MU-NLPC/Calc-aqua_rat huggingface dataset:
The ratio of the arithmetic mean of two numbers to one of the numbers is 5:7. What is the ratio of the smaller number to the larger number?	Choices.
A) 2:3	B) 2:5	C) 3:7	D) 4:9	E) 5:6

Solution: For two numbers, the arithmetic mean is the middle of the two numbers.   The ratio of the mean to the larger number is 5:7, thus the smaller number must have a ratio of 3.   The ratio of the smaller number to the larger number is 3:7.   The answer is 3:7.
Answer: C
At a tanning salon, customers are charged $10 for their first visit in a calendar month and $5 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those visits were the only source of revenue for the salon, what was the revenue for the last calendar month at the salon?  Pick one
A) $1220	B) $1200	C) $1300	D) $1340	E) $1880

Solution: I get B. This question seems too straightforward for 600+. Am I missing something?   100 first-time visits --> 100(10) = $1000   30 + 10= 
30 + 10 = 40
40 subsequent visits --> 40(5)= $200   Total revenue: 1000+ 200= 
1000+ 200 = 1_200
$1200   The answer is $1200.
Answer: B
Light glows for every 16 seconds . How many times did it between 1:57:58 and 3:20:47 am
Choose the most appropriate option
A) 311  B) 322  C) 313  D) 314  E) 385

Solution: the diff in sec between 1:57:58 and 3:20:47 is 4969 sec, 4969/16 = 310.   so total 311 times light ll glow   311NSWER:311
Answer: A
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?	Choose the correct option:
A) 33/95	B) 33/91	C) 33/94	D) 33/16	E) 33/17

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is   = ¹²C₄/¹⁵C₄ = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)   = 33/91   Answer:33/91
Answer: B
A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black? Select the correct option:	A) 35/145	B) 36/145	C) 36/140	D) 36/141	E) 31/142

Solution: The probability that first ball is white:   =12C130C1=12C130C1   =1230=1230   =25=25   Since, the ball is not replaced; hence the number of balls left in bag is 29.   Hence, the probability the second ball is black:   =18C129C1=18C129C1   =1829=1829   Required probability,   =(25)×(1829)=(25)×(1829)   =36/145   36/145
Answer: B
What is the area of square field whose side of length 15 m?  Pick:
A) 225
B) 777
C) 266
D) 288
E) 261

Solution: 15 * 15= 
15 * 15 = 225
225 sq m   225nswer: 225
Answer: A
If seven numbers are randomly selected without replacement from set {1, 2, 3, 4, 5, 6, 7}, what is the probability that the numbers are selected in ascending order?	Answers.
A) 1/2560 B) 1/6400 C) 1/4820 D) 1/5040 E) 1/1280

Solution: The total number of ways to arrange 7 numbers is 7! = 5040.   There is only one way to arrange the numbers in ascending order.   P(ascending order) = 1/5040   The answer is 1/5040.
Answer: D
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/5.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? Pick one
A) 5. B) 4. C) 3. D) 2. E) 7.

Solution: We need to get some number which is less than 50 and exactly divisible by 5,5 and 10   Lets take LCM of three balls 5,5 and 10 = 10.   The probability of drawing a blue ball is 1/5...For every 8 balls we get 1 BLUE ball then out of 10 balls we get 2 BLUE balls.   The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 10 balls we get 2 REB balls.   The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 10 balls we get 1 GREEN BALLS.   Then out of 10 - ( 2 + 2 + 1 )= 
10 - ( 2 + 2 + 1 ) = 5
5 YELLOW balls.   IMO option 5. is correct.
Answer: A
How many numbers from 45 to 110 are exactly divisible by 12?
Choose the correct choice from the following answers:	A) 5	B) 7	C) 6	D) 11	E) 12

Solution: Option '6'   45/12 = 3 and 110/12 = 9 ==> 9 - 3= 
9 - 3 = 6
6 Numbers
Answer: C
A train passes a station platform in 36 sec and a man standing on the platform in 24 sec. If the speed of the train is 54 km/hr. What is the length of the platform?  Choose the correct choice from the following: A) 767 m B) 240 m C) 180 m D) 176 m E) 186 m

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 24= 
15 * 24 = 360
360 m.   Let the length of the platform be x m . Then,   (x + 360)/36= 15 => x = 180 m.   Answer:180 m
Answer: C
Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 150 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
Choose one.
A) 1200 B) 800 C) 480 D) 192 E) 400

Solution: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.   But we are told that one of these individual works is 150hrs. hence, possible scenarios, if   (1)2x =150 => 16x = 1200 (2) 3x =150 => 16x = 800 (3) 5x =150 => 16x = 480 (4) 6x =150 => 16x = 400   Hence Answer is 192 192 which can not be any of these.
Answer: D
There are 2 sections A and B in a class, consisting of 24 and 16 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, Find the average of the whole class?	Pick:
A) 35.29kg B) 37.25kg C) 42kg D) 38kg E) 29.78kg

Solution: Total weight of 36+44 students = 24*40 + 16*35= 
24*40 + 16*35 = 1_520
1520   Average weight of the class is= 1520/40= 
1520/40 = 38
38 kg   Answer is 38kg
Answer: D
The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 56 with him, what was the average amount with the group before his joining the group? Choose the correct choice from the following:	A) s.13	B) s.12	C) s.15	D) s.22	E) s.14

Solution: Total members in the group = 7   Average amount = Rs. 20   Total amount with them = 7 * 20 = Rs. 140   One number has Rs. 56. So, the amount with remaining 6 people = 140 - 56 = Rs. 84   The average amount with them = 84/6 = Rs.14.   Answer:s.14
Answer: E
Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 40% nuts, what percent of the combined mixture is dried fruit? Choose the correct choice.
A) 16.7%	B) 23.33%	C) 25%	D) 33.3%	E) 46.7%

Solution: 40% is 10%-points above 30% and 20%-points below 60%.   So the ratio of Sue's mix to Jane's mix is 2:1.   2/3*70% = 140%/3 = 46.7%   The answer is 46.7%.
Answer: E
If it is assumed that 65 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed? Choose the most appropriate option:  A) 400  B) 420  C) 461.5  D) 500  E) 600

Solution: Minimum no of mail to be sent for getting 300 responses at 65%   = 300/0.65 = 461.5   Option 461.5
Answer: C
The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 40 per kg. The inflation rate for the years 1994 and 1995 are expected to be 18% each. The expected price of sugar on January 1, 1996 would be  Choose the most appropriate option:
A) 57.6 B) 58.4 C) 54.4 D) 24.6 E) None of these

Solution: Explanation :   Increase in the price of sugar = (18+2)= 
(18+2) = 20
20%   Hence, price of the sugar on Jan 1, 1996=> (40 * 120 * 120)/( 100 * 100 ) = Rs 57.60.   57.6nswer : 57.6
Answer: A
Susan weighs 10 pounds more than Anna does, and together they weigh a total of 110 pounds. Which of the following represents Anna’s weight in pounds?	Choose the correct choice from the following choices:
A) 50
B) 60
C) 70
D) 80
E) 85

Solution: Total weight = 110   50nna's weight = 110-10 /2 = 50   50nswer : 50
Answer: A
If the pice of sugar rises from Rs. 6 per kg to Rs. 7.50 per kg, a person, to have no increase in his expenditure on sugar, will have to reduce his consumpion of sugar by Choose one:  A) 22  B) 20  C) 98  D) 77  E) 32

Solution: Explanation:   Let original consumption = 100 kg and new consumption = x kg,   So,   Reduction in consumption = 20%.   Answer: 20) 20
Answer: B
Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 3.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn? Choose the correct choice from the following answers:
A) 1/3 B) 1/30 C) 1/42 D) 2 E) 30

Solution: Pete covered 3.5*60= 
3.5*60 = 210
210 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/210=1/42.   Answer: 1/42.
Answer: C
For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?	Choose the correct choice from the following:
A) 1 : 4	B) 3 : 4	C) 2 : 7	D) 3 : 7	E) 1 : 3

Solution: Let the speed of the train be x km/hr and that of the car be y km/hr.   Then, 120 + 480 = 8 1 + 4 = 1 ....(i)   x y x y 15   And, 200 + 400 = 25 1 + 2 = 1 ....(ii)   x y 3 x y 24   Solving (i) and (ii), we get: x = 60 and y = 80.   Ratio of speeds = 60 : 80 = 3 : 4.   3 : 4
Answer: B
A seller of used cars has 16 cars to sell and each of his clients selected 2 cars that he liked most. If each car was selected exactly thrice, how many clients visited the garage?	Pick one:
A) 8
B) 10
C) 12
D) 14
E) 24

Solution: IfNo caris selected more than once then the number of clients = 16/2= 
16/2 = 8
8   But since every car is being selected three times so No. of Clients must be thrice as well= 8*3= 
8*3 = 24
24   Answer: option 24
Answer: E
If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle. Options:
A) 40 cm B) 45 cm C) 50 cm D) 52 cm E) 57 cm

Solution: Explanation:   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.   Answer: Option 50 cm
Answer: C
How much is it cost $0.50 each tire for 8 tires? Choose the correct choice.
A) $3.00
B) $9.00
C) $2.00
D) $4.00
E) $7.00

Solution: D. $4.00
Answer: D
Set A {3,3,3,4,5,5,5} has a standard deviation of 1. What will the standard deviation be if every number in the set is multiplied by 5?  Choose the correct answer
A) A)1 B) B)2 C) C)4 D) D)8 E) E)5

Solution: Points to remember -   1. If oneAdd/Subtractthe same amont from every term in a set, SD doesn't change.   2. If oneMultiply/Divideevery term by the same number in a set, SD changes by same number.   Hence the answer to the above question is 5
Answer: E
If a certain manager had received a 10% raise instead of the 12% raise that she actually received, her salary would have been $65000. What was her actual salary after the raise? Choose the most appropriate option
A) 60000 B) 66181.8 C) 66800 D) 68000 E) 59000

Solution: salary(let X) included 10% increase can be written as   (1+10/100)X=65000   X=65000/1.10------>59090.9   if there is 12% rise in 59090.90   then the salary now is 12% of 59090.9   12*59090.90/100=7090.90   then toal salary after increment=59090.9+7090.90----->66181.8   Ans 66181.8
Answer: B
Multiplication of 2 numbers is 9375 and the quotient, when the larger one is divided by the smalleris 15. Find the sum of the numbers?	Pick.
A) 200	B) 300	C) 400	D) 500	E) 600

Solution: Let the numbers be x and y.   Then, xy = 9375 and	x	= 15.   y   xy	=	9375   (x/y)	15   y2 = 625.   y = 25.   x = 15y = (15 x 25) = 375.   Sum of the numbers = x + y = 375 + 25= 
375 + 25 = 400
400.   400
Answer: C
45 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?	Choose one:
A) 80 litres  B) 90 litres  C) 120 litres  D) 170 litres  E) None of these

Solution: Explanatory Answer   To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*45= 
800/600*45 = 60
60 litres.   However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.   i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.   Therefore, with a 1200 cc engine, quantity of diesel required= 1200/800*60= 
1200/800*60 = 90
90 litres.   Answer 90 litres
Answer: B
If q and s are positive integers such that (2^q)(4^s) = 16, then 2q + s =  Pick one
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: lets get the eq into simplest orm..   (2^q)(4^s) = 16..   (2^q)(2^2s) = 2^4..   or q+2s=4..   since q and s are positive integers, only q as 2 and s as 1 satisfy the Equation..   so 2q+s=2*2+1=5..   5
Answer: D
Find the smallest positive integer n such that tn of the arithmetic sequence 20,19¼ ,18½ ,… is nagative
Pick
A) 27 B) 28 C) 29 D) 30 E) 31

Solution: Here we have , a= 20 = d = 19 ¼-20=-3/4   We	want	to	find	the	first	positive	integer	n such thattn<0   20+(n-1)(-3/4)<0   n>27.33   hence, 28th term is first negative term   ANSWER 28 28
Answer: B
Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Pick one.
A) 19.7 B) 19.9 C) 20.9 D) 21.9 E) 22

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   19.7)
Answer: A
The side of a square has the length of 7. What is the area of the region shaded?
Choose one: A) 48-8π B) 48-6 π C) 24+6π D) 48-7π E) 64-8π

Solution: The area of a square whose side is 7 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded   The correct answer is 48-7π.
Answer: D
Two friends plan to walk along a 33-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 20% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other?  Answers
A) 15
B) 16
C) 17
D) 18
E) 19

Solution: If Q complete x kilometers, then P completes 1.2x kilometers.   x + 1.2x = 33   2.2x=33   x = 15   Then P will have have walked   1.2*15= 
  1.2*15 = 18
18 km.   The answer is 18.
Answer: D
The ratio between the sale price and the cost price of an article is 6:5. What is the ratio between the profit and the cost price of that article?
Answers:
A) 2:9 B) 1:5 C) 3:6 D) 2:0 E) 2:1

Solution: Let C.P. = Rs. 5x and S.P. = Rs. 6x.   Then, Gain = Rs. x   Required ratio = x : 5x = 1:5   Answer:1:5
Answer: B
How many 7 in between 1 to 90?  Choose the correct choice from the following choices:
A) 19
B) 20
C) 22
D) 23
E) 24

Solution: 7,17,27,37,47,57,67,   70,71,72,73,74,75,76,77(two 7's),78,79,87,   19 7's between 1 to 90   19NSWER:19
Answer: A
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :
Select the correct option
A) 2500
B) 2700
C) 2900
D) 3100
E) 3500

Solution: Explanation:   Total number of votes = 7500   Given that 20% of Percentage votes were invalid   => Valid votes = 80%   Total valid votes = 7500 X80/100   1st candidate got 55% of the total valid votes.   Hence the 2nd candidate should have got 45% of the total valid votes   => Valid votes that 2nd candidate got = total valid votes x 45/100   =7500 X 80/100 X 45/100 =2700   ANSWER IS 2700
Answer: B
If the compound interest on a certain sum of money for 4 years at 10% per annum be Rs. 993, what would be the simple interest? Choices:
A) Rs. 880  B) Rs. 890  C) Rs. 1200  D) Rs. 900  E) None

Solution: Let P = Principal   A - Amount   We have a = P(1 + R/100)3 and Rs. 1200I = A - P   ATQ 993 = P(1 + R/100)3 - P   ? P = 3000/-   Now SI @ 10% on 3000/- for 4 yrs = (3000 x 10 x 4)/100   = 1200/-   Answer: Rs. 1200.
Answer: C
ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 6. How many different 5-digit numbers areSvennumbers?  Choose the correct choice from the following choices
A) 20	B) 80	C) 160	D) 220	E) 250

Solution: ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 7. How many different 5-digit numbers areSvennumbers?   4/9*5/10*2/10*2/10*2/10=160/9000   B. 80
Answer: B
How many words can be formed from the letters of the word "AFTER", so that the vowels never comes together	Choose the correct choice from the following answers.
A) 48  B) 52  C) 72  D) 120  E) None of these

Solution: Explanation:   We need to find the ways that vowels NEVER come together.   Vowels are A, E   Let the word be FTR(AE) having 4 words.   Total ways = 4! = 24   Vowels can have total ways 2! = 2   Number of ways having vowel together = 48   Total number of words using all letter = 5! = 120   Number of words having vowels never together = 120-48= 
120-48 = 72
72   Option 72
Answer: C
Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?	Pick one:	A) 9:37	B) 9:31	C) 9:33	D) 9:78	E) 9:32

Solution: 1/4 : 3/4 = (1:3)5 = 5:15   1/5 : 4/5 = (1:4)4 = 4:16   ------   9:31   Answer: 9:31
Answer: B
The speed of a train that is 250 meter in length passing from a railway platform is 150 km/hour. The length of platform is 500 meter. What is the time taken by the train to cross the platform?	Choose the correct answer
A) 1 minute B) 2 minute C) 3 minute D) 4 minute E) 5 minute

Solution: The time starts when the head of first compartment enters the platform from one side. To cover platform, the train has to cover its own length plus the length of the compartment, that is 250 meter + 500 meter = 750 meter. To cover 150 km or 150x1000 meter=15000 meter, train takes 60 minutes or 60x60=3600 seconds. Therefore, to cover 750 meter, the train would take 180 seconds or 3 minutes.   Answer: 3 minute.
Answer: C
The difference between the place values of two sixes in the numerical 81369206 is  Options: A) 0 B) 599 C) 5994 D) 59994 E) None of them

Solution: Required difference = (60000-6)= 
(60000-6) = 59_994
59994.   Answer is 59994
Answer: D
A 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds. What is the length of the platform?
Options:	A) 39.9	B) 37.88	C) 35	D) 38.88	E) 38.09

Solution: Speed = [200 / 42] m/sec = 100/21 m/sec.   Let the length of the platform be x meters.   Then, x + 200 / 50 = 100/21   21(x + 200) = 5000 è x = 38.09 m. Answer: 38.09
Answer: E
Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?  Options:  A) 28 sec  B) 37 sec  C) 17 sec  D) 23 sec  E) 27 sec

Solution: 27 sec   Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds.
Answer: E
Pipe A can fill a tank in 4 hours, pipe B in 6 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled?	Choose the correct choice from the following answers.
A) 1.2  B) 1.4  C) 1.6  D) 1.8  E) 2

Solution: The part filled by A + B + C in 1 hour is 1/4 + 1/6 + 1/12 = 1/2   All the three pipes together will fill the tank in 2 hours.   The answer is 2.
Answer: E
In a business, A and C invested amounts in the ratio 4 : 3 , whereas the ratio between amounts invested by A and B was 1 : 2 . If Rs 182100 was their profit, how much amount did B receive?	Choose the most appropriate option.
A) 97120
B) 100000
C) 90000
D) 95000
E) None of these

Solution: Explanation :   Assume that investment of A = x   Then, investment of B =2x   Investment of C = 3x/4   A:B:C = 1x : 2x : 3x/4 = 1 : 2 : 3/4 =4 : 8 : 3   B's share = 182100 * 8/(4+8+3) = 182100*8/15   = 12140*8= 
12140*8 = 97_120
97120.   97120nswer : Option 97120
Answer: A
The third proportional to 1 and 2 is?  Choose the correct choice from the following
A) 2
B) 1
C) 4
D) 8
E) 7

Solution: (2*2)/1= 
(2*2)/1 = 4
4   Answer: 4
Answer: C
160% of 5/8 =
Select
A) 0.2
B) 0.5
C) 0.6
D) 0.75
E) 1.0

Solution: Should be simple.   1.6*5/8 = 8/8= 
8/8 = 1
1.0   Correct Option : 1.0
Answer: E
What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?  Answers
A) 3
B) 27
C) 30
D) 21
E) 18

Solution: Explanatory Answer   Useful result pertaining to remainders   You can solve this problem if you know this rule about remainders.   Let a number x divide the product of A and B.   The remainder will be the product of the remainders when x divides A and when x divides B.   Using this rule,   The remainder when 33 divides 1044 is 21.   The remainder when 33 divides 1047 is 24.   The remainder when 33 divides 1050 is 27.   The remainder when 33 divides 1053 is 30.   ∴ the remainder when 33 divides 1044 * 1047 * 1050 * 1053 is 21 * 24 * 27 * 30.   Note: The remainder when a number is divided by a divisor 'd' will take values from 0 to (d - 1). It cannot be equal to or more than 'd'.   The value of 21 * 24 * 27 * 30 is more than 33.   When the value of the remainder is more than the divisor, final remainder will be the remainder of dividing the product by the divisor.   i.e., the final remainder is the remainder when 33 divides 21 * 24 * 27 * 30.   When 33 divides 21 * 24 * 27 * 30, the remainder is 30.   30hoice 30
Answer: C
The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?  Choose the correct choice from the following options:
A) 399  B) 272  C) 999  D) 277  E) 311

Solution: Answer: Option 999   Explanation:   a2 = 3136 => a = 56   56 * 4 * 3= 
56 * 4 * 3 = 672
672 – 6= 666 * 1.5= 
666 * 1.5 = 999
999 Answer: 999
Answer: C
P is three times as fast as Q and working together, they can complete a work in 18 days. In how many days can Q alone complete the work? Choose the correct choice from the following answers.
A) 24	B) 77	C) 88	D) 55	E) 778

Solution: P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 18 days, which means Q can do the work in 72 days.   Hence, P can do the work in 24 days.   24nswer:24
Answer: A