MU-NLPC/Calc-aqua_rat huggingface dataset:
A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be	Choose the correct choice from the following options:
A) 7744  B) 2388  C) 3778  D) 2992  E) 2888

Solution: Explanation:   length of wire = {\color{Blue}2 \Pi r}= 2 *(22/7 )*56= 
2 *(22/7 )*56 = 352
352 cm   side of the square= 352/4= 
352/4 = 88
88cm   area of the square= 88*88= 
88*88 = 7_744
7744sq cm   7744nswer: 7744) 7744
Answer: A
The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 3 ?  Pick.
A) 95  B) 106  C) 122  D) 116  E) 122

Solution: Average = total runs / no.of innings = 32   So, total = Average x no.of innings = 32 * 20= 
32 * 20 = 640
640   Now increase in avg= 4 runs. So, new avg = 32+3= 
32+3 = 35
35 runs   Total runs= new avg x new no. of innings = 35 * 21= 
35 * 21 = 735
735   Runs made in the 11th inning= 735-640= 
735-640 = 95
95   95NSWER:95
Answer: A
If 36 men can do a piece of work in 25 hours, in how many hours will 13 men
do it ?  Select the correct option: A) 65 hours B) 69 hours C) 30 hours D) 62 hours E) 66 hours

Solution: Let the required number of hours be x. Then,   Less men, More hours	(Indirect Proportion)   13 : 36 : : 25 : x	(13 x x) = (36 x 25)	(36 x 25)/13= 69   Hence, 15 men can do it in 60 hours.   Answer is 69 hours.
Answer: B
If one of the followings is the product of the two 3-digit integers 8L7 and 6K9 (K and L denote the tens digit of the respective integers), then that product must be  Choose the correct option:
A) 511,913  B) 478,823  C) 531,875  D) 538,424  E) 569,114

Solution: To know the unit digit you can multiply both digit number: 7 x 9 = 63   This eliminates C, D, and E, because the number must end with a 3   To know the answer you can multiply both the thousand digit giving 8 x 6 = 48 so the number must be bigger than 480.000.   So the answer is 511,913
Answer: A
The total of 344 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is Select.
A) 238 B) 277 C) 278 D) 200 E) 300

Solution: Explanation:   Let the number of 20 paise coins be x. Then the no of 25 paise coins = (344 - x).   0.20 * (x) + 0.25 (344 - x) = 71 => x = 300..   Answer: 300) 300
Answer: E
Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 60 kmph respectively. In what time will they cross each other completely?  Answers:
A) 15 sec
B) 19 sec
C) 12 sec
D) 12.9 sec
E) 11 sec

Solution: Explanation:   12.9 sec = 250 m + 250 m = 500 m   RS = 80 + 60= 
80 + 60 = 140
140 * 5/18= 350/9   T = 500 * 9/350 = 12.9 sec   Answer: Option 12.9 sec
Answer: D
Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3649
Choose the most appropriate option
A) 3649  B) 9654  C) 5945  D) 7963  E) 8216

Solution: The product of first two digits in a number equals the last two digits, except in 3649. Hence, it is the odd one.   The answer is 3649.   3649NSWER:3649
Answer: A
60% of a number is added to 120, the result is the same number. Find the number? Select:
A) 300
B) 388
C) 776
D) 2991
E) 212

Solution: (60/100) * X + 120 = X   2X = 600   X = 300   300nswer: 300
Answer: A
How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
Choose the correct choice from the following options:	A) 4	B) 5	C) 6	D) 7	E) 3

Solution: Explanation:   132 = 4 x 3 x 11   So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.   264 -> 11,3,4 (/)   396 ->11,3,4 (/)   462 ->11,3 (X)   792 ->11,3,4 (/)   968 ->11,4 (X)   2178 ->11,3 (X)   5184 -> 3,4 (X)   6336 ->11,3,4 (/)   Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.   Required number of number = 4.   4NSWER IS 4
Answer: A
In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?
Pick one: A) 20% B) 40% C) 50% D) 60% E) 70%

Solution: 70 + 55 + 35= 
70 + 55 + 35 = 160
160%   The number is 60% above 100% because 60% of the counties were counted twice.   The answer is 60%.
Answer: D
Insert the missing number.
2, 6, 12, 20, 30, 42, 56,72, 90, 110 (....)  Select.
A) 22  B) 132  C) 72  D) 66  E) 19

Solution: Explanation:   The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8,8 x 9, 9 x 10,10 x 11.   So, the next number is 11 x 12 = 132.   Answer: 132) 132
Answer: B
Given that 29a031 × 342 = 100900b02 where a and b denote two missing
digits, what is the value of a + b ?
Choices:
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: Recall the tests for divisibility by 9 and by 11. Since 342 is divisible by 9, the number   100900b02 is as well. So b has to be 6. But then 100900b02 is divisible by 11. Since 342 is   not divisible by 11, we deduce 29a031 must be divisible by 11. So a has to be 5, and a + b = 11.   correct answer 11
Answer: E
If 0.75 : x : : 5 : 8, then x is equal to Pick one: A) 1.12 B) 1.25 C) 1.20 D) 1.3 E) None

Solution: Sol.   (x×5) = (0.75×8) ⇒ x = 6/5 = 1.20.   Answer 1.20
Answer: C
There are 14 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks?	Select the correct option:
A) 1/5 B) 11/22 C) 81/724 D) 91/946 E) 101/987

Solution: 14/44*13/43 = 91/946   The answer is 91/946.
Answer: D
What Should come in place of the question mark in the following number series ?
Q. 5 8 10 12 16 (?)	Pick one:
A) 15	B) 18	C) 17	D) 21	E) 23

Solution: Explanation :   The series is 5, and 5 + odd prime numbers  5 + 3= 
 5 + 3 = 8
8, 5 + 5= 10, 5 + 7 = 12, 5+ 11 = 16, 5 + 13 = 18   Answer : Option 18
Answer: B
A furniture dealer purchased a desk for $180 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?  Choose the most appropriate option:
A) $40	B) $60	C) $80	D) $120	E) $100

Solution: Purchase price = 180   Selling price = x   180 + 0.4*x = x   0.6*x = 180   x = 300   Profit = 300 - 180= 
300 - 180 = 120
120   ANSWER:$120
Answer: D
Some pens are divided among A, B, C and D. A gets twice the number of pens that B gets. C gets the same number of pens as D gets. If A gets 25 pens more than D and the ratio of the number of pens that B and C get is 2:3, then find the number of pens that D gets?	Answers:
A) 45 pens
B) 65 pens
C) 75 pens
D) 95 pens
E) 14 pens

Solution: Let the number of pens that A, B, C and D get be a, b, c and d respectively.   a:b = 2:1   a = c + 25   b:c = 2:3   a:b:c:d = 4:2:3:3   a, d get 4p, 3p pens   => 4p - 3p = 25 => p = 25   => D gets 3p = 3 * 25= 
3 * 25 = 75
75 pens.   Answer: 75 pens
Answer: C
A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?  Choose the correct choice from the following answers:
A) 2 hours B) 8 hours C) 6 hours D) 1 hours E) 9 hours

Solution: |-----------20--------------------|   50 40   D = 20   RS = 50 – 40 = 10   T = 20/10= 
20/10 = 2
2 hours   2 hoursnswer:2 hours
Answer: A
The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds that it is a jack?	Choose the correct choice from the following options
A) 1/52
B) 1/13
C) 5/13
D) 1/4
E) 1/26

Solution: The question should ask about the probability not the odds.   There are 13 spades, the probability that the spade we already have is a jack is therefore 1/13.   Answer: 1/13.
Answer: B
A certain store sold pens for $0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of $3.50, what total number of pens and pencils did the customer purchase?
Select
A) 8 B) 9 C) 10 D) 11 E) 12

Solution: Answer: Algebraically, the question looks like this: 2.5 = 0.35x + 0.25y There are six possible numbers of pens that fit that requirement:   1 pen: $0.35   2 pens: $0.70   3 pens: $1.05   4 pens: $1.40   5 pens: $1.75 balance can fetch 7 pencils for $0.25 each. That's 5 pens and 7 pencils for a total of 12 pens and pencils. Choice (12) is correct.
Answer: E
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 2028 sq m, then what is the breadth of the rectangular plot? Select the correct option.
A) 11
B) 17
C) 26
D) 101
E) 1322

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 2028   3b2 = 2028   b2 = 676 = 26 (b > 0)   b = 26 m.   Answer: 26
Answer: C
Stacy and Heather are 40 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?
Choose the correct answer.
A) 4 miles	B) 8 miles	C) 17 miles	D) 6 miles	E) 12 miles

Solution: Original distance between S and H = 40 miles.   Speed of S = 5+1= 
5+1 = 6
6 mph, Speed of H= 5 mph.   Time traveled by H = t hours ---> time traveled by S = t+24/60 = t+2/5 hours.   Now, the total distances traveled by S and H = 40 miles ---> 6*(t+2/5)+5*t=40 ---> t= 188/55 hours. Thus H has traveled for 188/55 hours giving you a total distance for H = 5*188/55 = 17 miles.   C is thus the correct answer.   P.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.
Answer: C
How many different 6-letter sequences are there that consist of 1A, 3B's and 4C's ?	Choose the correct choice from the following choices: A) 6 B) 80 C) 120 D) 360 E) 720

Solution: How many different 6-letter sequences are there that consist of 1 A, 380's, and 4 C's?   (A) 6   (80) 80   (C) 120   (D) 360   (E) 720 (ANS 80)
Answer: B
Given distinct positive integers 1, 11, 4, x, 2, and 9, which of the following could be the median?
Choose the most appropriate option.
A) 2  B) 3  C) 6  D) 8  E) 9

Solution: The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.   Arrange numbers in ascending order: 1, 2, 4, 9, 11, and x.   Now, x can not possibly be less than 4 as given that all integers are positive and distinct (and we already have 1, 2, and 4).   Next, if x is 4<x<9 then the median will be the average of 4 and x. As all answers for the median are integers, then try odd values for x:   If x=5, then median=(4+5)/2= 
(4+5)/2 = 9/2 = around 4.5
4.5 --> not among answer choices;   If x=8, then median=(4+8)/2= 
(4+8)/2 = 6
6 --> OK;   Answer: 6
Answer: C
How many pounds of salt at 80 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb? Options.
A) 5
B) 15
C) 40
D) 50
E) 25

Solution: Selling price is 48 cents/lb   For a 20% profit, cost price should be 40 cents/lb (CP*6/5 = 48)   Basically, you need to mix 35 cents/lb (Salt 1) with 80 cents/lb (Salt 2) to get a mixture costing 40 cents/lb (Salt Avg)   weight of Salt1/weight of Salt2 = (Salt2 - SaltAvg)/(SaltAvg - Salt1) = (80 - 40)/(40 - 35)= 
(80 - 40)/(40 - 35) = 8
8/1   We know that weight of salt 1 is 40 lbs. Weight of salt 2 must be 5 lbs.   5nswer (5)
Answer: A
The average (arithmetic mean) of the even integers from 0 to 200 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 100 inclusive?
Select: A) 10 B) 25 C) 50 D) 100 E) 200

Solution: The sum of even numbers from 0 to N is 2 + 4 +...+ N   = 2(1 + 2 + ...+ N/2)   = 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)   The average is (N/2)(N/2+1)/(N/2+1) = N/2   The average of the even numbers from 0 to 200 is  200/2= 
 200/2 = 100
100   The average of the even numbers from 0 to 100 is  100/2= 
 100/2 = 50
50   The answer is 50.
Answer: C
The distance between Delhi and Mathura is 100 kms. A starts from Delhi with a speed of 50 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 45 kmph at 8 p.m. from Delhi. When will they meet?	Choose the correct option: A) 11 B) 77 C) 8 3/4 D) 8 1/2 E) 8

Solution: D = 100 – 50 = 50   RS = 45 + 50= 
45 + 50 = 95
95   T= 90/45 = 0.5 hours   8 a.m. + 0.5 = 8 1/2 a.m..Answer: 8 1/2
Answer: D
There are 4 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total number of chess games possible to be played in the tournament?	Pick.
A) 10
B) 8
C) 40
D) 60
E) 120

Solution: Each person is one participant of 4 games. So there are in all 4*4= 
4*4 = 16
16 instances of one participant games. 8ut each game has 2 participants so total number of games= 16/2= 
16/2 = 8
8   8
Answer: B
What is the greatest 6-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 3, 4, 5, 6 and 7 respectively? Choose the correct choice from the following answers.
A) 456780
B) 678910
C) 997479
D) 997917
E) 997920

Solution: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 7 when we divide by 10, so 997917 is the only possible answer.
Answer: D
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 100 kmph. Find the speed of the boat in still water and the speed of the stream?
Select:
A) 10 kmph
B) 17 kmph
C) 19 kmph
D) 17 kmph
E) 20 kmph

Solution: Speed of the boat in still water   = (60+100)/2= 
(60+100)/2 = 80
80 kmph. Speed of the stream= (100-60)/2= 
(100-60)/2 = 20
20 kmph.   Answer: 20 kmph
Answer: E
If Reena says, “Anjali's father Raman is the only son of my father-in-law Ramanand”, then how is Piyu, who is the sister of Anjali, related to Ramanand ?  Choose the correct choice from the following answers:
A) Grand-daughter	B) Wife	C) Daughter	D) None of these	E) None of these33

Solution: Explanation:   Only son of Reena's father-in-law Ramanand is Reena's husband. So, Raman is Reena's husband and Anjali & Piyu are his daughter's, Thus, Piyu is Grand-daughter of Ramanand.   Grand-daughterNSWER: Grand-daughter
Answer: A
Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Sachin	Choose the correct choice from the following answers: A) 24.58 B) 24.5 C) 24.3 D) 24.9 E) 24.1

Solution: If Rahul age is x, then Sachin age is x-7,   so (x-7)/x = 7/9   => 9x-63 = 7x   => 2x = 63   => x = 31.5   So Sachin age is   31.5 - 7= 
  31.5 - 7 = 24.5
24.5   Answer: 24.5
Answer: B
A train covers a distance of 1250 km in 25hrs. Find the speed of the train? Pick.
A) 30km/hr B) 40km/hr C) 50km/hr D) 60km/hr E) 100km/hr

Solution: Speed = 1250/25= 
1250/25 = 50
50km/hr   Answer is 50km/hr
Answer: C
Arrange fractions in descending order Choices:  A) 9/11 > 8/9 > 3/5 > 4/7  B) 9/11 > 8/9 > 4/7 > 3/5  C) 8/9 > 9/11 > 3/5 > 4/7  D) 9/11 >3/5 > 8/9 > 4/7  E) None of these

Solution: Explanation:   9/11 = .818 , 8/9 = .88 , 3/5 = .6, 4/7 = .571   So order is 8/9 > 9/11 > 3/5 > 4/7   Option 8/9 > 9/11 > 3/5 > 4/7
Answer: C
In an exam, Bobby scored 38 percent, Bonny scored 56 percent, Vijay scored 66 percent and Libin scored 75 percent. The maximum score awarded in the exam is 500. Find the average mark scored by all the three boys? Choose the correct choice from the following choices:
A) 293 B) 293.75 C) 294 D) 295.5 E) 298.25

Solution: Average mark scored by all the three boys =   [38/100 (500) + 56/100 (500) + 66/100 (500) + 75/100(500)] / 4   (190+280+330+375)/4= 
(190+280+330+375)/4 = 1_175/4 = around 293.75
293.75   Answer: 293.75
Answer: B
A man borrowed Rs 24000 from two money lenders. For one loan, he paid 15% per annum and for the other 18% per annum. At the end of one year, he paid Rs 4050. How much did he borrow at each rate ?	Choose the correct choice from the following options.
A) Rs.16000 B) Rs.12000 C) Rs.15000 D) Rs.13000 E) None of these

Solution: Explanation:   Let the sum at 15% be Rs x and that at 18% be Rs (24000 - x).   {(x * 15 * 1)/100 } + { [(24000 – x) * 18 * 1]/100 } = 4050   or 15 x + 432000 - 18x = 405000 or x = 9000.   Money borrowed at 15% = Rs 9000 .   Money borrowed at 18% = Rs 15000.   Answer: Rs.15000
Answer: C
Company Z has 48 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday.  Choose the correct choice.
A) 6	B) 7	C) 8	D) 9	E) 12

Solution: Say the number of people having birthdays on Wednesday is x and the number of people having birthdays on each of the other 6 days is y. then x + 6y = 48.   Now, plug options for x. Only A and E give an integer value for y. But only for E x > y as needed.   Answer: 12.
Answer: E
The faces of pyramid are to be painted by 4 different colors. In how many ways can be this be done? Choose the correct choice
A) A.720  B) B.256  C) C.24  D) D.12  E) E.36

Solution: If I have to paint 4 sides with 4 different colour...   First face can have 4c1 options,   2nd would have 3c1, and subsequent ones would have 2c1 and 1 options respectively.   Total options = 4c1 x 3c1 x 2c1 x 1 = 24 distinct ways   C.24orrect answer - C.24
Answer: C
Two pipes A and B can fill a tank in 36 hours and 46 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?	Choose the correct option:	A) 20.195 hrs	B) 21.195 hrs	C) 22.195 hrs	D) 23.195 hrs	E) 20.495 hrs

Solution: a fill in one hour = 1/36   b fill in one hour = 1/46   both fill in one hour = 1/36+1/46   = 82/1656   time taken by both pipes = 1656/82   =20.195 hrs   20.195 hrsNSWER:20.195 hrs
Answer: A
The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 800 per sq.metre.	Choose the correct answer
A) Rs.15500	B) Rs.16500	C) Rs.17500	D) Rs.18500	E) Rs.19500

Solution: Area = 5.5 × 3.75 sq. metre.   Cost for 1 sq. metre. = Rs. 800   Hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = Rs. 16500   Answer: Rs.16500
Answer: B
Which number is the odd one out in the list ?	Choose the correct choice from the following:  A) 38442  B) 78426  C) 84029  D) 67626  E) 72927

Solution: C   84029   All the others are three digit numbers followed by their square root, eg 729 followed by its square root, 27.   Answer: 84029
Answer: C
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 13? Choose the correct choice from the following answers:
A) 0
B) 1
C) 2
D) 13
E) 5

Solution: There are several algebraic ways to solve this question including the one under the spoiler. But the easiest way is as follows:since we can not have two correct answersjust pick a prime greater than 3, square it and see what would be the remainder upon division of it by 13.   n=5 --> n^2=25 --> remainder upon division 25 by 13 is 12.   Answer: 13.
Answer: D
1,234
1,243
1,324
.....
....
+4,321
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exact;y once in each integer. What is the sum of these 24 integers? Pick: A) 24,000 B) 26,664 C) 40,440 D) 60,000 E) 66,660

Solution: Using the symmetry in the numbers involved (All formed using all possible combinations of 1,2,3,4), and we know there are 24 of them. We know there will be 6 each with the units digits as 1, as 2, as 3 and as 4. And the same holds true of the tens, hundreds and thousands digit.   The sum is therefore = (1 + 10 + 100 + 1000) * (1*6 +2*6 +3*6 +4*6) = 1111 * 6 * 10= 
1111 * 6 * 10 = 66_660
66660   ANS:66,660
Answer: E
If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum? Select the correct option:
A) 227
B) 299
C) 270
D) 585
E) 271

Solution: 90 = (450*4*R)/100   R = 5%   I = (450*6*5)/100= 
(450*6*5)/100 = 135
135   450 + 135= 
450 + 135 = 585
585   Answer: 270
Answer: C
The average weight of 10 persons increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? Choose the most appropriate option:
A) 107 kg  B) 80 kg  C) 120 kg  D) 90 kg  E) 100

Solution: Solution   Total weight increased	= (10 x 4.2)kg   = 42 kg.   Weight of new person	= (65 + 42)= 
(65 + 42) = 107
107kg.   107 kgnswer 107 kg
Answer: A
Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
Choose the correct choice from the following answers
A) 22	B) 21	C) 22	D) 28	E) 11

Solution: Speed Ratio = 1:7/6 = 6:7   Time Ratio = 7:6   1 -------- 7   4 --------- ? è 28 m.Answer: 28
Answer: D
Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?  Choose the correct choice from the following choices:
A) Rs.128  B) Rs.129  C) Rs.125  D) Rs.198  E) Rs.120

Solution: 3x * 2x = 3750 => x = 25   2(75 + 50) = 250 m   250 * 1/2   =Rs.125   Answer:Rs.125
Answer: C
At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?	Choices:
A) 24min
B) 44min
C) 14min
D) 21min
E) 74min

Solution: In this type of problems the formuae is   (5*x+ or - t)*12/11   Here x is replaced by the first interval of given time. Here x is 5.   t is spaces apart   Case 1 : (5*x + t) * 12/11   (5*5 + 3) * 12/11   28 * 12/11 = 336/11= min   therefore the hands will be 3 min apart at 31 5/11 min past 5.   Case 2 : (5*x - t) * 12/11   (5*5 -3 ) * 12/11   22 *12/11= 
22 *12/11 = 24
24 min   therefore the hands will be 3 min apart at 24 min past 5   24minnswer: 24min
Answer: A
An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases?  Options.
A) 8:6 B) 8:7 C) 8:9 D) 8:4 E) 8:1

Solution: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.   Let the dimensions of the carpet in the second case be 7y, 3y units respectively.   From the data,.   2(3x + 2x) = 2(7y + 3y)   => 5x = 10y   => x = 2y   Required ratio of the areas of the carpet in both the cases   = 3x * 2x : 7y : 3y   = 6x2 : 21y2   = 6 * (2y)2 : 21y2   = 6 * 4y2 : 21y2   = 8:7   Answer: 8:7
Answer: B
The perimeter of a semi circle is 108 cm then the radius is?  Choose one:
A) 17 B) 21 C) 19 D) 11 E) 12

Solution: 36/7 r = 108 => r   = 21   Answer: 21
Answer: B
In a bag of small balls 1/4 are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue? Choose the correct choice from the following answers.
A) 6	B) 5	C) 4	D) 3	E) 8

Solution: Let us first find the fraction of green, blue and yellow balls   1/4 + 1/8 + 1/12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator   = 11 / 24 , add numerators   The fraction of white balls is given by   24 / 24 - 11 / 24 = 13 / 24   So the fraction 13 / 24 corresponds to 26 balls. If x is the total number of balls then   (13 / 24) of x = 26 balls   or (13 / 24) ? x = 26   x = 26 ? (24 / 13) = 48 , total number of balls   The fraction of blue balls is 1 / 8 of x. The number of blue balls is given by   (1 / 8) of 48 = 6 balls.   correct answer 6
Answer: A