mathewhe/aqua_rat huggingface dataset:
Question: If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 48?
(A) 12
(B) 18
(C) 24
(D) 30
(E) 36
Rationale: The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.
The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5.
48=2*3*8 is divisible by 12. therefore the greatest common divisor is 12
A
Answer: (A) 12
Question: Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 70, the three numbers in order are?
(A) 60, 120, and 30
(B) 60, 30, and 120
(C) 30, 60, and 120
(D) 30, 120, and 60
(E) 120, 30, and 60
Rationale: Let the numbers be 2x, x and 4x
(2x + x + 4x)/3 = 70
7x/3 = 70
x = 30
The numbers in order are 60, 30, and 120
The answer is B.
Answer: (B) 60, 30, and 120
Question: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 40 hours. If one additional machine were used under the same operating conditions, in how manyfewerhours of simultaneous operation could the production order be fulfilled?
(A) 6
(B) 9
(C) 10
(D) 27
(E) 48
Rationale: If 3 Machines can do the work in 40 hr then 4 Machines can do the work in 3/4*40 = 30 Hrs. hence time saved will be 10hr
option C is the correct answer
Answer: (C) 10
Question: X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600:
(A) 200
(B) 250
(C) 300
(D) 350
(E) 400
Rationale: X = Rs.5000/-
Y = Rs.15000/-
X share 1 part & Y share 3 parts
Total 4 parts -----> Rs.1600/-
----> 1 part -------> Rs.400/-
X share = 1 part -----> Rs.400/-
E
Answer: (E) 400
Question: In how many ways letters of the word RSCUPERATE be arranged?
(A) 357687
(B) 247886
(C) 284757
(D) 456788
(E) 302400
Rationale: RESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways
E
Answer: (E) 302400
Question: A and B complete a work in 16 days. A alone can do it in 40 days. If both together can do the work in how many days?
(A) 1.0875 days
(B) 0.1875 days
(C) 0.0675 days
(D) 0.0875 days
(E) 0.0775 days
Rationale: 1/16 + 1/40 = 0.0875 days
ANSWER:D
Answer: (D) 0.0875 days
Question: In how many ways can the letters of the word 'LEADER' be arranged?
(A) 72
(B) 144
(C) 360
(D) 720
(E) None of these
Rationale: Explanation:
The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
Required number of ways =	6! / (1!)(2!)(1!)(1!)(1!) =360.
ANSWER IS C
Answer: (C) 360
Question: A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If25 were to be added to each score, which of these three statistics would change?
(A) The mean only
(B) The mean and the median
(C) The standard deviation only
(D) The median only
(E) The mean and the standard deviation
Rationale: The correct answer is B.
Answer: (B) The mean and the median
Question: In how many ways can 5 boys and 2 ladiesbe arranged at a table if 2 ladies are never together?
(A) 245
(B) 278
(C) 390
(D) 420
(E) 480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: (E) 480
Question: A farm has chickens, cows and sheep. There are five times the number of chickens and cows than sheep. If there are more cows than chickens or sheep, and together, cows and chickens have a total of 100 feet and heads, how many sheep live at the farm?
(A) 5
(B) 8
(C) 10
(D) 4
(E) 17
Rationale: Chicken - ch
Cows - C
Sheep -S
ch+C=6S
C> ch and c>s
Each cow has 4 legs and 1 head
Each chicken has 2 legs and 1 head
So 5c+3ch=100 (sum of legs and head)
There are 2 possible solutions to this equation
c=11 and ch=9 or
c=14 and ch=10
Since from first equation where ch+c=5s
The sum of ch and c should be divisbile by 5. 24 is not so the only possible solution is c=11 and ch=9. So s=4
Answer : D
Answer: (D) 4
Question: If m is an integer, what is the greatest possible value for m that would still make the following statement true: 11*10^m < 1/10 ?
(A)  –4
(B)  –3
(C)  –2
(D)  –1
(E)  0
Rationale: Just putting values, the LHS becomes
m =0 --> 11
m =-1 --> 11/10
m =-2 --> 11/100
m =-3 --> 11/1000
Anything lower will be smaller than 11/1000. m =-2, equality doesn't hold but it does for m =-3.
Answer is B.
Answer: (B)  –3
Question: Two men A and B start from place X walking at 4 1/2 kmph and 5 1/2 kmph respectively. How many km apart they are at the end of 3 1/2 hours if they are walking in the same direction?
(A) 4 3/9
(B) 4 3/5
(C) 4 3/8
(D) 4 3/2
(E) 4 3/1
Rationale: RS = 5 3/2 - 4 1/2 = 1 1/4
T = 3 1/2 h.
D = 5/4 * 7/2 = 35/8 = 4 3/8 km
Answer: C
Answer: (C) 4 3/8
Question: A shopkeeper mixed 7kg of salt worth Rs.6 per kg, 5kg of salt worth Rs.4 per kg and 6 kg of salt worth Rs.5 per kg. For what amount of money should he sell 4 kg of the mixed variety of salt in order to make a profit of 12½%?
(A) 22.95
(B) 23.95
(C) 24.95
(D) 25.95
(E) 26.95
Rationale: 7kg*Rs6---- Rs 42
5 kg*Rs4---- Rs 20
6kg*Rs5---- Rs 30
18kg for Rs--92 cost price of 1 kg=92/18=>Rs5.11111
cost of 4 kg ---- 4*5.11111=Rs 20.4444
Profit=12.5%
SP={(100+Gain%)/100}*CP
={(100+25/2)/100}*20.444
=22.95
ANSWER:A
Answer: (A) 22.95
Question: If 28a+30b+31c=427.
then a+b+c=?.a,b,c are natural numbers
(A) 6
(B) 14
(C) 12
(D) 45
(E) 28
Rationale: have a look on your calender
since,we all knw a year consist of 365 days
february is d only month which has 28 days
4 months in a year has 30 days
and,rest 7 months has 31 days..
so,following d given eq. we can write 28*1 + 30*4 + 31*9..
hence values of a,b and c are 1, 4 and 9 respectively..
a+b+c=14
ANSWER:B
Answer: (B) 14
Question: Find the odd one out:
125, 106, 83, 76, 65, 58, 53
(A) 33
(B) 83
(C) 26
(D) 18
(E) 222
Rationale: Explanation:
This sequence represents a series in which from the reverse order a prime number is added:
53+5=58
58+7=65
65+11=76
76+13=89
89+17=106
106+19=125
Hence 83 is the answer.
ANSWER: B
Answer: (B) 83
Question: P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days?
(A) 12 days
(B) 12.5 days
(C) 13 days
(D) 14.5 days
(E) 15.5 days
Rationale: Both together worked for 3 days.
In 3 days , P can do = 3 x
1
18
=
1
6
th work
In 3 days, Q can do = 3 x
1
15
=
1
5
th work
In 3 days , work finished =
1
6
+
1
5
=
11
30
Balance work =
19
30
Balance work finished by Q => Time taken by Q to finish the balance work =
19
30
x 15 = 9.5 days
The whole work was completed in 9.5 + 3 = 12.5 days
B
Answer: (B) 12.5 days
Question: If 4^x = 8^y, then the value of (x/y)-1 is equal to :
(A) 1/2
(B) 0
(C) 1/4
(D) 3/4
(E) 2/3
Rationale: 4^x = 8^y,
2^2x= 2^3y
so
2x=3y
x/y = 3/2
(x/y)-1 = (3/2)-1= 1/2
ANSWER:A
Answer: (A) 1/2
Question: complete the numerical series with the correct number
5+3+2=151022
9+2+4=183652
8+6+3=482466
5+4+5=202541
9+5+5= ?
(A) 468645
(B) 454586
(C) 454585
(D) 454386
(E) 444586
Rationale: Correct Answer : C
number is formed as
5+3+2
5*3 3*2 2*5 = 151022
similarly,
9*5 9*5 (9*5+9*5-5)= 454585
Answer: (C) 454585
Question: A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
(A) 6.4 days
(B) 4.4 days
(C) 5.4 days
(D) 8.4 days
(E) 2.4 days
Rationale: A
6.4 days
1 day work of the three persons = (1/15 + 1/20 + 1/25) = 47/300
So, all three together will complete the work in 300/47 = 6.4 days.-
Answer: (A) 6.4 days
Question: The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?
(A) 17
(B) 19
(C) 16
(D) 12
(E) 14
Rationale: 63 + 83 + 103
= a3 => a
= 12
Answer:D
Answer: (D) 12
Question: The average age of a husband and his wife was 26 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
(A) 11
(B) 18
(C) 21
(D) 287
(E) 27
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (26 * 2 + 5 * 2) + 1 = 63 years.
Required average = (63/3) = 21 years.
Answer: C) 21
Answer: (C) 21
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 33. Find the profit percentage?
(A) 65%
(B) 50%
(C) 59%
(D) 40%
(E) 53%
Rationale: L.C.M of 15 and 12
= 60
CP of 60 articles
= Rs. 100 (25 * 4)
SP of 60 articles
= Rs. 165 (33 * 5)
Profit percentage
= (165 - 100)/100 * 100 = 65%
Answer: A
Answer: (A) 65%
Question: A soccer team played 158 games and won 40 percent of them. How many games did it win?
(A) 84
(B) 63.2
(C) 104
(D) 50.8
(E) 15.8
Rationale: 40% of 158=x
0.40*158= x
63.2=x
answer :B
Answer: (B) 63.2
Question: Given a bag with 2 red balls and 3 yellow balls, you randomly select one of them, in order. If the second ball you take is yellow, what is the probability that the first one was also yellow?
(A) 1/2
(B) 1/5
(C) 3/4
(D) 1/3
(E) 3/5
Rationale: This is a conditional probability question. Basically we are told that out of 2 balls picked one is yellow and are asked to find the probability of the other one also to be yellow.
So, possible options for this other ball would be: W, W, B, B (as one yellow is already picked)
So the probability for that ball to be yellow too is 2/4=1/2.
Option A
Answer: (A) 1/2
Question: If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 186 m, what is its area?
(A) 2510
(B) 2535
(C) 2530
(D) 2030
(E) 2520
Rationale: length = breadth +23. Therefore,
4× breadth +2×23=186 m
⇒ breadth =35 m
length =35+23=58 m
Area =58×35=2030 m2
Answer is D.
Answer: (D) 2030
Question: Sequence P is defined by pn=pn−1+3, p1=11, sequence Q is defined as qn=qn−1–4, q3=103. If pk>qk+2, what is the smallest value k can take?
(A) 6
(B) 9
(C) 11
(D) 14
(E) 15
Rationale: Set P = {11, 14, 17,.....}
Set Q = {110, 107, 103,....}
For Arithmetic progression a(n)=a(1)+(n−1)d
Started with C) 11 does not satisfy pk > qk+2
and D) 14, pk = qk+2
So Answer is E
Answer: (E) 15
Question: Out of seven given numbers, the average of the first four numbers is 4 and that of the last four numbers is also 4. If the average of all the seven numbers is 3, fourth number is
(A) 3
(B) 4
(C) 7
(D) 11
(E) 12
Rationale: (a+b+c+d)/4=4
=>(a+b+c+d)=16...........(1)
(d+e+f+g)/4=4
=>(d+e+f+g)=16
=>(e+f+g)=16-d...........(2)
Also, (a+b+c+d+e+f+g)/7=3 (Given)
using (1) and (2) equations
16+16-d=21
=> d=11
ANSWER:D
Answer: (D) 11
Question: Tough and Tricky questions: Percents.
Over the course of a year, a certain microbrewery increased its beer output by 80 percent. At the same time, it decreased its total working hours by 10 percent. By what percent did this factory increase its output per hour?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: Lets assume the initial production was 100 litres of beer for 100 hr.
With the 80% increase the total amount of beer production will be 180 litres and with 10 % decrease in total hours will be reduced to 90 hr.
100hr ----> 100 lts
1hr -----> 1 lts
90hr -----> 180 lts
1hr -----> 2 lts
Total Increase in production for 1 hr = 200%
Answer B
Answer: (B) 200
Question: A man can swim in still water at 3 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.7
(B) 1.4
(C) 1.1
(D) 1.5
(E) 1
Rationale: M = 3
S = x
DS = 3 + x
US = 3 + x
3 + x = (3 - x)2
3 + x = 6 -2x
3x = 3
x = 1
Answer:E
Answer: (E) 1
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 40% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
(A) 36%
(B) 60%
(C) 66%
(D) 80%
(E) 84%
Rationale: Chris won't be able to attend the game if it be raining on Monday evening and Tuesday evening. The probability of that is 0.4*0.4 = 0.16. So, the probability that he will be able to attend is 1 - 0.16 = 0.84.
Answer: E.
Answer: (E) 84%
Question: Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 12 different shirts, 10 different pairs of jeans, and 7 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?
(A) 30
(B) 840
(C) 240
(D) 480
(E) 960
Rationale: Total # of outfits = 12 * 10 * 7 = 840
Answer - B
Answer: (B) 840
Question: There are 36 students in a certain geometry class. If one third of the students are boys and one fourth of the boys are under six feet tall, how many boys in the class are under six feet tall?
(A) 3
(B) 12
(C) 18
(D) 24
(E) 27
Rationale: Total Students = 36
One third of the students are boys = 1/3*36 = 12
One fourth of the boys are under six feet tall = 1/4*12 = 3 ...
Therefore Number of boys in the class under six feet tall = 3 ... Answer A....
Alternatively... Number of boys in the class under six feet tall = 1/4 of 1/3 of Total Students = 1/4*1/3*36 = 3...
Answer A
Answer: (A) 3
Question: John and Jacob set out together on bicycle traveling at 15 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)
(A) 3
(B) 3 1/3
(C) 3 1/2
(D) 4
(E) 1 1/4
Rationale: John's speed - 15 miles/hr
Jacob's speed - 9 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles.
Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles.
Now, when John starts riding back, the distance between them is 7.5 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 15-9 = 6 miles/hr.
Thus, to cover 7.5 miles at 6 miles/hr, John will take 7.5/6 = 1.25 hours
Answer E
Answer: (E) 1 1/4
Question: Five marbles are randomly selected, one at a time (without return), from a bowl of 100 marbles (20 green, 30 blue, 10 yellow, and 40 black). What is the probability that all five marbles are black? (Answer in lowest terms).
(A) 201/125
(B) 9139/1045660
(C) 11350/146790
(D) 21/75
(E) 2/5
Rationale: Let K = black. The bowl has 40 black marbles (we don't care what color the other marbles are because success is black only), so the probability of getting black is P(K) = 40/100 on the first selected marble.
Because selection is (without return), the P(K) has changed for following selections. Now, there are 99 marbles and black is dependent upon whether first marble was black, or not... and so on.... Therefore, conditional probability! The probability that event B occurs, given that event A has already occurred is:
Formula = P(A\B) = P(A and B)/P(B).
P(A\B) = (40/100)(39/99)(38/98)(37/97)(36/96) = 78960960/9034502400 = 9139/1045660
Answer: B
Answer: (B) 9139/1045660
Question: If the largest three digit number is subtracted from the smallest five digit number, then the remainder is
(A) 1
(B) 9000
(C) 9001
(D) 90001
(E) None
Rationale: Solution
Required remainder	= (10000 - 999)
=9001
Answer C
Answer: (C) 9001
Question: Look at this series: 15, __, 27, 27, 39, 39, ... What number should fill the blank?
(A) 51
(B) 39
(C) 23
(D) 15
(E) None
Rationale: Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.
Answer: Option D
Answer: (D) 15
Question: What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum
(A) 110
(B) 120
(C) 130
(D) 140
(E) None of these
Rationale: Explanation:
Let the present worth be Rs.x
Then,S.I.= Rs.(132 - x)
=� (x*5*2/100) = 132 - x
=� 10x = 13200 - 100x
=� 110x = 13200
x= 120
Answer: B
Answer: (B) 120
Question: With what number must 0.580 be multiplied in order to obtain the number 580?
(A) 100
(B) 1,000
(C) 10,000
(D) 100,000
(E) None of these
Rationale: Explanation: The decimal must be moved three places to the right. To do this, we must multiply by a number with three zeroes. The correct answer is 1000.The decimal must be moved three places to the right. To do this, we must multiply by a number with three zeroes. The correct answer is 1000.
Answer : (B)
Answer: (B) 1,000
Question: 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
(A) 127 days
(B) 667 days
(C) 177 days
(D) 187 days
(E) 225 days
Rationale: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/6
15 women's 1 day work = (1/6 - 10/100) = 1/15
1 woman's 1 day work = 1/225
1 woman alone can complete the work in 225 days.
Answer:E
Answer: (E) 225 days
Question: A School Bus is used to transport students from home to college. There are total of 20 students who want to take the bus. There are 10 seats in the bus. 2 in the front row, 4 in the middle row and 4 in the last row. Bus driver has to make sure that front 2 seats are for nausea students. 4 students have nausea and can only sit in the front 2 seats. How many ways can the students sit in the bus.
(A) 100068
(B) 24443
(C) 2392329
(D) 445678
(E) 5405400
Rationale: 4C2 Select 2 students from 4 who have nausea and can sit in front seats only.
16C4 Select 4 students from 16 who have to sit in middle row. (As 4 students who have nausea cannot sit anywhere else/ 20-4 = 16)
12C4 Select 4 students who will sit in the last row. (As 4 students who have nausea cannot sit anywhere else. 4 are sitting in the middle row. 20-4-4 = 12)
Total Number of selection = 4C2 * 16C4 * 12C4 = 5405400
Ans = E
Answer: (E) 5405400
Question: Percentage of profit earned by selling a book e for $1920 is equal to the percentage loss incurred by selling the same book for $1280. What price should the book be sold to make 25% profit?
(A) $500
(B) $1000
(C) $1500
(D) $1700
(E) $2000
Rationale: Let C.P. be Rs. x.
Then,	1920 - x	x 100 =	x - 1280	x 100
x	x
1920 - x = x - 1280
2x = 3200
x = 1600
Required S.P. = 125% of Rs. 1600 = Rs. 125	x 1600 = $2000
100
E
Answer: (E) $2000
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the integers between 100 and 200?
(A) 4545
(B) 5050
(C) 6525
(D) 4352
(E) 4652
Rationale: sum = 100*101/2 = 50*101 = 5050
Answer is B
Answer: (B) 5050
Question: In the reading room of a library, there are 25 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader?
(A) 17
(B) 16
(C) 15
(D) 14
(E) 9
Rationale: 1+2+3+4+5+6+7+8 = 36
so, 8 spots are occupied by users
25-8 = 17,
ANSWER:A
Answer: (A) 17
Question: Whats the next number in this number series ?
18, 46, 94, 63, 52, ?
(A) 23
(B) 12
(C) 34
(D) 61
(E) 55
Rationale: D
61
Reversed digits of squares of number in descending order.
Answer: (D) 61
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 9
(B) 10
(C) 12
(D) 20
(E) 22
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9/54 x 60) min = 10 min.
Answer:B
Answer: (B) 10
Question: How many different possible permutations can be made from the word ‘VULLAT’ such thatthe vowels are never together?
(A) 120
(B) 200
(C) 240
(D) 260
(E) 270
Rationale: The word ‘BULLAT’ contains 6 letters of which 1 letter occurs twice = 6! / 2! = 360
No. of permutations possible with vowels always together = 5! * 2! / 2! = 120
No. of permutations possible with vowels never together = 360-120 = 240.
C
Answer: (C) 240
Question: Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -6 then by what factors will the Mean,Variance and Standard Deviation respectively change ?
(A) -6,-6,-6
(B) -6,6,6
(C) 1,1,1
(D) -6,36,6
(E) 6,6,36
Rationale: Mean: If all values are multiplied by -6 then their sum will also be multiplied by -6 so Mean will also get -6
Variance:
Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values
When we multiply all the values by -6 then the difference between the mean and the individual values also gets multiplied by -6 and the square of that difference becomes 36. So, the variance gets multiplied by a factor of 36
SD:
Standard Deviation is the square root of variance so sqrt(36)=6. So SD gets multiplied by a factor of 6.
So, answer will be D.
Answer: (D) -6,36,6
Question: A committee has 4 men and 6 women. What are the number of ways of selecting 2 men and 4 women from the given committee?
(A) 75
(B) 90
(C) 105
(D) 120
(E) 135
Rationale: The number of ways to select two men and four women = 4C2 * 6C4 = 6 * 15 = 90
The answer is B.
Answer: (B) 90
Question: Two men are walking towards each other alongside a railway track. A freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming from the opposite direction. The train passes this man is 18 seconds. Assume the velocities are constant throughout. How long after the train has passed the second man will the two men meet?
(A) 89.7 minutes
(B) 90 minutes
(C) 90.3 seconds
(D) 91 seconds
(E) None of these
Rationale: Explanation :
Let ‘L’ be the length of train, ‘x’ be the speed of the first man, ‘y’ be the speed of the second man and ‘z’ be the speed of the train.
=>20=1/(z−x) and
=>18=1/(z+x)
=>z=10x+9y.
Distance between the two men =600(z+y).
Time = (600(z+y)-600(x+y))/(x+y).
=>600(9x+9y)/(x+y).
=> 90 minutes.
Answer : B
Answer: (B) 90 minutes
Question: A cube of side 3 meter length is cut into small cubes of side 15 cm each. How many such small cubes can be obtained?
(A) 8078
(B) 1040
(C) 1058
(D) 1021
(E) 8000
Rationale: Along one edge, the number of small cubes that can be cut
= 300/15 = 20
Along each edge 20 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 20 * 20 * 20 =8000
Answer:E
Answer: (E) 8000
Question: x = 13.165
y = 7.686
z = 11.545
The number A is obtained by first rounding the values of x, y, and z to the hundredths place and then adding the resulting values. The number B is obtained by first adding the values of x, y, and z and then rounding the sum to the hundredths place. What is the value of A – B?
(A) 0.01
(B) 0.02
(C) 0.03
(D) 0.1
(E) 0.2
Rationale: Rounding off the values:
x = 13.17
y = 7.69
z = 11.55
A = 13.17 + 7.69 + 11.55 = 32.41
x + y + z = 13.165 + 7.686 + 11.545 = 32.206
B = 32.21
A - B = 0.2
Option E
Answer: (E) 0.2
Question: A boat travels 32 km downstream in 8 hours and 24 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.
(A) 3 km/hr, 1 km/hr
(B) 5 km/hr, 4 km/hr
(C) 1 km/hr, 6 km/hr
(D) 2 km/hr, 1 km/hr
(E) 4 km/hr, 1 km/hr
Rationale: Downstream speed=32km/8hrs
=4kmph
upstream speed=24km/12hrs
=2kmph
speed of boat=avg of downstream and upstream speeds
speed of boat=(4+2)/2kmph
=3kmph.
current speed=half of the difference of downstream and upstream speeds
currend speed=(4-2)/2kmph
=1kmph
ans is 3km/hr,1km/hr
ANSWER:A
Answer: (A) 3 km/hr, 1 km/hr