mathewhe/aqua_rat huggingface dataset:
Question: Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 45 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?
(A)  3
(B)  5
(C)  6
(D)  16
(E)  9
Rationale: Total work = 4*45 machine hrs
Time taken = 4* 45 /5 => 36 hours...
Thus all five machines, operating simultaneously will take ( 45 - 36 ) 9 hours..
Answer will be (E) 9
Answer: (E)  9
Question: Fill in the missing number:
18 ? 12 11 10.5 10.25
(A) 10.1
(B) 10.4
(C) 10.2
(D) 14
(E) 10.3
Rationale: 14
Divide each number by 2 and then add 5 to it.
ANSWER D
Answer: (D) 14
Question: Find the length ofa rectangle is decreased by 40cm & the width is increased by 5cm, a square with the same area asthe original rectangle result. Find the perimeter ofthe original rectangle?
(A) 30 cm
(B) 40 cm
(C) 50 cm
(D) 60 cm
(E) 70 cm
Rationale: Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7 ----(1)
Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)
(x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(2)
Solving 1 & 2 , we get x = 16 and y = 9.
Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.
C
Answer: (C) 50 cm
Question: A man can row a boat at 26 kmph in still water. If the speed of the stream is 12 kmph, what is the time taken to row a distance of 66 km downstream?
(A) 30/16 hours
(B) 33/19 hours
(C) 34/15 hours
(D) 36/13 hours
(E) 30/13 hours
Rationale: Speed downstream = 26 + 12 = 38 kmph.
Time required to cover 66 km downstream = d/s = 66/38 = 33/19 hours.Answer:B
Answer: (B) 33/19 hours
Question: The ratio of the volumes of two cubes is 1728 : 1331. What is the ratio of their total surface areas?
(A) 144 : 121
(B) 141 : 127
(C) 144 : 191
(D) 181 : 161
(E) 81 : 182
Rationale: Explanation:
Ratio of the sides = ³√1728 : ³√1331 = 12 : 11
Ratio of surface areas = 12^2 : 11^2 = 144 : 121
Answer: Option A
Answer: (A) 144 : 121
Question: How many 4-digit numerals begin with a digit that represents a prime and end with a digit that represents a prime number?
(A) 1600
(B) 80
(C) 160
(D) 180
(E) 240
Rationale: prime digits 2,3,5 and 7.
three digit numbers _ _ _
1st place can be filled in 4 ways
2nd place can be filled in 10 ways
3rd place can be filled in 10 ways
3rd place can be filled in 4 ways
Total=4*10*10*4=1600
Ans : A
Answer: (A) 1600
Question: The arithmetic mean of the 13 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 6?
(A) 2 + s + a
(B) 22 + a
(C) 2s
(D) 2a + 2
(E) a
Rationale: (13s+78)/13=s+6=a
(9s+54)/9=s+6=a
E
Answer: (E) a
Question: When the positive integer g is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer h is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of g-h?
(A)  12
(B)  24
(C)  35
(D)  16
(E)  30
Rationale: If I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:
n = 5g + 3
n = 7h + 4
I will need to check for the smallest such number.
I put h= 1. n = 11. Is it of the form 5g + 3? No.
Put h= 2. n = 18. Is it of the form 5g + 3? Yes.
When 18 is divided by 5, it gives a remainder of 3. When it is divided by 7, it gives a remainder if 4.
Next such number will be 35 + 18 because 35 will be divisible by 5 as well as 7 and whatever is the remainder from 18, will still be the remainder
Next will be 35*2 + 18
and so on...
Difference between such numbers will be a multiple of 35 so your answer is 35.
your answer is C
Answer: (C)  35
Question: A boat travels for three hours with a current of 3 mph and then returns the same distance against the current in four hours. What is the boat's speed in calm water? How far did the boat travel one way?
(A) .14
(B) 2.14
(C) 3.14
(D) 5.14
(E) 7.14
Rationale: boat speed=1.5(approx)
one way dist=5.14
ANSWER:D
Answer: (D) 5.14
Question: The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is?
(A) 12%
(B) 13%
(C) 15%
(D) 14%
(E) 18%
Rationale: Explanation:
P.W = 2562 - 122 = Rs.2440
Rate=100×122/2440×13Rate=100×1222440×13
=15%
Answer: C
Answer: (C) 15%
Question: In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 10
(B) 11
(C) 12
(D) 15
(E) 14
Rationale: Let speed of the boat in still water = a and speed of the stream = b
Then
a + b = 14
a - b = 8
Adding these two equations, we get 2a = 22
=> a = 11
ie, speed of boat in still water = 11 km/hr
Answer is B.
Answer: (B) 11
Question: On a purchase of $130, a store offered a payment plan consisting of a $30 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan?
(A) 23.5%
(B) 24.5%
(C) 23.1%
(D) 25.5%
(E) 26.5%
Rationale: 12*10 + 30 = 150.
(30/130)* 100 = 23.1
Answer : C
Answer: (C) 23.1%
Question: A straight fence is to be constructed from posts 3 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following couldnotbe the length of the fence in feet? (12 inches = 1 foot)
(A) 17
(B) 28
(C) 34
(D) 39
(E) 50
Rationale: The fence begins and ends with a post: {post = 0.5 feet}{chains = 5 feet}{post = 0.5 feet}...{chains = 5 feet}{post = 0.5 feet}
The minimum length is with 2 posts = 0.5 + 5 + 0.5 = 6 feet. To increase the fence, each time we should add{post = 0.5 feet}{chains = 5 feet}, so 5.5 feet. Thus, the lengths could be:
3 feet;
3 + 5.5 = 8.5 feet;
11.5 + 5.5 = 14 feet;
17 + 5.5 = 19.5 feet;
22.5 + 5.5 = 25 feet;
28 + 5.5 = 30.5 feet;
33.5 + 5.5 = 36 feet.
...
We skipped 34 feet.
Answer: C.
Answer: (C) 34
Question: Which of the following cannot be the range of a set consisting of 5 odd multiples of 7?
(A) 56
(B) 112
(C) 224
(D) 448
(E) 425
Rationale: Solution: sequence of 7 lets say sequence is 7n, 7(n+1), 7(n+2), 7(n+3), 7(n+4)
so range is 7n+28-7n = 28
if we put the different values of n we will get different but the range will be multiple of 28
and only 425 is not multiple of 28
Answer : E
Answer: (E) 425
Question: Find the area of circle whose diameter is 8 m.
(A) 50.00 square meter
(B) 50.04 square meter
(C) 50.28 square meter
(D) 50.24 square meter
(E) 50.43 square meter
Rationale: Diameter = 8 meter.
Radius = diameter/2.
= 8/2.
= 4 meter.
Area of a circle = Ï€r2.
Here, pi (Ï€) = 3.14 meter, radius (r) = 4.
Area of a circle = 3.14 Ã— 4 Ã— 4..
= 3.14 Ã— 16.
= 50.28 square meter ANSWER : C
Answer: (C) 50.28 square meter
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 10 pumps work to empty the tank in 1 day?
(A) 4.8
(B) 3.6
(C) 1.1
(D) 1.2
(E) 1.3
Rationale: 3 pumps take 16 hrs total (8 Hrs a day)
If 1 pump will be working then, it will need 16*3=48 hrs
1 pump need 48 Hrs
If I contribute 10 pumps then
48/10=4.8 hrs.
answer :A
Answer: (A) 4.8
Question: In how many ways can the letters of the word RECPECT be arranged?
(A) 1234
(B) 1643
(C) 2520
(D) 2856
(E) 3977
Rationale: RECPECT has 7 words, but E is repeated two times. Thus ways = 7! / 2! = 2520 ways
C
Answer: (C) 2520
Question: The sale price sarees listed for Rs.345 after successive discount is 12% and 25% is?
(A) 321
(B) 276
(C) 342
(D) 228
(E) 245
Rationale: Explanation:
345*(88/100)*(75/100) = 228
Answer: D
Answer: (D) 228
Question: If taxi fares were $1.00 for the first 1/5 mile and $0.50 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was
(A) $1.56
(B) $2.40
(C) $3.80
(D) $4.20
(E) $8.00
Rationale: In 3 miles , initial 1/5 mile charge is $1
rest of the distance = 3 - (1/5) = 14/5
rest of the distance charge = 14(0.5) = $7 (as the charge is 0.5 for every 1/5 mile)
=> total charge for 3 miles = 1+7 = 8
Answer is E.
Answer: (E) $8.00
Question: P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?
(A) 8
(B) 5
(C) 4
(D) 6
(E) 3
Rationale: Explanation :
Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6
Answer : Option D
Answer: (D) 6
Question: A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is ?
(A) 25%
(B) 26%
(C) 27%
(D) 28%
(E) 29%
Rationale: Explanation:
Let original length = x
and original width = y
Decrease in area will be
=xy−(80x/100×90y/100)
=(xy−18/25xy)=7/25xy
Decrease = (7xy/25xy×100)%=28
Option D
Answer: (D) 28%
Question: A computer wholesaler sells nine different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display?
(A) 15/56
(B) 3/28
(C) 1/12
(D) 1/56
(E) 1/168
Rationale: Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 7 avilable. so 7C1 is the numerator.
Total no of ways we can choose 3 from 9 is 9c3, which is the denominator.
So, the probability: 7c1/9c3= 1/12 ans is C.
Answer: (C) 1/12
Question: A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 80 percent of books that were loaned out are returned and there are 67 books in the special collection at that time, how many books of the special collection were loaned out during that month?
(A) 20
(B) 30
(C) 35
(D) 40
(E) 55
Rationale: there are 8 books less(75-68) which represents 20% of the loaned books (100-80)
So total loaned out books = 40
Answer D
Answer: (D) 40
Question: If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books ?
(A) 600
(B) 1200
(C) 1800
(D) none of these
(E) 1900
Rationale: Explanation:
Least Cost Price = Rs. (200 * 8) = Rs. 1600.
Greatest Selling Price = Rs. (425 * 8) = Rs. 3400.
Required profit = Rs. (3400 - 1600) = Rs. 1800. Answer: C
Answer: (C) 1800
Question: At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
(A) 6%
(B) 6.5%
(C) 7%
(D) 7.5%
(E) 8%
Rationale: Explanation:
Let the rate be R% p.a.
Then, 1200 x(1 +R/100)2=1348.32
=(1 +R/100)2=134832/120000=11236/10000
(1 +R/100)2=(106/100)2
=>1 +R/100=106/100
R = 6%
ANSWER IS A
Answer: (A) 6%
Question: Calculate the circumference of a circular field whose radius is 6 centimeters.
(A) 2 π cm
(B) 1 π cm
(C) 15 π cm
(D) 12 π cm
(E) 19 π cm
Rationale: Circumference C is given by
C = 2πr = 2π*6 = 12 π cm
Answer: D
Answer: (D) 12 π cm
Question: A certain list of 240 test scores has an average (arithmetic mean) of 85 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 242 test scores with a standard deviation less than d ?
(A)  80 and 80
(B)  80 and 85
(C)  80 and 90
(D)  85 and 86
(E)  85 and 90
Rationale: The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the aboveadding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 85 and 86 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD most.
Answer: D.
Answer: (D)  85 and 86
Question: x, 17, 3x - y2 - 2 and 3x + y2 - 30 are four consecutive terms of an increasing arithmetic sequence. The sum of the four numbers is divisible by:
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: Step by step solution
The question does NOT state that the terms are all integers. That is an unstated assumption and is essential to solve the question.
The four terms are in an arithmetic sequence and the sequence is an ascending sequence. i.e., the second term is greater than the first term and so on.
The sum of the four terms = x + 17 + 3x - y2 - 2 + 3x + y2 - 30 = 7x - 15
If we get an idea about the type of number x is, we will be able find the answer to the question.
Because these 4 terms are in an arithmetic sequence, the difference between any two terms will be the same.
So, 17 - x = (3x + y2 - 30) - (3x - y2 - 2)
i.e., 17 - x = 2y2 - 28
Or 45 - x = 2y2
Because y is an integer, 2y2 has to be an even integer.
Unless x is odd, 45 - x cannot be even.
So, we can deduce that x is odd.
The sum of the four terms is 7x - 15
x is odd;
So, 7x will also be odd.
Hence,
7x - 15 will be even.
Therefore, the sum of the 4 terms will be divisible by 2.
The correct answer is Choice A.
Answer: (A) 2
Question: If d and y are integers, then dy(d + y) is
(A) Always positive
(B) Always negative
(C) Positive when d is positive
(D) Negative when d is negative
(E) It cannot be determined by the information given
Rationale: Given d and y are integers, then dy(d + y)
Let's take even as 2 / -2 and odd as 3 / -3..we get the following.. and IMO option D is correct answer..
I presume its Option E if am not missing anything.
d=-3 and y=1
dy(d + y) is positive = 6
Answer: (E) It cannot be determined by the information given
Question: The market value of a certain machine decreased by 20 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later?
(A)  $8,000
(B)  $5,600
(C)  $3,200
(D)  $2,400
(E)  $4,800
Rationale: E.
Market value in 1982= $ 8000
Market value in 1983 = $ 8000- ($ 8000 x 20/100) = 8000-1600= $ 6400
Market value in 1984 = Market value in 1983 - (20 % of $8000)= 6400-1600 = $4800
Answer: (E)  $4,800
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
(A) 7000
(B) 8000
(C) 6000
(D) 5000
(E) 4000
Rationale: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
Answer: (B) 8000
Question: The ratio of three numbers is 1:2:3 and the sum of their squares is 2016. The sum of the numbers is?
(A) A)10
(B) B)12
(C) C)15
(D) D)14
(E) E)9
Rationale: Let the numbers be x,2x,3x
then, x^2+4x^2+9x^2 = 2016
14x^2 = 2016
x^2 = 144
x=12
Answer is B
Answer: (B) B)12
Question: A and B start a business jointly. A invests Rs.16000 for 5 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
(A) A)Rs.8000
(B) B)Rs.8200
(C) C)Rs.12293
(D) D)Rs.12804
(E) E)Rs.12830
Rationale: 16*5: x*4 = 5:2
x = 8 =>
Rs.8000
Answer: A
Answer: (A) A)Rs.8000
Question: A box contains ten bulbs out of which 6 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?
(A) 1/127
(B) 1/210
(C) 1/128
(D) 1/198
(E) 1/126
Rationale: Out of nine, five are good and four are defective. Required probability
= 6C6/10C6
= 1/210
Answer: B
Answer: (B) 1/210
Question: If paint costs $3.10 per quart, and a quart covers 20 square feet, how much will it cost to paint the outside of a cube 10 feet on each edge?
(A) $ 1.60
(B) $ 16.00
(C) $ 93.00
(D) $108.00
(E) $196.00
Rationale: total surface area = 6a^2 = 6*10*10 = 600
each quart covers 20 sqr ft
thus total number of quarts = 600/20 = 30
cost will be 30*3.1 = $93
Ans: C
Answer: (C) $ 93.00
Question: The sum of the ages of 4 children born at the intervals of 4 years each is 36 years. what is the age of the youngest child ?
(A) 3
(B) 18
(C) 10
(D) 99
(E) 38
Rationale: Let x = the youngest child. Each of the other four children will then be x+4, x+8, x+12
We know that the sum of their ages is 36 .
so, x+(x+4)+(x+8)+(x+12) = 36
therefore The youngest child is 3 years old
Answer: A
Answer: (A) 3
Question: Find the compound interest on $1200 for 2 years at 20% p.a. if CI is component yearly?
(A) $120
(B) $150
(C) $548
(D) $250
(E) $300
Rationale: A = P(1 + R/100)^T
= 1200(1 + 20/100)^2
=$1728
CI = $548
Answer is C
Answer: (C) $548
Question: What is the missing number of the following sequence.
3 48,?,24,30,12,90
(A) 56
(B) 10
(C) 33
(D) 61
(E) 16
Rationale: for Even places x/2 from the start
for Odd places x/3 from the end
EVEN places ODD Places
----------- ----------
48/2 = 24 90/3 = 30
24/2 = 12 30/3 = 10
ANSWER:B
Answer: (B) 10
Question: Last year Carlos saved 10 percent of his annual earnings. This year he earned 5 percent more than last year and he saved 12 percent of his annual earnings. The amount saved this year was what percent of the amount saved last year?
(A) 122%
(B) 124%
(C) 126%
(D) 128%
(E) 130%
Rationale: Earnings = 100 (assume).
Amount saved = 0.1*100 =10.
THIS YEAR:
Earnings = 100*1.05 = 105.
Amount saved = 0.12*105 =12.6.
The amount saved this year as a percent of the amount saved last year is (this yea)/(last year)*100 = 12.6/10*100 =126%.
Answer: C.
Answer: (C) 126%
Question: The smallest number which when diminished by 15, is divisible 10, 15, 25, 30 and 35 is:
(A) 1008
(B) 1055
(C) 1022
(D) 1032
(E) 1048
Rationale: Required number = (L.C.M. of 10, 15, 25, 30, 35) + 15
= 1050 + 15
= 1055
Answer: Option B
Answer: (B) 1055
Question: Synthia can buy watches at a price of Z dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of Z and X and Y, what is the percent of the markup from her buy price to her sell price?
(A) (YZ)/100X
(B) 100X-(YZ)
(C) 100X+(YZ)
(D) 100X*(YZ)
(E) 100X/(YZ)
Rationale: Algebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/Z *100 = 100X/(YZ)
Answer : E
Answer: (E) 100X/(YZ)
Question: The area of the floor of a room is 20 m2 that of a longer wall 15 m2 and of the shorter wall 12 m2, find the edge of the new cube?
(A) 33 m3
(B) 77 m3
(C) 60 m3
(D) 27 m3
(E) 29 m3
Rationale: lb = 20 ; lh = 15 ; fh = 12
(lbh)2 = 20 * 15 * 12 => lbh = 60 m3
Answer:C
Answer: (C) 60 m3
Question: The length of a rectangle is twice its breadth if its length is decreased by 5cm and breadth is increased by 5cm, the area of the rectangle is increased by 75 sq cm. Find the length of the rectangle?
(A) 22 cm
(B) 40 cm
(C) 28 cm
(D) 10 cm
(E) 11 cm
Rationale: let length = 2x and breadth = x then
(2x-5) (x+5) = (2x * x)+75
5x-25 = 75 => x=20
length of the rectangle = 40 cm
Answer: B
Answer: (B) 40 cm
Question: If x/5 - 6/x = 1/5, what are the values of 3x - 7?
(A) -22 and 11
(B) 8 and 24
(C) 17 and 21
(D) 12 and 29
(E) 17 and 29
Rationale: I got the same thing A is the answer -22 or 11
Answer: (A) -22 and 11
Question: A man sells a car to his friend at 14% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :
(A) Rs.22325.58
(B) Rs.32325.58
(C) Rs.52325.58
(D) Rs.62325.58
(E) None of these
Rationale: Explanation:
S.P = Rs.54,000. Gain earned = 20%
C.P = Rs.[100/120Ã—54000]
=Rs. 45000
This is the price the first person sold to the second at at loss of 14%.
Now S.P = Rs.45000 and loss = 14%
C.P. Rs.[100/86Ã—45000]= Rs.52325.58.
Correct Option : C
Answer: (C) Rs.52325.58
Question: The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 4 years is
(A) s.9621
(B) s.6921
(C) s.9724
(D) s.6261
(E) s.6361
Rationale: c.i=p(1+r/100)^n
=8000(1+5/100)^4
=Rs9724
ANSWER:C
Answer: (C) s.9724
Question: What is the least value of x. So that 22x57 is divisible by 3.
(A) 2
(B) 0
(C) 1
(D) 3
(E) 4
Rationale: Explanation:
The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 2 + x + 5 + 7 = 16 + x
Least value of x may be 2
Therefore 16 + 2 = 18 is divisible by 3.
Answer: Option A
Answer: (A) 2
Question: A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
(A) 15 kmph
(B) 36 kmph
(C) 21 kmph
(D) 17 kmph
(E) 19 kmph
Rationale: Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours
10x = 4 x 90 or x =36.
So, speed of goods train = 36kmph.
Ans: B
Answer: (B) 36 kmph
Question: How many positive integers n have the property that when 1,000,063 is divided by n, the
remainder is 63?
(A) 29
(B) 37
(C) 39
(D) 49
(E) 79
Rationale: Suppose n is a positive integer such that the remainder when 1,000,063 is divided
by n is 63. Then, 1,000,063 = nq + 63 where n > 63 (the remainder is always less than the
divisor). Thus 1,000,000 = 106 = nq. All we have to do is count the divisors of 106 that are
greater than 63. Now 106 = 2656 has 49 positive divisors. Exactly twelve are 63, namely
1; 2; 4; 8; 16; 32; 5; 10; 20; 40; 25; 50. Thus, the answer is 37.
correct answer B
Answer: (B) 37
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 11 days
(B) 77 days
(C) 30 days
(D) 88 days
(E) 17 days
Rationale: C = 1/5 – 1/6 = 1/30 => 30 days
Answer:C
Answer: (C) 30 days
Question: What is the probability that when a hand o f 6 cards is drawn from a well shuffled deck of 52 cards, It contains 2 Queen?
(A) 1/23445
(B) 113/22434
(C) 29187by1017926
(D) 1017926/29187
(E) None of these
Rationale: nCr = n!/(n-r)!r!
Total number of possible hands = 52C6
52C6 = (52!)/((52-6)! × 6!)
52C6 = 61075560.
Number of hands with 2 Queen and 4 non-Queen cards = 4C2 × 48C4
4C2 = (4!)/(2! × 2!) = 6.
48C4 = (48!)/(44! × 4!) = 3 × 47 × 46 × 45 = 291870
(other 2 cards must be chosen from the rest 48 cards)
P (2 Queen) = (4C2 × 48C4)/52C6 = 29187/1017926
C
Answer: (C) 29187by1017926
Question: What is the probability P of randomly selecting an arrangement of the letters of the wordMEDITERRANEANin which the first letter is E and the last letter is R?
(A) 1/13
(B) 1/20
(C) 1/26
(D) 1/50
(E) 1/100
Rationale: Why do you calculate the total combinations and everything, it is much easier to calculate as follows:
3/13 * 1 * 1 * 1 * 1 ..... * 2/12 = 6/156 = 1/26
This is because 3/13 = Probability that first letter will be E and 2/12 = probability that thefirstletter will be R. Between everything else cuts down to 1*1*1... e.g. probability of the second letter is P=11/11 = 1, > we do not care what's in between.C
Answer: (C) 1/26
Question: Three partners A,B and C invest Rs.18000, Rs.22500 and Rs.27000 respectively in a business. If total profit is Rs.18750 then A's share is (in Rs.)
(A) 10000
(B) 6500
(C) 5000
(D) 7500
(E) 8500
Rationale: 18000:22500:27000
4:5:6
A's share=18750*4/15=5000
ANSWER:C
Answer: (C) 5000