MU-NLPC/Calc-aqua_rat huggingface dataset:
If the ratio of a to b is 7 to 3 and the ratio of b to c is 1 to 5, what is the ratio of a to c?
Select the correct option
A) 4/15 B) 1/3 C) 2/5 D) 4/5 E) 7/15

Solution: a:b = 7:3 -- 1   b:c = 1:5   =>b:c = 3 :15 --2   From 1 and 2 , we get   a:c = 7:15   Answer 7/15
Answer: E
6 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?	Choose the correct choice from the following options
A) 120	B) 623	C) 160	D) 240	E) 256

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= 5   hence ans = 5 factorial = 120   hence 120
Answer: A
A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 200 more than A :
Pick
A) 2348
B) 7250
C) 2767
D) 1998
E) 5800

Solution: 5800xplanation:   A B C   investment 3x 4x 5x   Rate of return 6y% 5y% 4y%   Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100}   Total = (18+20+20)= 
(18+20+20) = 58
\inline \frac{58xy}{100}   B's earnings - A's earnings= \inline \frac{2xy}{100} = 200   Total earning = \inline \frac{58xy}{100} = 5800   Answer: 5800) Rs.5800
Answer: E
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 answer.
A) 92/37
B) 33/91
C) 71/28
D) 91/42
E) 91/33

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 = Â¹Â²Câ‚„/Â¹âµCâ‚„ = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91   Answer: 33/91
Answer: B
At 30 minutes past 9 o'clock, what is the angle between the two hands?  Choose the correct option:
A) 60	B) 75	C) 90	D) 105	E) 120

Solution: The hour hand moves 360 degrees in 12 hours.   The hour hand moves 30 degrees in 1 hour and 15 degrees in 30 minutes.   The minute hand moves 360 degrees in 60 minutes and 180 degrees in 30 minutes.   At 30 minutes past 9, the hour hand has moved 285 degrees.   At 30 minutes past 9, the hour hand has moved 180 degrees.   The angle between the two hands is 105 degrees.   The answer is 105.
Answer: D
2 boxes, 32 black n 31 red balls the probability of getting black ball is maximum the maximum probability is? Choose the correct choice from the following options.
A) 1/4	B) 3/4	C) 1/3	D) 2/3	E) 2/5

Solution: to maximize the probability we can send all but 1 black balls to other box making probability   1/2 (ie chosing one box) * 1(no. of black balls in it) + 1/2*31/62 (as we have no 31 black and 31 red balls in it)   finally we have 1/2*1 + 1/2*1/2 = 3/4   ANSWER:3/4
Answer: B
The operation is defined for all integers a and b by the equation ab = (a - 1)(b - 1). If y10 = 90, what is the value of y ?  Choose the correct choice from the following options:	A) 10	B) 12	C) 15	D) 11	E) 20

Solution: ab = (a - 1)(b - 1)   y10 = (y-1)(10-1) = 90 --> y-1=10 --> y=11   Answer: 11
Answer: D
The cost price of 24 articles is the same as the selling price of x articles. If the profit is 20%, what is x? Answers:
A) 14 B) 16 C) 18 D) 20 E) 22

Solution: Let the cost price = y   The cost price of 24 articles = 24y   The selling price of x articles = 1.20y*x   1.20y*x = 24y   x = 24 / 1.2= 
24 / 1.2 = 20
20   The answer is 20.
Answer: D
The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most? Choose the correct choice from the following choices:
A) 19 B) 20 C) 10 D) 15 E) 17

Solution: 19vg of 20 numbers = 0   sum of 20 nos/20 = 0   sum of 20 nos = 0 => there can be 19 positive nos   19NSWER 19
Answer: A
Select the missing Number from the given Responses
16 4 4
81 3 27
? 25 5
Choose the correct choice from the following choices:
A) 143
B) 125
C) 261
D) 132
E) 156

Solution: 125   125   4 × 4 => 16   27 × 3 => 81   Then,   5 × 25 => 125
Answer: B
The volume of a cube is 1331 cc. Find its surface.  Choose the correct option.
A) 864  B) 669  C) 658  D) 624  E) 726

Solution: a3 = 1331 => a = 116a2 = 6 * 11 * 11= 
6 * 11 * 11 = 726
726Answer: 726
Answer: E
In a garden, there are three blue flowers, three red flowers, three green flowers, and three pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers? Pick one
A) 55	B) 1/55	C) 41/78	D) 12/45	E) 4/8

Solution: P(all the same color) = P(1st flower is ANY colorAND2nd flower is same as firstAND3rd flower is also the same color)   = P(1st flower is ANY color)xP(2nd flower is same as 1st)ANDP(3rd flower is the same color)   = 1x2/11x1/10   = 1/55   Answer: 1/55
Answer: B
The tax on a commodity is diminished by 28% but its consumption is increased by 12%. Find the decrease percent in the revenue derived from it?  Choose the correct choice from the following choices:
A) 18%  B) 19%  C) 32%  D) 12%  E) 52%

Solution: 100 * 100= 
100 * 100 = 10_000
10000   72 * 112= 
72 * 112 = 8_064
8064   10000------- 1936   100 ------- ?= 19.36%   Answer:19%
Answer: B
A retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 80 percent greater than the wholesale price. If the retailer decreases the retail price by 25 percent this will have the same effect as increasing the wholesale price by what percent?  Choose the correct choice from the following answers
A) 26  B) 37.5  C) 35  D) 44  E) 50

Solution: Answer: C= 35.   Assume Rs. 100 to be the price at which the retailer buys from wholesaler.   80% increase makes Retail price = 180.   Now 25% decrease -> (1-25/100) * 180 = 135.   Now compared to the wholesale price of 100, 35% increase is what will have the same effect as increasing the wholesale price.
Answer: C
If a particular is never chosen, in how many ways can a cricket player be chosen out of 14 players?  Answers:
A) 84  B) 66  C) 78  D) 76  E) 68

Solution: A particular players is never chosen, it means that 11 players are selected out of 14 players.   => Required number of ways = 137811   = 13!/11!x2! = 78   78
Answer: C
When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students Pick
A) 55 B) 56 C) 57 D) 58 E) 59

Solution: Explanation:   Let the average weight of the 59 students be A.   So the total weight of the 59 of them will be 59*A.   The questions states that when the weight of this student who left is added, the total weight of the class = 59A + 45   When this student is also included, the average weight decreases by 0.2 kgs   59A+45/60=A−0.2   => 59A + 45 = 60A - 12   => 45 + 12 = 60A - 59A   => A = 57   Answer: Option 57
Answer: C
If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units Z digit of (a+2)^2?
Pick one:
A) 1
B) 3
C) 5
D) 6
E) C. 14

Solution: I also got A. By punching in numers:   Z...7^2=...9   ...8^2=...4   ...9^2=...1.1
Answer: A
Find the simple interest on Rs. 78000 at 15(2/5) % per annum for 9 months.
Choose the most appropriate option:
A) Rs. 7804 B) Rs. 8979 C) Rs. 8046 D) Rs. 9009 E) None of these

Solution: Explanation:   P = Rs. 78000, R = 77/5 % p.a and T = 9/12 years = ¾ years   Therefore,   S.I = (P*R*T)/100   = (78000* 77/5 * ¾ * 1/100)   = Rs. 9009   ANSWER Rs. 9009
Answer: D
A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?	Select the correct option.
A) 32:46
B) 32:42
C) 32:45
D) 32:40
E) 32:49

Solution: A : B   (8000*4)+(4000*8) : (9000*6)+(6000*6)   64000 : 90000   32 : 45   Answer: 32:45
Answer: C
A bookseller has two display windows. She plans to display 3 new fiction books in the left window, and 4 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows? Choose the correct option.
A) 24
B) 72
C) 140
D) 336
E) 144

Solution: The left window will have permutations of the 3 fiction books, so the number of possibilities for that window is   permutations = 3! = (3)(2)(1) = 6   The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is   permutations = 4! = (4)(3)(2)(1) = 24   Any of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 24*6= 
24*6 = 144
144   Answer: 144
Answer: E
A company pays 20.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares? Choose the correct choice from the following options:
A) 25 B) 66 C) 18 D) 19 E) 41

Solution: Explanation:   Dividend on 1 share = (20.5 * 50)/100 = Rs.10.25   Rs.25 is income on an investment of Rs.100   Rs.10.25 is income on an investment of Rs. (10.25 * 100)/25 = Rs.41   ANSW41R: 41
Answer: E
A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?  Select.
A) neither profit nor loss
B) 3%
C) 5%
D) 4%
E) 6%

Solution: SP of first article = 1000   Profit = 20%   CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3   SP of second article = 1000   Loss = 20%   CP = (SP)*[100/(100-L)] = 5000/4= 
5000/4 = 1_250
1250   Total SP= 2000   Total CP = 2500/3 + 1250 = 6250/3   CP is more than SP, he makes a loss.   Loss = CP-SP = (6250/3)- 2000 = 250/3   Loss Percent = [(250/3)/(6250/3)]*100 =   0.04 * 100= 
0.04 * 100 = 4
4%   ANSWER:4%
Answer: D
In an election contested by two parties, Party ADMK secured 24% of the total votes more than Party DMK. If party DMK got 266,000 votes, by how many votes did it lose the election?  Choose the correct option
A) 34,000	B) 56,000	C) 164,000	D) 168,000	E) 200,000

Solution: A168,000MK + 168,000MK = 100 ---- (1)   A168,000MK - 168,000MK = 24 ---- (2)   Solving (1) and (2) A168,000MK = 62% and 168,000MK = 38%   38% of Total = 266000   Total = 700000   A168,000MK = 434000   168,000ifference = 434000 - 266000= 
434000 - 266000 = 168_000
168000   Answer: 168,000
Answer: D
A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability J that the sum of the three numbers on the balls selected from the box will be odd?	Select the correct option: A) 1/4 B) 3/8 C) 1/2 D) 5/8 E) 3/4

Solution: The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd);   P(OOO)=(1/2)^3;   P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE);   So finally J=1/8+3/8=1/2.   Answer: 1/2.
Answer: C
The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Choose the correct option
A) 25 B) 27 C) 29 D) 32 E) 34

Solution: The total of seven numbers = 7X18 = 126   The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99   So, the middle number is  (126 - 99 )= 
 (126 - 99 ) = 27
27   27
Answer: B
If x is a positive number and 1/4 the square root of x is equal to 3x, then x =
Choose the most appropriate option
A) 1/16  B) 12  C) 1/12  D) 144  E) 1/144

Solution: 1/4 of sqrt(x) = 3x, which means that sqrt(x) = 12x   or x = 144x^2 -> divide by x   1=144x   x=1/144   1/144.
Answer: E
find value for x from given equation? x + 1 = -3	Choose the correct choice from the following choices
A) 1  B) x=-4  C) -3  D) -5  E) 5

Solution: 1 . Subtract 1 from both sides:   x + 1 - 1 = -3 - 1   2. Simplify both sides:   x = -4   x=-4
Answer: B
If 25 typists can type 60 letters in 20 minutes, then how many letters will 75 typists working at the same rate complete in 1 hour?  Choose the correct choice from the following options
A) 270	B) 540	C) 610	D) 510	E) 500

Solution: No. of letters typing by 25 typists in 20 minutes = 60   No. of letters typing by 25 typists in 60 minutes = 60*3= 
60*3 = 180
180   No. of letters typing by 75 typists in 60 minutes= 180/25*75= 
180/25*75 = 540
540   Answer : 540
Answer: B
In one day, Juan sends Keith two times as many messages as he sends Laurence, and Laurence sends Missy 8 times as many messages as he receives from Juan. If Missy received 40 messages from Laurence, how many messages does Keith receive from Juan?
Choose the most appropriate option:
A) 10
B) 12
C) 16
D) 18
E) 56

Solution: Juan --> Laurence = x messages;   Juan --> Keith = 2x messages (Juan sends Keith two times as many messages as he sends Laurence);   Laurence --> Missy = 8x =40 (Laurence sends Missy 8 times as many messages as he receives from Juan).   8x =40 --> x = 5 --> 2x = 10.   10nswer: 10.
Answer: A
Last year the range of the annual yield on equal amount of investments in 100 mutual funds was $10,000. If the annual yield this year for each of the 100 mutual funds has improved by 15 percent this year than it was last year, what is the range of the annual yield on mutual funds this year?	Options:
A) $12700 B) $13000 C) $23000 D) $11500 E) $33000

Solution: let the lowest yield be x.   Therefore, highest yield is x +10000.   Now yield of each mutual fund investment is improved by 10%.   Therefore the yields will remain arranged in the same order as before.   or Lowest yield = 1.15x and Highest = 1.15 * (x+10000)   or Range = highest - lowest = 1.15* (x+10000) - 1.15x   = 11500, Hence, $11500
Answer: D
Find the least positive integer divisible by each of the integers between 5 through 10 (including 10). Choose the correct answer:
A) 560  B) 380  C) 900  D) 2560  E) 2520

Solution: The integer should be divisible by: 5, 6, 7,8,9,and 10. The least common multiple of these integers is LCM=420.   Answer: 5*3^2*7*2^3   The answer is 2520)
Answer: E
How many diagonals does a 63-sided convex polygon have? Choose the correct choice from the following options.
A) 3780 B) 1890 C) 3843 D) 3906 E) 1953

Solution: Explanatory Answer   The number of diagonals of an n-sided convex polygon = n(n−3)/2   This polygon has 63 sides. Hence, n = 63.   Therefore, number of diagonals = 63∗60 /2 = 1890.   Choice 1890
Answer: B
Country X taxes each of its citizens an amount equal to 13 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income? Choose the correct option:
A) $54,000 B) $56,000 C) $64,000 D) $66,667 E) $80,000

Solution: Equation is correct, so math must be a problem.   0.13*40,000+0.2*(x-40,000)=8,000 --> 5,200+0.2x-8,000=8,000 --> 0.2x=10,800 --> x=54,000.   $54,000nswer: $54,000.
Answer: A
A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number of days that the student earned that amount. What is the amount of money that the student earned per day for the 5th day?
Amounts earned per day : $96 $84 $80 $70 $48
Number of days : 4 7 4 3 2	Choose the correct choice from the following:
A) (1) $96
B) (2) $84
C) (3) $80
D) (4) $70
E) (5) $48

Solution: 4+7+4+3+2= 
4+7+4+3+2 = 20
20   The series is as follows. Arrange the terms in increasing order of amounts earned and cumulatively add up the number of days of each amount.   1st to 2nd term= 48 (2 days)   3rd to 5th term = 70 (3 days)   Pick (4) $70
Answer: D
A sum of money is put out at compound interest for 2 years at 20%. It would earn Rs.482 more if the interest were paid half-yearly. Calculate the sum.
Choose the correct option.
A) 2878
B) 279
C) 279
D) 482
E) 661

Solution: P(11/10)4 - P(6/5)2 = 482   P = 2000   Answer: 482
Answer: D
A, B, C, D, E, F, G, and H are all integers, listed in order of increasing size. When these numbers are arranged on a number line, the distance between any two consecutive numbers is constant. If G and H are equal to 5^12 and 5^11, respectively, what is the value of A?	Choose one:
A) -24(5^12) B) -23(5^12) C) -24(5^6) D) 23(5^12) E) 24(5^12)

Solution: Ans : D   Assume that the numbers appear as shown below on the number line   A-----B-----C-----D-----E-----F-----G-----H   (5^12) (5^13)   As the values for G and H are given , we can calculate the difference between any two terms of the series .   Common Difference ,d = (5^13) - (5^12)   = (5^12) *[ 5-1 ]   = (5^12)*(4)   Also F + d = G as the terms are in equidistant and in increasing order.   So F + (5^12)*(4) = (5^12).   That is , F = (5^12) - (5^12)*(4)   = (5^12)[ 1-4]   = (5^12) (-3)   Similarly , E = F - d   = (5^12)[-3-4]   = (5^12)*(-7)   You can see a -4 getting added to the non-exponent part of the values . That is , according to the pattern , 23(5^12) SHOUL23(5^12) BE (5^12)*(-7-4)= (5^12)*(-11)   Following this pattern , A = (5^12)*(23)   23(5^12)
Answer: D
To be considered grade AB, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AB eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AB eggs are used, the shells are all discarded, and no mass is lost in the cooking process?  Answers
A) 800
B) 840
C) 864
D) 900
E) 1,080

Solution: We're asked for the smallest possible mass, so what could the lowest mass be per egg AB? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is 840.
Answer: B
In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?  Choose the correct choice: A) 20 B) 40 C) 216 D) 720 E) 729

Solution: GGG RRR   Therefore total number of ways is   6! but there are two groups of 3 identical things.   Therefore total number of "different" ways is   6!/ (3!) (3!) = 20 20NS:20
Answer: A
Find large number from below question The difference of two numbers is 1360. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder Pick
A) 1254 B) 1376 C) 1456 D) 1555 E) 1629

Solution: Let the smaller number be x. Then larger number = (x + 1360).   x + 1360 = 6x + 15   5x = 1345   x = 269   Large number = 269+1360= 
269+1360 = 1_629
1629   1629
Answer: E
A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?	Select:
A) 2 cm B) 7 cm C) 1 cm D) 4 cm E) 9 cm

Solution: Explanation:   Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.   π(16)2 * h = (4/3)π (12)3 => h = 9 cm   Answer: Option 9 cm
Answer: E
Amit and Sumit started a business with initial investments in the ratio 2 : 3, after some months Sumit withdrawn his investment, and their share in the annual profits were in the ratio 8 : 7. Then how long Sumit was in the business ? Choose the correct answer
A) 6 months	B) 8 months	C) 9 months	D) 5 months	E) 7 months

Solution: Let Sumit in the business for ‘a’ months.   Investment Ratio Amit to Sumith = 2 : 3.   Profit sharing ratio = 8 : 7.   Amit is in the business for 12 months.   Then Sumit in the business for   (2×12) / (3×a) = 8 / 7   => 24a = 168 or   a = 168 / 24= 
168 / 24 = 7
7   or 7 months   Option 7 months
Answer: E
A boat can move upstream at 15 kmph and downstream at 35 kmph, then the speed of the current is? Choose the correct choice from the following.
A) 5 B) 6 C) 7 D) 10 E) 32

Solution: US = 15   10S = 35   M = (35 - 15)/2= 
(35 - 15)/2 = 10
10   Answer: 10
Answer: D
There are 12 magazines lying on a table; 6 are fashion magazines and the other 6 are sports magzines. If 5 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazine will be selected?	Choose one:  A) 521/525  B) 522/525  C) 520/525  D) 519/525  E) 517/525

Solution: 1- 6c5/10c5 =1-4/525=521/525   521/525nswer : 521/525
Answer: A
If {g} denote the remainder when 3g is divided by 2 then which of the following is equal to 1 for all positive integers g?
I. {2g+1}
II. {2g}+1
III. 2{g+1}
Pick
A) I only  B) II only  C) I and II  D) III only  E) II and III

Solution: I and II - I and II   3g/2 = 0 or 1   I just substituted 1 in the equations and solved.
Answer: C
One pipe can fill a pool three times faster than a second pipe. When both pipes are opened, they fill the pool in seven hours. How long would it take to fill the pool if only the slower pipe is used?
Choices:  A) 10 hr  B) 12 hr  C) 15 hr  D) 20 hr  E) 28 hr

Solution: fast pipe + slow pipe = together   One pipe fills the pool three times faster than the other pipe so,   hourly fill rates:   1/x + 1/3x = 1/7   Let x = number of hours it would take the fast pipe to fill the pool thus,   x=9.3 hours   9.3*3 = 28 hours   Answer: 28 hr
Answer: E
If the price of an article went up by 25%, then by what percent should it be brought down to bring it back to its original price?
Choose the correct choice from the following: A) 20% B) 2/8% C) 2/1% D) 1/3% E) 2/7%

Solution: Let the price of the article be Rs. 100.   25% of 100 = 25.   New price = 100 + 25 = Rs. 125   Required percentage = (125 - 100)/125 * 100   = 25/125 * 100= 
25/125 * 100 = 20
20%.   20%nswer:20%
Answer: A
A factory has 500 workers, 16 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?
Choose the correct choice from the following options.
A) 3
B) 10
C) 25
D) 30
E) 35

Solution: Currently the factory has 0.16*500= 
0.16*500 = 80
80 women.   After 50 additional workers are hired, there will be total of 550 workers and we need 0.2*550= 
0.2*550 = 110
110 of them to be women, so we need 110-80= 
110-80 = 30
30 more women.   Answer: 30.
Answer: D
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 100 sq cm. Find the area of the square?  Pick:  A) 482  B) Cannot be determined  C) 260  D) 120  E) 632

Solution: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .   Area of the square cannot be found.   Answer: Cannot be determined
Answer: B
Two trains 119 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Choose one:  A) 7.19  B) 7.17  C) 7.2  D) 7.15  E) 7.05

Solution: T = (119 + 165)/ (80 + 65) * 18/5   T = 7.05   Answer:7.05
Answer: E
A meeting has to be conducted with 5 managers. Find the number of ways in which the managers may be selected from among 8 managers, if there are 2 managers who refuse to attend the meeting together.
Choose the correct choice:
A) 36
B) 40
C) 45
D) 51
E) 56

Solution: The total number of ways to choose 5 managers is 8C5 = 56   We need to subtract the number of groups which include the two managers, which is 6C3 = 20.   56 - 20= 
56 - 20 = 36
36   The answer is 36.
Answer: A
A man buys 52 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
Pick one:
A) 7.6 %  B) 7.7 %  C) 11.32 %  D) 11.91 %  E) 7.8 %

Solution: Explanation:   Let Marked price be Re. 1 each   C.P. of 52 pens = Rs. 46   S.P. of 52 pens = 99% of Rs. 52 = Rs. 51.48   Profit % = (Profit /C.P.) x 100   Profit% = (5.48/46) x 100 = 11.91 %   ANSWER: 11.91 %
Answer: D