..
Total preferring that carrer = x/2+9x/4=11x/4
Now 5x= 360, so x=360/5=72..
so 72*11/4=198
ans 198
B
Answer: (B) b) 198 degree
Question: A strain of bacteria reproduces @ 25% every 12 min. In how much time will it triple itself ??
(A) 96 min
(B) 72 min
(C) 60 min
(D) 48 min
(E) 40 min
Rationale: The original question is:
A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?
1.25^x = 3 --> x = ~5 --> five 12 minute periods = 60 minutes.
Answer: C.
Answer: (C) 60 min
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 50
(B) 86
(C) 85
(D) 25
(E) 28
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x =50.
Answer: A
Answer: (A) 50
Question: A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 7:00 a.m., at what time was it one-eighth full?
(A) 9:00 a.m.
(B) 7:00 a.m.
(C) 6:00 a.m.
(D) 4:00 a.m.
(E) 2:00 a.m.
Rationale: To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 7:00 a.m -1 hour = 6:00 a.m.
Answer: C.
Answer: (C) 6:00 a.m.
Question: A basketball team composed of 12 players scored 100 points in a particular contest. If none of the individual players scored fewer than 7 points, what is the greatest number of points W that an individual player might have scored?
(A) 7
(B) 13
(C) 16
(D) 21
(E) 23
Rationale: General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
Thus to maximize the number of points of one particular player minimize the number of points of all other 11 players.
Minimum number of points for a player is 7, so the minimum number of points of 11 players is 7*11=77.
Therefore, the maximum number of points W for 12th player is 100-77=23.
Answer: E.
Answer: (E) 23
Question: What least value should be replaced by * in 223431* so the number become divisible by 5
(A) 0
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Explanation:
Trick: Number is divisible by 5, if last digit is 0 or 5
so that least number is 0.
Answer: Option A
Answer: (A) 0