MU-NLPC/Calc-aqua_rat huggingface dataset:
Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 27 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks	Choose the correct choice from the following choices:
A) 27/8 B) 3 C) 4 D) 9 E) 12

Solution: In 15 mins, Timothy travels=9/4 miles.   Now, let his mother takes x hours to reach him, traveling at 27mph.   So, 27x=9x+9/4   x=1/8 hrs.   Thus, the distance traveled by his mother to reach= 27*1/8=27/8miles. 27/8ns 27/8
Answer: A
Sandy invested a certain sum of money at 12% p.a. simple interest for 'n' years. At the end of 'n' years, Sandy got back 4 times the original investment. What is the value of n?
Choose the correct choice from the following answers.
A) 20 B) 25 C) 30 D) 35 E) 40

Solution: n* 0.12 * principal + principal = 4 * principal   n * 0.12 = 3   n = 25 years   The answer is 25.
Answer: B
A train 550 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Choose the correct choice: A) 5 sec B) 6 sec C) 7 sec D) 10 sec E) 30 sec

Solution: Solution   Speed of train relative to man =(60+6) km/hr= 66km/hr   =(66x5/18) m/sec =(55/3) m/sec   ∴ Time taken to pass the man = (550 x 3/55)sec = 30 sec   Answer 30 sec
Answer: E
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
Pick one
A) 2%  B) 2.02%  C) 4%  D) 4.04%  E) 5%

Solution: Correct value is 100x100.   Measured value is 102x102.   Therefore ERROR Value is (102x102)-(100x100) = 404.   Error% = (error value/ true value)*100.   = (404/100x100)x100 = 4.04.   answer :4.04%
Answer: D
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 200 revolutions. How many revolutions does the second wheel make in covering d feet?
Choose the correct choice from the following:
A) 200x/y
B) 200y - x
C) 200x - y
D) 200y/x
E) 200xy

Solution: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)   Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)   Revolutions = distance/circumference   So, from equation (1)   200 = d/(x*pi)   d = 200 * x * pi ---------- (3)   From equation (2)   Revolutions = d/(y*pi) = (100 * x * pi) / (y*pi) = 200x/y   200x/ynswer (200x/y)
Answer: A
A certain barrel, which is a right circular cylinder, is filled to capacity with 300 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?	Options.
A) There is no empty capacity B) 2100 gallons C) 2300 gallons D) 2100 gallons E) 2800 gallons

Solution: Radius of first cylinder=r, diameter=2r, height=h   Radius of second cylinder=2r, diamter=2d and height=2h   Volume of first cylinder=pie (r^2)*h=300   Volume of second cylinder=pie(2r^2)2h   Put the value of pie (r^2)*h=300 in the second cylinder,volume= pie (r^2)*4*2=300*8= 
300*8 = 2_400
2400 gallons   Empty capacity=2100 gallons   Answer 2100 gallons
Answer: D
Tommie spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommie won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?
Select.
A) 330
B) 500
C) 520
D) 540
E) 620

Solution: I drew a diagram:   1 - $20   2 -   3 -   4 - $320   5 -   6 -   Total: $1,620   Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3= 
300 / 3 = 100
100). So each day, he earned $100 more. This means on day 6, tommie earned$520. Answer choice 520.
Answer: C
If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?
1. Line L must passes through the first quadrant.
2. Line L does pass the origin.
3.The slope of L is negative	Choices
A) I only B) II only C) III only D) I and II E) II and III

Solution: Slope of the given line= 3-n/n-3   Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.   1) n<3 (n=2)   3-2/2-3= -1   2) n<3 (n= 0)   3-0/0-3= -1   3) n<3 (n=-3)   3+3/ -3-3= -2/3   4) n>3   3-4/4-3= -1   Answer III only
Answer: C
In an examination, 35% of total students failed in Hindi, 45% failed in English and 20% in both. The percentage of these who passed in both the subjects is : Options
A) 23
B) 37
C) 28
D) 40
E) 81

Solution: Explanation:   Formula n(a∪b) = n(a) + n(b) − n(a∩b)   Fail in Hindi or English = 35 + 45 – 20 = 60   Therefore students who passed = 100 – 60 = 40.   Answer: 40
Answer: D
A can do a piece of work n 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each. How long will they take to do it working together 8 2/5 hours a day?
Choices: A) 3 days B) 6 days C) 2 days D) 8 days E) 4 days

Solution: A can complete the work in (7*9)= 
(7*9) = 63
63 days   B can complete the work in   (6*7)= 
  (6*7) = 42
42 days   --> A’s one hour’s work= 1/63 and B’s one hour work = 1/42.   (A+B)’s one hour work = 1/63+1/42 = 5/126   Therefore, Both can finish the work in 126/5 hours.   Number of days of 8 2/5 hours each = (126*5/(5*42))= 
(126*5/(5*42)) = 3
3 days   3 daysnswer : 3 days
Answer: A
What is the probability that in the rearrangements of the word AMAZED, the letter ’E’ is positioned in between the 2 ’A’s (Not necessarily flanked)? Choose the correct choice:
A) 1/6
B) 1/4
C) 1/3
D) 1/5
E) 1/8

Solution: In any rearrangement of the word, consider only the positions of the letters A, A and E.   These can be as A A E, A E A or E A A.   Therefore, effectively one-third of all words will have ’E’ in between the two ’A’s.   ANSWER:1/3
Answer: C
If b does not equal zero, and ab = b/6, what is the value of a? Select:
A) A)1/6 B) B)1/4 C) C)1/3 D) D)1/2 E) of the above

Solution: Explanation:   To solve for a, divide both sides of the equation by b: ab = b/6   (ab)/b = (b/6)/b   a = (b/6)*1/b   a = 1/6   1/6nswer: (1/6).
Answer: A
How many ways are there to split a group of 8 boys into two groups of 4 boys each? (The order of the groups does not matter) Select the correct option:	A) 35	B) 40	C) 42	D) 44	E) 46

Solution: the combination is 8C4 /2   = 8!/4!*4! *2 = 35   35
Answer: A
If A is thrice as fast as B and together can do a work in 12 days. In how many days A alone can do the work?	Select the correct option:
A) 16  B) 42  C) 28  D) 54  E) 45

Solution: 16’s one day’s work= 1/X   B’s one day’s work= 1/3x   16 + B’s one day’s work= 1/x + 1/3x = 1/12   = 3+1/3x = 4/3x = 1/12   x = 12*4/3= 
12*4/3 = 16
16   16NSWER:16
Answer: A
Length of a rectangular plot is 28 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?	Pick:
A) 54 m	B) 64 m	C) 74 m	D) 84 m	E) 94 m

Solution: Let breadth = x metres.   Then, length = (x + 28) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 28) + x] = 200   2x + 28 = 100   2x = 72   x = 36.   Hence, length = x + 28 = 64 m   64 m
Answer: B
The sum of two number is 25 and their difference is 13. Find their product.  Choose the correct option
A) 104
B) 114
C) 315
D) 325
E) 271

Solution: Let the numbers be x and y.   Then, x + y = 25 and x - y = 13.   4xy = (x + y)2 - (x- y)2   = (25)2 - (13)2   = (625 - 169)= 
(625 - 169) = 456
456   xy= 114.   Answer: 114
Answer: B
Two dice are tossed. The probability that the total score is a prime number is Select
A) 2/13
B) 5/7
C) 31/7
D) 6/7
E) 5/12

Solution: n(S)=36   5/12= {(1,1),(1,2), (1,4),….(6,5)}   n(5/12)=15   P(5/12)=15/36   =5/12   Ans: 5/12
Answer: E
A certain elevator has a safe weight limit of 2,500 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds?  Choose the correct option:
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: Lets assume there are 2X people.   Half of them have average weight of 200 and other half has 230.   Maximum Weight is = 2500   So 200*X + 230*X = 2500   => 430X = 2500   => X is approximately equal to 6.   So total people is  2*6= 
 2*6 = 12
12   We are not taking 12 as answer because say 11th person has minimum of 180 weight then   200*6 + 230*6= 
200*6 + 230*6 = 2_580
2580 (Which is more than 2500)   Answer 11.
Answer: E
The Royals softball team played 75 games and won 55 of them. What percent of the games did they lose? (round to the nearest tenth)  Select:
A) 26.7% games lost  B) 27.7% games lost  C) 25.7% games lost  D) 20.7% games lost  E) 22.7% games lost

Solution: Total 100%=75   Won=55   Lost=20   75-55= 
75-55 = 20
20   x/100=20/75   Multiply the opposites:   100 x 20 = 2000   Divide by the remaining number:   26.667/2000.000   75   26.7% games lost (rounded to tenth)   correct answer 26.7% games lost
Answer: A
Some of the people in Town B are left-handed, some are tall, some are both, and some are neither. In Town Y, three times as many people are left-handed > as are left-handed in Town B, three times as many people are tall as are tall in Town B, three times as many people are both as are both in Town B, but no one is neither. If the total number of people in Town B is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town B who are neither left-handed nor tall?
Select the correct option.
A) 23
B) 39
C) 72
D) 143
E) 199

Solution: Yes, correct answer is indeed D.   {B}={Left} + {Tall} - {Both} + {Neither};   {Y} = 3*{Left} + 3*{Tall} - 3*{Both};   Since the total number of people in Town B is four times greater than the total number of people in Town Y, then:   {Left} + {Tall} - {Both} + {Neither}=4*(3*{Left} + 3*{Tall} - 3*{Both});   {Neither}=11*({Left} + {Tall} - {Both}), which means that # of people in Town B who are neither left-handed nor tall must be a multiple of 11.   Only answer choice D, is a multiple of 11: 143=11*13.   Answer: 143.
Answer: D
January 1, 2007 was Monday. What day of the week lies on Jan. 5, 2008? Choose the correct choice from the following
A) Monday  B) Tuesday  C) Wednesday  D) Saturday  E) Sunday

Solution: The year 2007 is an ordinary year. So, it has 1 odd day.   day of the year 2007 was Monday   day of the year 2008 will be 5 days beyond Monday   Hence, It will be Saturday. answer : Saturday
Answer: D
Beth received 1/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?	Choose the correct answer.
A) 1/5 B) 2/7 C) 3/8 D) 7/20 E) 1/2

Solution: Let the total votes be 10. Beth received 2 votes, other votes  10-2= 
 10-2 = 8
8. In order to have received 1/2 of the votes she needed 5 votes so 3 more, which is 3/8 of the other votes.   Answer: 3/8.
Answer: C
One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:  Choose the correct choice from the following answers:
A) 180 min B) 160 min C) 280 min D) 18 min E) 190 min

Solution: Let the slower pipe alone can fill the tank in x minutes   Then the faster pipe can fill the tank in x/4 minutes   Part filled by the slower pipe in 1 minute = 1/x   Part filled by the faster pipe in 1 minute = 4/x   Part filled by both the pipes in 1 minute = (1/x)+(4/x)   180 minnswer is 180 min   It is given that both the pipes together can fill the tank in 36 minutes   ⇒ Part filled by both the pipes in 1 minute = 1/36   (1/x)+(4/x)=1/36   5/x=1/36   x=5×36=180   i.e.,the slower pipe alone fill the tank in 180 minutes
Answer: A
the present average age of a couple and their daughter is 35 years. Fifteen years from now, the age of the mother will be equal to the sum of present ages of the father and the daughter. Find the present age of mother? Pick one:
A) 38 B) 49 C) 55 D) 45 E) 50

Solution: 45   45   (f + m + d)/3 = 35   => f + m + d = 105 --- (1)   m + 15 = f + d   Substituting f + d as m + 15 in (1), we get   2m + 15 = 105   2m = 90 => m = 45 years.
Answer: D
A firm has 4 senior partners and 6 junior partners. How many different groups Q of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
Options.
A) 48 B) 100 C) 120 D) 288 E) 600

Solution: What seems to work as well, though its tougher to come up with this solution:     (10*9*8) * 2/3 + (10*9*4)*1/3= 
  (10*9*8) * 2/3 + (10*9*4)*1/3 = 600
600. Divided by all possible permutations (=3!) yields 100.   Explanation: For the first spot you have 10 possible canditates, for the 2nd 9. For the 3rd spot you need to differentiate if a senior partner has been picked for one of the first 2 spots or not. If yes, then you can pick one of the 8 remaining guys, so 10*9*8. If no senior partner has been picked yet, you need 10*9*4.   Now you need to weight the 2 cases with the corresponding probabilities: probability of no senior partner being picked in the first 2 draws = 6/10*5/9=1/3, so you weight 10*9*4 with 1/3. For the complementary case (senior partner was picked in the first 2 draws) you just take the complementary prob (1-1/3)= 2/3 and weight 10*9*8 with it.   Now you just need to divide the answer (600) by the number of different positions (=3!) and get Q=600/6=100.100
Answer: B
A software programmer does 20% of the work in 70% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X? Pick:
A) 13x /15
B) 15x/15
C) 7x/15
D) 2x/30
E) 13x/30

Solution: Take X=30 lines   70% of 30 = 24 lines   20% of 30 = 6 lines   W - R - T   6 lines - r1 - 24 (first 70% of the 30 days)   24 lines - r2 - 6 ( last 20% of the 20 days)   r1 = 1/4r2 = 4   Now Work in last 14 days = 6 days programmer worked at r2 + 8days programmer worked at r1   => 6 * 4 + 8 * 1/4 = 24 + 2= 
24 + 2 = 26
26   Insert, X=30 in all options => 15x/15 is the answer.
Answer: B
The average marks obtained by 100 candidates in an examination is 50. Find how many candidates have passed in the examination, if the average marks of candidates who passed is 70 and that of failed candidates is 20.  Choose the correct choice:  A) 33  B) 77  C) 60  D) 29  E) 11

Solution: Explanation:   Let the number of students who passed the examination be X   Number of students failed = (100 - X)   Total marks of students who have passed = 70X   Total marks of 100 students = 100 * 50= 
100 * 50 = 5_000
5000   Total marks of students who have failed= 20(100 – X)   20(100 – X) + 70X = 5000   2000 – 20 X + 70X = 5000   50 X = 3000   X = 60   ANSWER: 60
Answer: C
David has d books, which is 2 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?
Choose the correct answer
A) 5/6*d	B) 7/3*d	C) 10/3*d	D) 7/2*d	E) 9/2*d

Solution: Although we could plug in a real value for d, the problem can be just as easily solved by setting up equations. However, let’s start by defining some variables. Since we are given that David has d books, we can use variable d to represent how many books David has.   number of books David has = d   number of books Jeff has = j   number of books Paula has = p   We are given that David has 3 times as many books as Jeff. We can now express this in an equation.   d = 2j   d/2 = j   We are also given that David has ½ as many books as Paula. We can also express this in an equation.   d = (1/2)p   2d = p   Notice that we immediately solved forj in terms of d and p in terms of d. Getting j and p in terms of d is useful when setting up our final expression. We need to determine, in terms of d, the sum of the number of books for David, Jeff, and Paula. Thus, we have:   =d + d/2 + 2d   =7d/2   The answer is 7/2*d
Answer: D
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?  Options.
A) 0	B) 1	C) 10	D) 19	E) 21

Solution: Explanation:   Average of 20 numbers = 0.   Sum of 20 numbers (0 x 20) = 0.   It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a)   ANSWER IS 19
Answer: D
At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $55,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
Pick one
A) $10,000 B) $11,200 C) $12,000 D) $19,800 E) $13,200

Solution: 1 machine of type B will cost: 20% down payment of 55,000 = 11,000plusremaining sum (55,000-11,000=44,000) with 40% of finance charges 44,000*1.4=61,600 --> 11,000+61,600=72,600;   2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;   Difference = 72,600 - 52,800 = 19,800.   Answer: $19,800.
Answer: D
A watch was sold at a loss of 10%. If it was sold for Rs.182 more, there would have been a gain of 4%. What is the cost price?  Choose the correct choice:
A) s:1000	B) s:1067	C) s:1278	D) s:1300	E) s:1027

Solution: 90%   104%   --------   14% ---- 182   100% ---- ? =>   Rs:1300   Answer: s:1300
Answer: D
If the complement of a certain angle is three times the measure of that certain angle, then what is the measure of that certain angle?
Select the correct option:
A) 45 B) 30 C) 22.5 D) 18 E) 15

Solution: The original angle is x, so the complement is 3x, and together, these add up to 90 degrees.   x + 3x = 90   4x = 90   x = 22.5   Answer = (22.5)
Answer: C
The length of a rectangular garden is three times its width. If the area of the rectangular garden is 432 square meters, then what is the width of the rectangular garden?	Answers
A) 8	B) 9	C) 10	D) 11	E) 12

Solution: Let x be the width of the garden.   3x^2 = 432   x^2 = 144   x = 12   The answer is 12.
Answer: E
If the number 517*324 is completely divisible by 7, then the smallest whole number in the place of * will be: Choose one.
A) 3	B) 1	C) 2	D) 4	E) 6

Solution: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 7.   x = 6.   6
Answer: E
Vijay 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?
Select the correct option:
A) 19
B) 19.7
C) 21
D) 21.1
E) 23

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: B
In a certain population, there are 4 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is  Choose the correct answer.
A) 4 to 5  B) 1 to 3  C) 1 to 4  D) 2 to 3  E) 3 to 4

Solution: Consider the ratio of the under population of 21 to over the 21 as 4:1   therefore 4x:1X   Now the ratio of the under to the whole population becomes 4x/4x+1x   = 4/5   4 to 5nswer is 4 to 5
Answer: A
In how many ways can 8 Indians , 4 Americans and 4 Englishmen be selected in a row so that all persons of the same nationality sit together? Select the correct option:
A) 3!8!4!4!
B) 2!4!4!
C) 8!
D) 4!4!4!
E) 4!4!

Solution: Treat each nationality as one. So there are 3 persons can be arranged in 3! ways   8 Indians can be arranged in 8! ways   4Englishman can be arranged in 4!ways   43!8!4!4!merican can be arranged in 4! ways   Required number of ways = 3!8!4!4!   3!8!4!4!nswer is 3!8!4!4!
Answer: A
Sonika bought a V.C.R. at the list price of 18,400. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R.  Choose the correct choice from the following.
A) 19,872
B) 19,780
C) 19,680
D) 19,380
E) None of these

Solution: Sol. List price of V.C.R. =18,400   Rate of sales tax = 8%   ∴ Sales tax = 8% of 18,400   = 8⁄100 × 18400 = 1472   So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,400 + 1472   = 19,872. 19,872nswer 19,872
Answer: A
A word is defined as a sequence of four dots arranged in a row. Each dot is colored either red, yellow, or blue. How many distinct words can be formed? Choose the most appropriate option:
A) 36
B) 48
C) 64
D) 81
E) 120

Solution: 3^4 = 81   The answer is 81.
Answer: D
The area of a triangle is with base 4m and height 6m?
Choose the correct choice from the following options
A) 11 m2	B) 10 m2	C) 18 m2	D) 19 m2	E) 12 m2

Solution: 1/2 * 4 * 6= 
1/2 * 4 * 6 = 12
12 m2   Answer: 12 m2
Answer: E
A can do a piece of work in 21 days and B in 28 days. Together they started the work and B left after 4 days. In how many days can A alone do the remaining work?	Choose the correct answer:	A) 33	B) 276	C) 27	D) 14	E) 66

Solution: Let A worked for x days.   x/21 + 4/28 = 1 => x/21 = 6/7 => x = 18   A worked for 18 days. So, A can complete the remaining work in   18 - 4= 
  18 - 4 = 14
14 days.   Answer: 14
Answer: D
House owner decides to repaint the house. He want to make a particular wall in the hall, decorative and decides to put 7 coloured horizontal stripes in it. The seven colours he chose is Violet, Indigo, Blue, Green, Yellow, Orange, Red. As Blue, Violet and Indigo are very similiar shades he decides not to put them next to each other. How many different patterns do he have to choose from?
Pick one:  A) 6! - (5!×3!)  B) 7! - (5!×2!)  C) 6! - (2!×4!)  D) 7! - (5!×3!)  E) 7! - (6!×3!)

Solution: The answer is not direct. Problem require us to find the number of different arrangements of 7 coloured stripes. The constraints we have is that B, V and I should not come next to each other. We can find the answer by substracting the number of arrangments in which B, V and I come together from the total arrangements of 7 stripes. Arrangements in which B, V and I come together: we can consider B, V and I as a single object, but remembering that there can be 3! different such objects. For each BVI object we can arrange BVI, R, O, Y, G in 5! Ways. There four in total there is 5! × 3! Ways of arranging 7 stripes with B, V, I together. And total arrangement of 7 stripes is 7!. Therefore the answer we need is D. (7! -( 5!×3!))
Answer: D
Four equal circles are described about the four corners of a square so that each touches two of the others. If a side of the square is 14 cm, then the area enclosed between the circumferences of the circles is :	Select the correct option.
A) 24 cm2 B) 42 cm2 C) 154 cm2 D) 196 cm2 E) None of these

Solution: The shaded area gives the required region.   Area of the shaded region = Area of the square – area of four quadrants of the circles   = (14)2 - 4 × 1⁄4π(7)2   = 196 - 22⁄7 × 49 = 196 - 154= 
196 - 154 = 42
42 cm2   Answer 42 cm2
Answer: B