mathewhe/aqua_rat huggingface dataset:
Question: In a survey conducted to find out the readership of three Newspapers A,B and C, it was found that the number of newspaper A is at least 20 and at most 40. The number of people who read newspaper B is at least 50 and at most 70. The number of people who read newspaper C is at least 70 and at most 83. It was also found that 7 people read all three newspapers. Find the minimum number of people who read both A and B but not C.
(A) A)1
(B) B)2
(C) C)3
(D) D)0
(E) E)5
Rationale: I wish I could draw a diagram to show you but by giving you number A and B, it might help a little.
A and B and C is 7 - that means A and B is at least 7. This seems trivial given the value intervals of A and B but definitely helps to think through how to minimize A and B but not C
A and B but not C = |A|-|B| - 7
So i would pick A=35 and B =50 to minimize the value to a 1. (ANS A)
Answer: (A) A)1
Question: A is 1.5 times as fast as B. A alone can do the work in 30 days. If A and B work on alternative days, beginning with A, in how many days will the work be completed?
(A) 23
(B) 22
(C) 21
(D) 36
(E) 25
Rationale: A can finish 1 work in 30 days
B can finish 1/1.5 work in 30 days - since A is 1.5 faster than B
This means
B can finish 1 work in 30*1.5 days = 45 days
Now using the awesome GMAT formula when two machines work together they can finish the job in = AB/ (A+B) = 45*30/(45+30) = 20*30/50 = 18 days
Since they alternate on days, it will take them double this time so total time = 18 * 2 = 36 days
So answer is D
Answer: (D) 36
Question: An apple orchard grows red and green apples. On the first day of harvest, 496 apples are collected. There are three times as many red apples as there are green apples. How many green apples were harvested?
(A) 99
(B) 112
(C) 118
(D) 124
(E) 130
Rationale: Let x be the number of green apples.
There were 496 total apples; there are three times as many red apples as green apples. Therefore,
x + 3x = 496
4x = 496
x = 124
Answer: D
Answer: (D) 124
Question: If A's height is 45% less than that of B, how much percent B's height is more than that of A?
(A) 66.66%
(B) 81.81%
(C) 66.766%
(D) 86.66%
(E) 66.65%
Rationale: Excess of B's height over A's = [(45/(100 - 45)] x 100%
= 81.81%
Answer: B)
Answer: (B) 81.81%
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
(A) Rs.500
(B) Rs.750
(C) Rs.1250
(D) Rs.1500
(E) Rs.1800
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
ANSWER:D
Answer: (D) Rs.1500
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 50/r years. If Luke's parents invested $12,500 in a long term bond that pays 12 percent interest compounded annually, what will be the approximate total amount of the investment 12 years later, when Luke is ready for college?
(A) 62,000
(B) 85,500
(C) 95,500
(D) 100,500
(E) 100,000
Rationale: Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).
Answer: A.
Answer: (A) 62,000
Question: The value of ((x – y)³ + (y - z)³ + (z – x)³)/(18 (x – y) (y – z) (z – x))
is equal to :
(A) 0
(B) 1/6
(C) 1
(D) 1/4
(E) 1/3
Rationale: Since (x – y) + (y – z) + (z – x) = 0,
so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).
(3 (x – y) (y – z) (z – x))/(18(x – y) (y – z) (z – x)) = 1/6.
ANSWER:B
Answer: (B) 1/6
Question: If mn > 0, which of the following must be negative?
(A) 2m+n
(B) 2m/n
(C) m/n
(D) -2mn
(E) -m/-n
Rationale: - * + = -
Answer : D
Answer: (D) -2mn
Question: There are 2 sections A and B in a class, consisting of 50 and 40 students respectively. If the average weight of section A is 50kg and that of section B is 70kg, Find the average of the whole class?
(A) 50.78kg
(B) 49.32kg
(C) 61.67kg
(D) 58.88kg
(E) 70.89kg
Rationale: Total weight of 50+40 students = 50*50 + 40*70 = 2500+2800
Average weight of the class is = 5300/90 = 58.88 kg
Answer is D
Answer: (D) 58.88kg
Question: The median of a triangle is the line from any vertex to the midpoint of the opposite side. Triangle ABC has vertices A = (0, 5), B = (–1, –1), and C = (5, 2). What is the slope of the median from A to the midpoint of BC?
(A) –3/4
(B) >–4/3
(C) –5
(D) –5/2
(E) –9/4
Rationale: First to find the midpoint of B & C — average the x-coordinates: (–1+ 5)/2 = 2; and average the y-coordinates: (–1 + 2)/2 = 1/2. Thus, the midpoint has coordinates (2, 1/2). We want the slope from A = (0, 5) to (2, 1/2). The rise is the change in the y-coordinates: 1/2 – 5 = -9/2. The run is the change in the x-coordinates: 2 – 0 = 2. Slope = rise/run = [–9/2]/2 = –9/4. Answer = (E)
Answer: (E) –9/4
Question: A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 3 books from the list, including at most 2 novels. How many selections of 3 books satisfy the requirements?
(A) 40
(B) 115
(C) 130
(D) 144
(E) 195
Rationale: Ans: B
Solution: Selection requires at most 2 novels, means=
0N4P + 1N3P + 2N2P
6c0*4c3+ 6c1*4c2
= 4+ 36
= 40
Ans: A
Answer: (A) 40
Question: In a bowl, the number of marbles gets doubled after every minute. If the bowl gets filled after two hours of such process, how long do you think it will take for it to be half filled.
(A) 1 hour and 59 minutes
(B) 2 hour and 59 minutes
(C) 4 hour and 59 minutes
(D) 4 hour and 59 minutes
(E) 5 hour and 59 minutes
Rationale: Solution:
The correct way to solve this question is go backwards. If the number of marble gets doubled every minute and after two hours, it is filled completely, one minute ago it would be half.
So, it will take 1 hour and 59 minutes for it to be filled half.
Answer A
Answer: (A) 1 hour and 59 minutes
Question: A string of 13 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.02, what is the probability that the string of light bulbs will fail during the time period T?
(A) 0.02
(B) (0.02)^13
(C) 1 - (0.02)^13
(D) (0.98)^13
(E) 1 - (0.98)^13
Rationale: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.
The opposite event is when none of the 13 light bulbs fails, since the probability of each light bulb not to fail is 1-0.02=0.98 the the probability that none of the 13 light bulbs fails is 0.98^13.
Hence, the probability that at least one light bulb fails is 1-0.98^13.
Answer: E.
Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 13, then according to your logic the probability that the string of light bulbs will fail would be 100*0.02=2, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: (E) 1 - (0.98)^13
Question: R is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can R be?
(A) 300,000
(B) 349,999
(C) 350,000
(D) 399,999
(E) 400,000
Rationale: R 1,000,000-300,000=700,000 integers
700,000/2= 350,000 even integers.
350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.
350,001-2=349,999
B
Answer: (B) 349,999
Question: Four different children have jelly beans: Aaron has 5, Bianca has 7, Callie has 8, and Dante has 13. How many jelly beans must Dante give to Aaron to ensure that no child has more than 1 fewer jelly beans than any other child?
(A)  2
(B)  3
(C)  4
(D)  5
(E)  6
Rationale: Since Bianca and Callie are both within 1 jelly bean of each other and Aaron has 5, Dante must provide 3 of his 13 jelly beans so each child has no more than 1 fewer jelly bean than any other child.
Dante + Aaron = 13+5 =18/2 = 9
13-8 = 5 so Dante must provide 5 jelly beans to Aaron.
Answer (D)
Answer: (D)  5
Question: A sum of Rs. 125000 amounts to Rs. 16000 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) 7%
Rationale: S.I. = (16000 - 12500) = Rs. 3500\
Rate = (100 * 3500) / (12500 * 4) = 7%
ANSWER:E
Answer: (E) 7%
Question: A car covers a distance of 540 km in10 hrs. What is its speed in mps.
(A) 40 m/s
(B) 25 m/s
(C) 20 m/s
(D) 15 m/s
(E) 16 m/s
Rationale: Explanation:
Distance = Speed x Time
Speed = (540/10) = 54 kmph
Spees in mps = 54 x 5/18 = 3 x 5 = 15 mps.
Answer: Option D
Answer: (D) 15 m/s
Question: How many such three letter passwords can exist?
(A) 216
(B) 26C6 *3
(C) (26C6)^3
(D) ((26C6)^3) *63
(E) 215
Rationale: 1st ring: 6 out of 26 alphabets can be selected in 26C6 ways.
And is for 2nd and 3rd ring.
Also, these 3 set of 6 letters can be arranged amongst themselves in 63 ways.
Hence, total number of 3 letter passwords = 26C6 * 26C6 *26C6 *63 ways.
ANSWER:D
Answer: (D) ((26C6)^3) *63
Question: The average (arithmetic mean)E of the four distinct positive integers p, q, s and t is x. If p and q are odd, and s and t are even, which of the following must be true?
I. x is an integer
II. (x−0.5) is an integer.
III. 2x is an odd integer.
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) None of the above
Rationale: Given :
p + q = EVEN (odd + odd =even)
p + q + s + t = EVEN (even + even = even) nothing more....
(p + q + s + t) / 4 = x
I.
x may or may not be integer, we only know sum of 4 variables is even not necessarily multiple of 4. I is out.
II.
Similarly, x an integer if sum of 4 variables is multiple of 4 but not an integer if it is not multiple of 4, we only know it is even. II is out.
III.
As in II, if X is integer 2x is Even, if X has decimal part (a.5), 2x is odd. III is out.
Answer E, None.
Answer: (E) None of the above
Question: What amount does Kiran get if he invests Rs. 18000 at 12% p.a. simple interest for four years?
(A) 29893
(B) 26640
(C) 29989
(D) 28800
(E) 29883
Rationale: Simple interest = (18000 * 4 * 12)/100 = Rs. 8640
Amount = P + I = 18000 + 8640 = Rs. 26640
Answer: B
Answer: (B) 26640
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 80/6 sec
(B) 80/7 sec
(C) 88/7 sec
(D) 80/9 sec
(E) 82/7 sec
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35
=80/7 sec.
Answer:B
Answer: (B) 80/7 sec
Question: A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 4120 a year. What is his average monthly income?
(A) 2000
(B) 2010
(C) 2100
(D) 2200
(E) 2300
Rationale: Total expenditure for the first 3 months = 3 × 1600 = 4800
Total expenditure for 4 months = 4 × 1550 = 6200
Total expenditure for 5 months = 5 × 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4800 + 6200 + 9000 + 4120 = Rs. 24120
So, Average monthly income = 24120/12 = Rs. 2010
B
Answer: (B) 2010
Question: The Square of a Positive Number A is divided by 2 and then the Result is Multiplied by 4 if the result is equal to A * 8 then what is the value of A?
(A) 4
(B) 9
(C) 6
(D) 3
(E) 8
Rationale: (A*A)/2*4= 2(A*A)
2(A*A)=8A
2A=8
So the Correct Answer is 4
Answer: (A) 4
Question: If w,x,y,z are consecutive positive integers ; then which of the following is always odd?
[1] w*x+(y+2)^2*z
[2] w^x + z^y
[3] 2w^3
(A) 2
(B) 2
(C) 3
(D) 1 and 2
(E) 2 and 3
Rationale: Plug in some numbers
w = 1
x = 2
y = 3
z = 4
Check the options -
[1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4 = 102{ Not an odd Number }
[2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number }
3 2w^3 = 2*1^3 = even
2
A
Answer: (A) 2
Question: What is the unit digit in {pow(2114,563) x pow(425,213) x pow(3371,67)}?
(A) 0
(B) 2
(C) 3
(D) 5
(E) 7
Rationale: Solution
Unit digit in pow((2114, 563)
= Unit digit in pow(4,563)
= Unit digit in [pow(pow(4,2),281) x 4]
= Unit digit in (6 x 4)
= 4 Unit digit in pow(425,213)
= Unit digit in pow(5,213)
= 5 Unit digit in pow(3371,67)
= Unit digit in pow(1,67) = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
Answer A
Answer: (A) 0
Question: A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 27 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?
(A) 14
(B) 45
(C) 54
(D) 65
(E) 52
Rationale: Just check the answers and reverse the numbers until you get 27.
52 - 25 = 27
Answer E
Answer: (E) 52
Question: A and B can do a piece of work in 3 days. With the help of C they finish the work in 2 days. C alone can do that piece of work in?
(A) 6 DAYS
(B) 5 DAYS
(C) 4 DAYS
(D) 3 DAYS
(E) 2 DAYS
Rationale: C = 1/2 – 1/3= 1/6 => 6 days
Answer:A
Answer: (A) 6 DAYS
Question: Manoj borrowed Rs.3600 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?
(A) 22877
(B) 5455
(C) 2778
(D) 6787
(E) 1771
Rationale: Let the sum lent by Manoj to Ramu be Rs.P.
Amount gained by Manoj = P. 3.9 /100 = 3600.3.6/100 = Rs.824.85
27P = 64800 = 82485
P = (82485 + 64800)/27 = 3055 + 2400 = Rs.5455
Answer: B
Answer: (B) 5455
Question: Four friends (A, B, C and D) started a business in partnership by investing capitals in the proportion 3 : 5 : 4 : 6. During the period of one-year, these capitals were utilized in the proportion of 6 : 4 : 5 : 3 respectively. If, at the end of the year, a profit of Rs. 15,550 was made, what will be the share of D?
(A) 3682.89
(B) 3682.87
(C) 3682.81
(D) 3682.82
(E) 6222.33
Rationale: Explanation:
A = (Investment * capital utilized) = (3 * 6) = 18
B = (5 * 4) = 20
C = (4 * 5) = 20
D = (6 * 3) = 18
Thus, out of Rs. 76 (18 +20 + 20 + 18), D's share is Rs. 18. Hence, out of Rs. 15,500 the share of D would be given as (18/76) * 15550 = Rs. 3682.89
ANSWER: A
Answer: (A) 3682.89
Question: In each term of a sequence, 15 is added to get the next term. If the first term is 10, what is the eighty-first term?
(A)  1630
(B)  1210
(C)  1110
(D)  1720
(E)  1750
Rationale: 1rst term + 80 terms = 10 + 15+15+15+15+15+15+15+...+15 (80 times)
10 + (15 x 80) = 10 + 1200 = 1210
Answer B
Answer: (B)  1210
Question: Set #1 = {A, B, C, D, E}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: So Not a vowel in Set-1 : 3/5
And not a vowel in Ser-2:5/6
Now,
3/5∗5/6=12
This is for not a vowel.
Then for at least one vowel will be = 1−1/2=1/2
Answer will be C.
Answer: (C) 1/2
Question: find out the wrong number in the given sequence of numbers
15,16,34,105,424,2124,12756
(A) 105
(B) 424
(C) 2124
(D) 15
(E) 34
Rationale: 15*1+1=16
16*2+2=34
34*3+3=105
105*4+4=424
424*5+5=2125
2125*6+6=12756
wrong number is 2124
ANSWER:C
Answer: (C) 2124
Question: Lloyd normally works 7.5 hours per day and earns $4.00 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?
(A) $33.75
(B) $48.00
(C) $51.75
(D) $54.00
(E) $70.00
Rationale: Daily working hour*Regular Rate + Overtime*Increased Rate
7.5*4.0+ 3*4.0*1.5=48
Answer B
Answer: (B) $48.00
Question: If x is an integer, and 225 < x^2 <= 361, which of the following is the sum of all possible values of x?
(A)  None of the above
(B)  124
(C)  116
(D)  105
(E) 135
Rationale: The range of x is from 16 .. to 19 and -16 to -19 so the sum is 0 hence ans A, I guess, unless I am missing something!
Answer: (A)  None of the above
Question: Which of the following is closer to √0.1+√0.05?
(A) 0.5
(B) 0.7
(C) 0.9
(D) 1.1
(E) 1.2
Rationale: √0.1+√0.05=approximately √0.09+√0.04=0.3+0.2=0.5. Hence, the correct answer is A.
Answer: (A) 0.5
Question: If A is 25% greater than B then how much percentage is B smaller than A?
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 45%
Rationale: A = 125
B = 100
A-B/A × 100 = 25/125 × 100 = 20 % smaller smaller than A
B)
Answer: (B) 20%
Question: A train 120 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 22
(B) 48.2
(C) 99
(D) 288
(E) 12
Rationale: Speed of the train relative to man = (120/10) m/sec = (12) m/sec. [(12) * (18/5)] km/hr = 43.2 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 43.2 ==> x = 48.2 km/hr.Answer: B
Answer: (B) 48.2
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) 5 kmph
(B) 10 kmph
(C) 15 kmph
(D) 20 kmph
(E) 12 kmph
Rationale: Explanation:
M = 15
S = 5
DS = 15 + 5 = 20kmph
Answer: D
Answer: (D) 20 kmph
Question: 5356 x 51 = ?
(A) 273156
(B) 273243
(C) 273247
(D) 273250
(E) 273258
Rationale: 5356 x 51	= 5356 x (50 + 1)
= 5356 x 50 + 5356 x 1
= 267800 + 5356
= 273156.
A
Answer: (A) 273156
Question: If the cost price of 140 pencils is equal to the selling price of 100 pencils, the gain percent is
(A) 36
(B) 37
(C) 38
(D) 39
(E) 40
Rationale: Let C.P. of each pencil be Re. 1.
Then, C.P. of 100 pencils = Rs. 100; S.P. of 100 pencils = Rs. 140.
Gain % = 40/100 * 100 = 40%
Answer:E
Answer: (E) 40
Question: (12345679 x 72) = ?
(A) 88888888
(B) 888888888
(C) 898989898
(D) 9999999998
(E) None
Rationale: Explanation: 12345679 x 72 = 12345679 x (70 +2)
= 12345679 x 70 + 12345679 x 2
= 864197530 + 24691358
= 888888888
Answer: Option B
Answer: (B) 888888888
Question: A cistern is normally filled in 6 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?
(A) 24 hours
(B) 20 hours
(C) 30 hours
(D) 40 hours
(E) 50 hours
Rationale: If leakage/hour=1/x, then 1/6 -1/x= 1/8, solving 1/x=1/24
So in 24 hours full cistern will be empty.
ANSWER:A
Answer: (A) 24 hours
Question: The pages of a report are numbered consecutively from 1 to 11. If the sum of the page numbers up to and including page number x of the report is equal to six more than the sum of the page numbers following page number x, then x =
(A) 5
(B) 6
(C) 7
(D) 8
(E) 4
Rationale: sum of the first few numbers =1+2+3+4+5+6+7+8 =36
sum of the last few = 9 +10+11 =30 page no.8 answer .D
Answer: (D) 8
Question: What is the average (arithmetic mean) of the numbers 100, 150, 200, 200, 250, and 300?
(A)  100
(B)  150
(C)  140
(D)  200
(E)  250
Rationale: {100, 150, 200, 200, 250, 300}={200-100,200-50, 200, 200,200+50,200+100} --> the average = 200.
Answer: D.
Answer: (D)  200
Question: Ajay can walk 3km in 1 hour. In how many hours he can walk 50km?
(A) 5hrs
(B) 16.6 hrs
(C) 15.6 hrs
(D) 20.4 hrs
(E) 30hrs
Rationale: 1 hour he walk 3km
he walk 50km in = 50/3 * 1 = 16.6hours
Answer is B
Answer: (B) 16.6 hrs
Question: an unbaised coin is tossed until it shows up the same face in 2 consicative throws wat is the probability that the no of tosses is not more than 4.
(A) 3/4
(B) 1/4
(C) 7/8
(D) 1/8
(E) 6/8
Rationale: using 0 and 1 for head and tail respectively and considering binary system , we find that
Out of 16 possibilities, 14 are desired options.
Then probability = 14/16=7/8
ANSWER:C
Answer: (C) 7/8
Question: A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled or emptied completely as the case may be ?
(A) Emptied; 16 min
(B) Filled; 8 min
(C) Emptied; 8 min
(D) Filled; 12 min
(E) None of these
Rationale: If both the pumps are opened together, then the tank will be emptied because the working efficiency of pump empting is more than that of the pump filling it. Thus in 1 min net proportion of the volume of tank filled
= (1⁄8 - 1⁄16) = 1⁄16
or the tank will be emptied in 16 min
⇒ 1⁄2 tank will be emptied in 8 min.
Answer C
Answer: (C) Emptied; 8 min
Question: A, B and C enter into a partnership. They invest Rs. 60,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?
(A) 9 : 3 : 4
(B) 9 : 2 : 4
(C) 9: 2 : 1
(D) 9: 8: 14
(E) none
Rationale: Sol.
A : B : C = (60000 * 36) : (80000 * 12 + 40000 * 24)
: (120000 * 24 + 40000 * 12) =216 : 192 : 336 = 9: 8: 14
Answer D
Answer: (D) 9: 8: 14
Question: A wheel of a car of radius 21 cms is rotating at 900 RPM. What is the speed of the car in km/hr?
(A) 71.28 km/hr
(B) 47.52 km/hr
(C) 7.92 km/hr
(D) 39.6 km/hr
(E) 3.96 km/hr
Rationale: Explanatory Answer
The radius of the wheel measures 21 cm.
In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.
∴ in one rotation this wheel will cover 2 * π * 21 = 132 cm.
In a minute, the distance covered by the wheel = circumference of the wheel * rpm
∴ this wheel will cover a distance of 132 * 900 = 118800 cm in a minute.
In an hour, the wheel will cover a distance of 118800 * 60 = 7128000 cm.
Therefore, the speed of the car = 7128000 cm/hr = 71.28 km/hr
Choice A is the correct answer.
Answer: (A) 71.28 km/hr
Question: If n is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: (D) 8
Question: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
(A) 22
(B) 77
(C) 12
(D) 41
(E) 76
Rationale: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48
Remaining work = (1 - 7/48) = 41/48
Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48
Number of boys required = 41/48 * 41 = 41.
Answer: D
Answer: (D) 41
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 160 meter length?
(A) 11 seconds
(B) 41.6 seconds
(C) 40 seconds
(D) 88 seconds
(E) 19 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+160 = 520 meter
Time = Distance/speed
= 520 * (2/25) = 41.6 seconds
Answer: B
Answer: (B) 41.6 seconds
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
(A) Rs.10595
(B) Rs.10529
(C) Rs.10598
(D) Rs.10508
(E) Rs.10500
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 24500 * 3/7
= Rs.10500
Answer:E
Answer: (E) Rs.10500