MU-NLPC/Calc-aqua_rat huggingface dataset:
Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Choose the most appropriate option:
A) 898
B) 165
C) 120
D) 168
E) 112

Solution: 4x 5x 6x   100 50 25   400x + 350x + 150x = 16000   x = 20   6x = 120   Answer:120
Answer: C
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
Select the correct option
A) 23/38 B) 23/29 C) 23/32 D) 23/35 E) 23/29

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green   = (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂   = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7   = 46/70 = 23/35   Answer: 23/35
Answer: D
If Hema walks at 12 km/hr instead of 8 km/hr, she would have walked 20 km more. The actual distance travelled by Hema is ?  Pick one.
A) 40 kms B) 30 kms C) 46 kms D) 32 kms E) 36 kms

Solution: Explanation:   Let the actual distance travelled be x km.   Then x/8=(x+20)/12   => 12x = 8x + 160   => 4x = 160   => x = 40 km.   40 kmsNSWER IS 40 kms
Answer: A
The speed of a car is 95 km in the first hour and 60 km in the second hour. What is the average speed of the car?  Select the correct option
A) 76 kmph B) 75 kmph C) 77.5 kmph D) 56 kmph E) 86 kmph

Solution: S = (95 + 60)/2= 
(95 + 60)/2 = 155/2 = around 77.5
77.5 kmph   Answer: 77.5 kmph
Answer: C
How many times digit 6 is used while writing numbers from 100 to 1400?	Choose the correct choice.
A) 648
B) 350
C) 252
D) 225
E) 26

Solution: There are 100 numbers which begin with 600   Next, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 6 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000   1000 - 100= 
1000 - 100 = 900
900/10= 
900/10 = 90
90   Number of 10s interval in this is 90. So 90 '6s'   So far we have calculated 190.   The total now comes to 280. The nearest to which is 350. Hence 350.
Answer: B
__2A
x__B
____
CC
In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 6, what is the value of C? Choose the correct choice from the following choices:
A) 8
B) 5
C) 4
D) 3
E) 2

Solution: If 8+B=6   assuming 8 and B are positive then 8*B<10 (they could be either 1,2,3,4,5)   therefore   8*B=C   2*B=C   8+B=6   Three simple equations - divide the 1st/2nd --> 8=2 plug it the 3rd --> B=4 --> C=8 (8NSWER 8)
Answer: A
If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days? Pick one
A) 186  B) 188  C) 810  D) 167  E) 861

Solution: 12 men 120 acres 36 days   54 men ? 54 days   120 * 54/12 * 54/36   10 * 54 * 3/2   54 * 15= 
54 * 15 = 810
810   Answer: 810
Answer: C
In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different Y sets can be produced by this process?
Pick
A) 41	B) 89	C) 125	D) 243	E) 512

Solution: Case 1: 1 used envelope => 1 way   Case 2: 2 used envelopes   - 4-1-0: Choose 4 from 5 cards: 5 ways   - 3-2-0: Choose 3 from 5 cards: 10 ways   Case 3: 41ll envelopes used   - 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways   - 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15   Total Y: 1+5+10+10+15= 
1+5+10+10+15 = 41
41=> 41nswer: 41
Answer: A
Of the 200 employees at company X, 80 are full-time, and 150 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
Options.
A) 20
B) 30
C) 50
D) 80
E) 100

Solution: 200 employees   80 are full-time   150 have worked at company X for at least a year   20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year.   How many full-time employees of company X have worked at the company for at least a year?   200-80= 
200-80 = 120
120 employees not full time   120-20= 
120-20 = 100
100 employees not full time who worked over a year   150 employees have worked at company X for at least a year-100 employees not full time who worked over a year= 50 full-time employees of company X have worked at the company for at least a year   C. 50
Answer: C
The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 300% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994?  Choose the correct choice from the following options:  A) 4N  B) 6N  C) 8N  D) 10N  E) 12N

Solution: In 1992, the company's assets were N.   In 1993, the company's assets were N + 3N =4N.   In 1994, the company's assets were 4N + 4N = 8N.   The answer is 8N.4  + 4= 
4  + 4 = 8
8N.   The answer is 8N.
Answer: C
A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 5. What could be the ratio of Cats to dogs in the pet store?
Select the correct option.
A) 1:3
B) 20:25
C) 1:5
D) 2:5
E) 4:6

Solution: Say theratioof cats to dogs is a/b. Then thenumberof cats would be ax and thenumberof dogs bx, for some positive integer x.   We are told that ax - bx = 5 --> x(a - b) = 5. Since 5 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*5.   The above implies that either x = 1 and a - b = 5 or x = 5 and a - b = 1.   Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13.   For the original question only option which fits is E, 4:5. Cats = 5*4= 
5*4 = 20
20 and dogs= 5*5= 
5*5 = 25
25.   Answer: 20:25.
Answer: B
A and B together have Rs. 1210. If of A's amount is equal to of B's amount, how much amount does B have?
Choose the correct choice from the following choices.
A) 484	B) 460	C) 550	D) 664	E) None of them

Solution: 4/15 A = 2/5 B   A = (2/5 x 15/4)B   A = 3/2 B   A/B = 3/2   A : B = 3 : 2.   Therefore, B's share = Rs. (1210 x 2/5)= Rs. 484.   484nswer is 484.
Answer: A
When 24 is divided by the positive integer d, the remainder is 4. Which of the following statements about d must be true?
I. d is even
II. dis a multiple of 5
III. d is a factor of 20  Options:	A) III only	B) I and II only	C) I and III only	D) II and III only	E) I, II, and III

Solution: 24= m*d + 4   m*d=20   put values of m   m=1 d=20   m=2 d=10   m=4 d=5   I. not true   II. true   III. true   D. correct
Answer: D
Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 34 years old, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat?
Choose the correct option:  A) 20  B) 21  C) 22  D) 23  E) 25

Solution: Check two extreme cases:   Jane = 18, child = 9, years ago = 34-18= 
34-18 = 16
16 --> child's age now= 9+16= 
9+16 = 25
25;   Jane= 24, child = 12, years ago = 34-24= 
34-24 = 10
10 --> child's age now= 12+10= 
12+10 = 22
22.   Answer: 25.
Answer: E
When 40 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?	Choose the correct choice from the following answers.
A) 3 : 4  B) 4 : 3  C) 1 : 1  D) Data inadequate  E) None of these

Solution: Let the first and the second numbers be x and y respect then   y + 40% of x = 140% of y   or, y + 0.4x = 1.4y   or, 0.4x = 0.4y   ∴ x : y = 0.4 : 0.4 = 4 : 4   Answer 1 : 1
Answer: C
In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is $560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is $1,290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat? Choices
A) $50
B) $320
C) $150
D) $100
E) $400

Solution: Let x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat.   4x + 4y + 2z = 560 :   9x + 9y + 6z = 1,290   3x + 3y + 2z = 430 : divide all terms of equation C by 3   x + y = 130 : subtract equation D from equation B   3(x + y) + 2z = 430 : equation D with factored terms.   3*130 + 2z = 430   z = 20 : solve for z   x + y + z = 130 + 20= 
130 + 20 = 150
$150   correct answer $150
Answer: C
One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Vimal?
Choose the most appropriate option:  A) 31  B) 32  C) 33  D) 36  E) 35

Solution: Let the age of Sooraj and Vimal, 1 year ago, be 6x and 7x respectively.   Given that, four years hence, this ratio would become 7:8   ⇒(6x+5):(7x+5)=7:8⇒8(6x+5)=7(7x+5)⇒48x+40=49x+35⇒x=5   Vimal's present age   =7x+1=7×5+1=36   Answer is 36.
Answer: D
If a and b are unique prime integers, which of the following must be odd? Choose the correct option:
A) a−b
B) 2a+2b
C) 2a−2b
D) 2a / 2b
E) ab^2

Solution: Any number multiplied by 2 has to be an even number. hence   a−bnswer a−b
Answer: A
A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?  Pick one.
A) 44 sec B) 49 sec C) 42 sec D) 47 sec E) None of these

Solution: Let the length of the train be x m.   When a train crosses an electric pole, the distance covered is its own length.   So, x = 12 * 36 * 5 /18= 
12 * 36 * 5 /18 = 120
120 m.   Time taken to cross the platform= (120 +350)/ 36 * 5/18 = 47 min.   ANSWER:47 sec
Answer: D
A man can row downstream at the rate of 18 Kmph and upstream at 6 Kmph. Find the man’s rate in still water and rate of current? Choose the correct option.
A) 8.5  B) 6.0  C) 9.5  D) 9.0  E) 8.25

Solution: Rate of still water = 1/2 (down stream + upstream)   = 1/2 (18 + 6) = 12 Kmph   rate of current = 1/2 (down stream - upstream)   = 1/2 (18 - 6)   = 1/2 (12)   = 6 kmph   Answer is 6.0.
Answer: B
A tank is filled by 3 pipes A,B,C in 3 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?  Choose the correct choice:	A) 25hr	B) 35hr	C) 40hr	D) 20hr	E) 21hr

Solution: Suppose pipe A alone take x hours to fill the tank   Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank.   1/x + 2/x + 4/x = 1/3   7/x = 1/3   x = 21 hours   Answer is 21hr
Answer: E
An iron cubes of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5 the sides are
Choices:
A) 10 cm, 50 cm B) 20 cm, 100 cm C) 40 cm, 200 cm D) None of these E) Cannot be determined

Solution: Solution   Let the sides of the sheet be x and 5x.   Then,volume of the sheet= volume of the cube   ‹=› x × 5x ×1/2   ‹=› 10×10×10   ‹=› 5x2= 2000   ‹=› x2= 400   ‹=› x = 20.   The sides are 20 cm and 100 cm.   Answer 20 cm, 100 cm
Answer: B
Pipe A can fill a tank in 10 hr, pipe B in 20hr and pipe C in 40hr. If all the pipes are open in how many hours will tank be filled?	Choose the correct choice:
A) 1hr	B) 30min	C) 15min	D) 17min	E) 10min

Solution: Part filled by (A+B+C) in 1hour = 1/10 + 1/20 + 1/40 = 7/40   All the 3 pipes together will fill the tank in 17min Approximately   Answer is 17min
Answer: D
If for any number N, f(N) is defined as the least integer that is greater than or equal to N^2, then what is the value of f(-1.5)?	Select the correct option:
A) -4	B) -3	C) 1	D) 2	E) 3

Solution: If N=-1.5, then N^2=2.25.   The least integer that is greater than or equal to 2.25 is 3, thus f(-1.5) = 2.25.   The answer is 3.
Answer: E
Find the invalid no.from the following series 15 46 63 71 75 77 78	Choose the correct choice:
A) 15
B) 46
C) 71
D) 75
E) 78

Solution: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on. 46   46
Answer: B
The function f(x) is defined for all positive integers x as the number of even factors of x and the function g(x) is defined for all positive integers x as the number of odd factors of x. For positive integers a and b if f(b)*g(a) = 0 and f(a) = 1, which of the following could be the least common multiple of a and b?  Choose the correct answer.
A) 12
B) 16
C) 20
D) 30
E) 36

Solution: f(b)∗g(a)=0 : any positive integer has at least one odd factor: 1. Thus, g(a) cannot be 0, which implies that f(b) = 0. This on the other hand means that b is an odd integer (odd integers does not have even factors).   f(a)=1f(a)=1: aa has 1 even factor. This means that aa must be 2 (the only positive integer which has only 1 even factor is 2).   The least common multiple of a=2a=2 and b=odd is 2∗odd. Only option D can be represented this way: 30=2∗1530=2∗15.   Answer: 30
Answer: D
The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 55% profit? Choose the correct choice from the following:
A) $480	B) $450	C) $992	D) $870	E) $660

Solution: C   Let C.P. = $ x.   Then, 832 - x = x - 448   2x = 1280 => x = 640   Required S.P. = 155% of $ 640 = 150/100 * 640 = $ 992.
Answer: C
In filling a room with gas 100 m * 10 m * 10 m the volumes of gas will be?  Choose the correct answer:
A) 100 cu.m
B) 1000 cu.m
C) 10000 cu.m
D) 100000 cu.m
E) 10000000 cu.m

Solution: 100 * 10 * 10= 
100 * 10 * 10 = 10_000
10000   ANSWER:10000 cu.m
Answer: C
Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is r, what is the difference between the probability that r is even and the probability that r is odd?	Choose the correct choice from the following.
A) 1/9  B) 1/6  C) 2/9  D) 1/4  E) 1/2

Solution: 1/9ge of Boys r:4, 6, 7   Sum of ages taken 2 at a time: 10,13,11   1/9ges of Girls:5, 8, 9   Sum of ages taken 2 at a time: 13,17,14   9 Combinations of sum between sets(10,12,11)(13,17,14)   =23,27,24- 16,30,17- 24,28,25   Prob(Even)= 5/9   Prob(Odd) =4/9   1/9nswer=5/9 - 4/9 = 1/9
Answer: A
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?	Pick.
A) 3.6 sec B) 18 sec C) 36 sec D) 72 sec E) None

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 120= 
240 + 120 = 360
360 m.   Time taken= 360/10= 
360/10 = 36
36 sec   ANSWER:36 sec
Answer: C
A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:	Options
A) 1/26
B) 1/52
C) 2/62
D) 2/26
E) 3/26

Solution: Here, n(S) = 52.   Let E = event of getting a queen of club or a king of heart.   Then, n(E) = 2.   P(E) = n(E)/n(S)   = 2/52   = 1/26   1/26nswer should be 1/26
Answer: A
Today Chris ate 15 jellybeans. Bella ate 2/3 of the jellybeans Chris did, Frances ate 5 more jellybeans than Bella did , and Sandhya ate 20% more than Frances. How many jellybeans did Sandhya eat?
Choose the correct choice from the following
A) 18 B) 20 C) 13 D) 25 E) 15

Solution: A   13   Chris ate 15 jellybeans   Bella ate 2/3 of the jellybeans Chris did.   Bella= 2/3 x 15   =10   Frances ate 5 more jellybeans than Bella.   Frances= 10+5 jellybeans.   =15   Sandhya ate 20% more jellybeans than Frances.   Sandhya = 15 + 15 × 20%   = 15 + 15 × 0.20   = 15 + 3= 
15 + 3 = 18
18   Sandhya ate 18 jellybeans.   The correct answer is 18.
Answer: A
In a shop 40% of the articles are sold at a profit of 20% and the remaining at a loss of 10%.what is the overall profit/loss?	Choose the correct choice from the following answers.
A) 6% loss B) 4% loss C) 2% profit D) 10% loss E) none

Solution: 40*1.2+60*0.9/100=1.02   ANSWER:2% profit
Answer: C
Vijay bought 160 shirts at the rate of Rs. 205 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?  Choose the correct choice from the following:
A) s.225  B) s.288  C) s.485  D) s.261  E) s.282

Solution: Total CP per shirt = 205 + 1400/160 + 1.75 + 320/160 = Rs. 217.5   SP = CP[(100 + profit%)/100]   = 217.5 * [(100 + 20)/100] = Rs.261.   Answer:s.261
Answer: D
A number is increased by 10% and then decreased by 10%, the final value of the number is ? Choose the most appropriate option
A) decreases by 1%	B) decreases by 2%	C) decreases by 3%	D) decreases by 4%	E) none of the above

Solution: Here, x = 10 and y = - 10   Therefore, the net % change in value   = ( x + y + xy/100)%   = [10 - 10 + (10 * -10)/100]% or - 1%   Since the sign is negative, there is a decrease in value by 1%.   decreases by 1%NSWER:decreases by 1%
Answer: A
Mangala completes a piece of work in 9 days, Raju completes the same work in 21 days. If both of them work together, then the number of days required to complete the work is
Pick one.
A) 6 days
B) 7 days
C) 8 days
D) 9 days
E) 11 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 9 Ã— 21/30 = 6 days.   6 days
Answer: A
What is the probability of getting a sum 9 from two throws of a dice? Options:
A) 1/6
B) 1/8
C) 1/9
D) 1/12
E) None of these

Solution: In two throws of a dice, n(S) = (6 x 6) = 36.   Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.   P(E) =n(E)/n(S)=4/36=1/9	.   Answer:1/9
Answer: C
In a covering a certain distance the speed of A and B are in the ratio of 6: 9, A takes 20 min more, than B to reach the destination. The time taken by A to reach the destination is:  Choose the correct option:
A) 1 Hour	B) 2 Hours	C) 1.5 Hours	D) 2.5 Hours	E) 3 Hours

Solution: Let the speed of 1 Hour and B are 6x Kmph   and 9x Kmph respectively,   Let the total distance to travel = y Km   y/6x - y/9x = 1/3   y/x(1/18 = 1/3   y = 6x   Required time = 6x/6x = 1 hour   1 Hournswer 1 Hour.6 /6= 
6 /6 = 1
1 hour   1 Hournswer 1 Hour.
Answer: A
In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.	Choose the correct choice from the following answers
A) 215,000 B) 216,000 C) 217,000 D) 218,000 E) 219,000

Solution: This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.   For this particular question : Increase in the population every 2 seconds = 7-2= 
7-2 = 5
5 people.   Total 2 second interval in a day= 24*60*60/2 = 43,200   Population increase = 43,200 * 5 = 216,000. Hence 216,000.
Answer: B
9 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
Pick one:
A) 40587	B) 60451	C) 16152	D) 24325	E) 40320

Solution: it is like a circular arrangement.   total ways for n people to arrange in a circle is = factorial (n-1)   in this case n= 9   hence ans = 8 factorial = 40320   hence 40320
Answer: E
A is twice as fast as B. If B alone can do a piece of work in 24 days, in what time can A and B together complete the work?	Choose the correct answer
A) 10	B) 12	C) 6	D) 2	E) 8

Solution: A can do the work in 24/2 i.e., 12 days.   A and B's one day's work = 1/12+ 1/24 = (2 + 1)/24 = 1/8   So A and B together can do the work in 8 days.   Answer: 8
Answer: E
The expression (5x-2)/(x+3) is equivalent to which of the following?
Choose the correct choice from the following choices.
A) (5-2)/3  B) 5 – (2/3)  C) 5 – (x)/(x+3)  D) 5 – (17)/(x+3)  E) 5 + (17)/(x+3

Solution: iven asked to find the value of (5x-2)/(x+3)...   Now take X as 1 then we get 3/4...   From the options check which one gets the same 3/4.   From option D = 5 – (17)/(x+3) => 5 - (17)/(1+3) => 3/4.. All other options will result in some other value..   Answer: 5 – (17)/(x+3) is the correct option
Answer: D
From a group of 7 women and 6 men, five persons are to be selected to form a committee so that at least 3 women are there in the committee. In how many ways can it be done? Choices
A) A)650
B) B)656
C) C)696
D) D)724
E) E)756

Solution: From a group of 7 women and 6 men, five persons are to be selected with at least 3 men.   Hence we have the following 3 options.   We can select 5 women ...(option 1)   Number of ways to do this = 7C5   We can select 4 men and 1 man ...(option 2)   Number of ways to do this = 7C4 × 6C1   We can select 3 women and 2 men ...(option 3)   Number of ways to do this = 7C3 × 6C2   Total number of ways   = 7C5 + (7C4 × 6C1) + (7C3 × 6C2)   = 7C2 + (7C3 × 6C1) + (7C3 × 6C2)[∵ nCr = nC(n - r) ]   =   7   ×   6   2   ×   1   +   7   ×   6   ×   5   3   ×   2   ×   1   ×   6   =7×62×1+7×6×53×2×1×6   +   7   ×   6   ×   5   3   ×   2   ×   1   ×   6   ×   5   2   ×   1   +7×6×53×2×1×6×52×1   =   21   +   210   +   525   =   756   =21+210+525= 
21+210+525 = 756
756   756)
Answer: E
There are 9 color balls at a row. From that how many ways can 9 different color balls be arranged in a row so that black, white, red and green are never together?
Choose the correct choice from the following answers:
A) 223600 B) 214600 C) 566600 D) 786789 E) 345600

Solution: Total number of ways in which 9 different colour balls can be arranged in a row   =9! ⋯(A)   Now we will find out total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are always together.   We have total 9 balls. Since black, white, red and green balls are always together, group these 4 balls together and consider as a single ball. Hence we can take total number of balls as 6. These 6 balls can be arranged in 6! ways.   We had grouped 4 balls together. These 4 balls can be arranged among themselves in 4! ways.   Hence, total number of ways in which 9 different colour balls be arranged in a row so that black, white, red and green balls are always together   =6!×4! ⋯(B)   From (A) and (B),   Total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are never together   =9!–6!×4!=6!×7×8×9−6!×4!=6!(7×8×9–4!)=6!(504–24)=6!×480=720×480=345600   345600
Answer: E
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is? Pick.
A) 76	B) 21	C) 26	D) 28	E) 11

Solution: Explanation:   Lot the total number of workers be v Then,   8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21.   Answer: 21
Answer: B
The area of a triangle is with base 4m and height 8m?
Pick
A) 11
B) 10
C) 787
D) 16
E) 12

Solution: 1/2 * 4 * 8= 
1/2 * 4 * 8 = 16
16 m2   Answer: 16
Answer: D