MU-NLPC/Calc-aqua_rat huggingface dataset:
A is twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work?  Choose the most appropriate option
A) 10  B) 99  C) 72  D) 26  E) 81

Solution: A can do the work in 30/2 i.e., 15 days.   A and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10   So A and B together can do the work in 10 days.   10nswer: 10
Answer: A
100 people are attending a newspaper conference. 40 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?
Choose the correct choice from the following answers
A) 21
B) 24
C) 28
D) 30
E) 32

Solution: {Total}={Writers}+{Editors}-{Both}+{Neither}.   {Total}=100;   {Writers}=40;   {Editors}>38;   {Both}=x;   {Neither}=2x;   100=40+{Editors}-x+2x --> x=60-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus x={Both}=60-39= 
60-39 = 21
21.   21nswer: 21.
Answer: A
How many two-element subsets of <1, 2,3,4,5,6> are there that do not contain the pair of elements 2 and 4? Choose the correct option:
A) 11 B) 12 C) 14 D) 15 E) 16

Solution: 6142 - 1 = 14 Answer is 14
Answer: C
A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 1170, what will be C's share of the earnings? Options:
A) $1100 B) $260 C) $1080 D) $1170 E) $630

Solution: Explanatory Answer   A, B and C will share the amount of $1170 in the ratio of the amounts of work done by them.   As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.   Similarly, B will complete 1/8th and C will complete 1/12th of the work.   So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12   Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.   We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.   i.e., the ratio in which A : B : C will share $1170 will be 4 : 3 : 2.   Hence, C's share will be  2*1170/9= 
 2*1170/9 = 260
260   correct choice is ($260)
Answer: B
A man can row with a speed of 15 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is? Select:
A) 10 kmph
B) 5 kmph
C) 20 kmph
D) 22 kmph
E) 25 kmph

Solution: M = 15   S = 5   DS = 15 + 10= 
15 + 10 = 25
25   ANSW25 kmphR:25 kmph
Answer: E
A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in --- hours. Pick one
A) 12 hours  B) 6 hours  C) 8 hours  D) 10 hours  E) 4 hours

Solution: Explanation :   Work done by 12 hours in 1 hour = 1/4   Work done by B and C in 1 hour = 1/3   Work done by 12 hours and C in 1 hour = 1/2   Work done by 12 hours,B and C in 1 hour = 1/4+1/3 = 7/12   Work done by B in 1 hour = 7/12 – 1/2 = 1/12 => B alone can complete the work in 12 hours   12 hoursnswer : Option 12 hours
Answer: A
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?  Choose the correct choice:
A) 39
B) 10
C) 88
D) 12
E) 18

Solution: Suppose they meet x hours after 7 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 110   45x = 135   x = 3.   So, they meet at 10 a.m.   Answer:10
Answer: B
Terry is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. He must also choose whether or not to have one of the two types of soup on the side. If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, and one type of olive for his salad, how many total options does he have for his lunch combo?
Select:
A) 9	B) 11	C) 24	D) 48	E) 54

Solution: Terry can pick one lunch salad bar....we can choose lettuce 2c1 , tomatoes - 3c1 and olives - 4c1...   Two types of soups , if he picks one then 2c1 ways.   Terry decided to have the combo : Soup + salad...Hmmm...   Using the above information, we get ( 2c1 * 2c1* 3c1 * 4c1 ) = 48..   ANS option 48 is correct answer..
Answer: D
s, q, and r are positive integers. If s, q, and r are assembled into the six-digit number sqrsqr, which one of the following must be a factor of sqrsqr?  Pick one:  A) 23  B) 19  C) 17  D) 7  E) none of the above

Solution: One short way -   sqrsqr = 1000sqr + sqr = (1000+1)= 
(1000+1) = 1_001
1001sqr   Therefore any factor of 1001 is a factor of sqrsqr   7 is a factor of 1001   So 7
Answer: D
In a family, the father took 1/4 of the cake and he had 3 times as much as each of the other members had. The total number of family members is  Pick one:  A) 3  B) 7  C) 10  D) 12  E) 15

Solution: 1-1/4 = remain cake 3/4   3/4*3 = 9/4   9/4+1/4 = 10   ANSWER:10
Answer: C
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are  Choices.
A) 39, 30	B) 41, 32	C) 42, 33	D) 43, 34	E) None of these

Solution: Solution   Let their marks be (x+9) and x.   Then, x+9	= 56/100(x + 9 +x)   ‹=› 25(x+9)   ‹=› 14 (2x + 9)   ‹=›3x = 99   ‹=›x = 33.   SO, their marks are 42 and 33.   Answer 42, 33
Answer: C
If a certain manager had received a 10% raise instead of the 12% raise that she actually received, her salary would have been $60,500. What was her actual salary after the raise? Choose the most appropriate option:
A) 55,000	B) 58,806	C) 59,290	D) 59,400	E) 61,600

Solution: salary(let X) included 10% increase can be written as   (1+10/100)X=60500   X=60500/1.10------>55000   if there is 12% rise in 55000   then the salary now is 12% of 55000   12*55000/100= 
12*55000/100 = 6_600
6600   then toal salary after increment=55000+6600----->61600   Ans 61,600
Answer: E
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 + S1. What is the value of K?
Choose the correct answer:	A) 67	B) 50	C) 45	D) 236	E) 36

Solution: I used brute force for this question:   S6: 36+30+94=160   S5: 25+25+94=144   S4: 16+20+94=130   S3: 9+15+94=118   S2: 4+10+94=108   S1: 1+5+94=100   S6-S5+S4-S3+S2-S1= 16+12+208= 
16+12+208 = 236
236   Answer 236
Answer: D
What number has a 5:1 ratio to the number 10?
Select
A) 11 B) 50 C) 99 D) 88 E) 66

Solution: 5:1 = x: 10   x = 50   Answer: 50
Answer: B
In a apartment, 30% of the people speak English, 20% speak Hindi and 15% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?  Select.
A) 1/13 B) 2/13 C) 5/20 D) 6/20 E) 7/20

Solution: P (7/20) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (7/20 âˆ© H) = 15 / 100 =   P (7/20 or H) = P (7/20 U H)   = P (7/20) + P (H) - P (7/20 âˆ© H)   = (3 / 10) + (1 / 5) - (15 / 100) = 35/100 = 7/20   7/20
Answer: E
The sale price of a trolley bag including the sale tax is Rs. 560. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:  Options
A) Rs 1000 B) Rs 900 C) Rs 400 D) Rs 600 E) None of these

Solution: Explanation :   112% of S.P. = 560   S.P. = Rs.(560x 100/112) = Rs.500.   C.P. = Rs (100/125x 500) = Rs 400   Answer : Rs 400
Answer: C
A square, with perimeter 8, is inscribed in a circle. What is the area of the circle?	Select the correct option.
A) 36π	B) 30π	C) 26π	D) 2π	E) 20π

Solution: Area of circuscribed circle = pi/2*area of square   Area of square = (8/4)^2 = 2^2= 4   Area of circle = pi/2*4=2pi   Answer 2π
Answer: D
There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 15, then find the smaller number?	Choose the correct choice from the following options.
A) 25	B) 66	C) 77	D) 88	E) 44

Solution: Let the two positive numbers be 5x and 8x respectively.   8x - 5x = 15   3x = 15 => x = 5   => Smaller number = 5x = 25.   25nswer: 25
Answer: A
Find the odd man out. 3, 8, 18, 38, 78, 158, 316  Choose one:
A) 38 B) 158 C) 316 D) 8 E) 78

Solution: Explanation :   3   3 × 2 + 2 = 8   8 × 2 + 2 = 18   18 × 2 + 2 = 38   38 × 2 + 2 = 78   78 × 2 + 2 = 158   158 × 2 + 2 = 318   Hence, 316 is wrong and 318 should have come in place of that   Answer : Option 316
Answer: C
If (x^2 + 1)y=8, which of the following is not a possible value for y?
Choose the correct choice from the following answers:
A) 8/2
B) 2/5
C) 18/3
D) 3
E) 17/2

Solution: Its simple   equation is (x^2 +1)y = 8 ===> x^2 = (8/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.   Hence, (8/y) - 1>= 0 ===> y =< 8. Now only option E has greater value of 'y' than 8.   Thus, correct ans is 17/2
Answer: E
A can eat 10 burgers in 2 days and B can eat 20 burgers in 1 day. For how long will 250 burgers last is both start eating them together? Select: A) 25 days B) 20 days C) 15 days D) 10 days E) 5 days

Solution: Explanation:   A can eat 5 burgers in 1 day and B can eat 20 burgers in 1 day   A and B together can eat 25 burgers in 1 day   =>They can eat 250 burgers in 10 days.   Answer: 10 days
Answer: D
A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?  Pick: A) 30/17 B) 30/19 C) 30/11 D) 30/13 E) 30/12

Solution: Speed downstream = 20 + 6= 
20 + 6 = 26
26 kmph.   Time required to cover 60 km downstream= d/s   = 60/26   = 30/13 hours.   Answer: 30/13
Answer: D
What is the difference between the local values of 4 in the number 54404?  Choices.
A) 2992
B) 3996
C) 2877
D) 2077
E) 1211

Solution: Explanation:   4000 â€“ 4 = 3996   Answer:3996
Answer: B
A pipe can fill a cistern in 77 minutes. Find the time in which 1/11 part of the cistern will be filled? Select the correct option: A) 5min B) 2min C) 3min D) 1min E) 7min

Solution: Full cistern filled in = 77 minutes   1/11 part filled in = 77*1/11= 
77*1/11 = 7
7minutes   Answer is 7min
Answer: E
W and X started a business by investing Rs.2100/- and Rs.4900/- respectively. Find the W’s share out of a total profit of Rs.6000:	Choose the correct choice from the following
A) 1800  B) 1850  C) 1900  D) 1950  E) 2000

Solution: W = Rs.2100/-   X = Rs.4900/-   W share 3 parts & X share 7 parts   Total 10 parts -----> Rs.6000/-   ----> 1 part -------> Rs.600/-   W share = 3 parts -----> Rs.1800/-   1800
Answer: A
A three-digit number 4a3 is added to another three-digit number 984 to give a four digit number 13b7, which is divisible by 11. What is the value of (a + b)?	Pick one:  A) 8  B) 10  C) 14  D) 17  E) 19

Solution: 4 a 3   9 8 4   13 b 7   => a + 8 = b ...(1)   13b7 is divisible by 11   => (1 + b) - (3 + 7) is 0 or divisible by 11   => (b - 9) is 0 or divisible by 11 ...(2)   Assume that (b - 9) = 0   => b = 9   Substituting the value of b in (1),   a + 8 = b   a + 8 = 9   => a = 9 - 8= 
9 - 8 = 1
1   If a= 1 and b= 9,   (a + b) = 1 + 9= 
1 + 9 = 10
10   10 is there in the given choices. Hence 10 is the answer.
Answer: B
The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?  Choose the correct choice from the following:
A) 6 2/3%
B) 6 8/3%
C) 6 2/6%
D) 6 3/3%
E) 6 2/1%

Solution: 4/9 P = (P*R*R)/100   R = 20/3   = 6 2/3%   6 2/3%nswer: 6 2/3%
Answer: A
At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 500-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $200? Options
A) 1,108
B) 4,100
C) 2,108
D) 2,124
E) 2,256

Solution: We have $200 and we have to maximize the number of hot dogs that we can buy with this amount.   Let's try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money, which in this case is 500 for $22.95.   For the sake of calculation, let's take $23. 23x8 gives 184 ,i.e. a total of 500x8 = 4000 hot dogs . We are left with ~$16. Similarly, let's use $3 for calculation. We can buy 5 20-pack hot dogs (3x5), a total of 20x5 = 100 hot dogs. So we have 4100 hot dogs.   2108 looks far-fetched (since we are not likely to be left with > $1.55). Hence, (b) 4100 (ANSWER 4,100)
Answer: B
A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box?
Choose the correct choice from the following answers:  A) 2 m  B) 3 m  C) 4 m  D) 7 m  E) 9 m

Solution: Let radius of the outer circle be R and radius of the inner circle be r.   Circumference of the outer circle =   Circumference of the inner circle =   But,   or, R - r =   Thus, width of the road = 7 m   7 m
Answer: D
The total of the ages of Amar, Akbar and Anthony is 45 years. What was the total of their ages four years ago ?
Choose the correct choice from the following choices
A) 29 years  B) 24 years  C) 20 years  D) 30 years  E) 21 years

Solution: Explanation:   Required sum = (45 - 4 x 4) years = (45 - 16)= 
(45 - 16) = 29
29 years.   29 yearsnswer: Option 29 years
Answer: A
It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 14 minutes, how much time will she spend doing yoga? (rounded to minutes)  Choices:	A) 10 min.	B) 41 min.	C) 17 min.	D) 23 min.	E) 25 min.

Solution: The ratio is 2:3 = gym:ride, so (14)(3/2) = 21 minutes at the gym, and   21 + 14= 
  21 + 14 = 35
35 minutes exercise, so (2/3)(35)= 23 minutes yoga.   Answer: 23 min.
Answer: D
A boy is travelling from his home to school at 3 km/hr and reached 7 min late. Next day he traveled at 6 km/hr and reached 8 min early. Distance between home and school? Choose the correct choice from the following answers:
A) 1.2km  B) 1.3km  C) 1.4km  D) 1.5km  E) 1.6km

Solution: Let the distance be x   T1 = x/3 hr   T2 = x/6hr   1.5kmifference in time = 7+8= 
7+8 = 15
15=1/4hr   x/3-x/6 = 1/4   x/6 = 1/4   x = 1.5 km   Answer is 1.5km
Answer: D
Two water pumps, working simultaneously at their respective constant rates, took exactly 7 hours to fill a swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?
Choose the correct choice
A) 25/3 B) 32/3 C) 35/3 D) 40/3 E) 44/3

Solution: Let the rate of the slow pump be x. Then the rate of the fast pump is 1.5x.   (x+1.5x) = 2.5x = 1/7 of the capacity of the whole pool per hour.   The rate of the fast pump is (1.5/2.5)*1/7 = 3/35 of the whole pool per hour.   The time it takes the faster pump to fill the pool would be 35/3 hours.   The answer is 35/3.
Answer: C
Number A is randomly selected from a set of all primes between 10 and 40, inclusive. Number K is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that A+K is odd?  Select the correct option:
A) 1/2
B) 2/3
C) 3/4
D) 4/7
E) 5/8

Solution: All primes except 2 are odd, thus A must be odd. For A + K = odd + K to be odd, K must be even.   There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd.   Therefore the probability that A + K is odd is 4/7.   Answer: 4/7.
Answer: D
Find the value of (1-(1/3))(1-(1/4))(1-(1/5))….(1-(1/100)). Choose the correct option:  A) 1/50  B) 4/50  C) 9/50  D) 7/50  E) None of them

Solution: Given expression = (2/3)*(3/4)*(4/5) *…….* (99/100) = 2/100 = 1/50   1/50nswer is 1/50.
Answer: A
On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 55 percent of the sales representatives prefer to stay at Hotel XYZ and 45 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer? Select.
A) 51 B) 52 C) 53 D) 54 E) 55

Solution: 30% of 60 will be accommodated at XYZ = 18   70% of 60 will be accommodated at ABC = 42   55% of 60 prefer XYZ = 33   45% of 60 prefer ABC = 27   we were asked to find number of maximum possible people who were accommodated at hotels they dont prefer,   So for 18 XYZ accommodations , we can choose 18 ABC preferring people (so xyz is filled up) Here 18 were given to people who don't prefer XYZ   for 42 ABC accommodations, we can choose 33 ABC preferring people and rest to ABC. Here 33 were given to people who don't prefer ABC.   So total people who were accommodated at hotel they dont prefer = 18+33= 
18+33 = 51
51   So answer is 51.
Answer: A
Farmer Brown purchased several rabbits (male and female) and bred them on his farm. The rabbit population grew 500% the first year. The population grew 900% the second year. What was the percent, population growth for the two year?  Select:  A) 100%  B) 5,000%  C) 2000%  D) 2500%  E) 500%

Solution: Let x be the initial population of rabbits Farmer Brown purchased; then, x + 5x is the rabbit population after the first year, and 5x + 9(5x) = 50x is the rabbit population after the second year.   Now, 50x/x = 50.   So, the percent, population growth is for the two years is 5,000%.   Answer is 5,000%
Answer: B
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Select the correct option: A) 200 B) 220 C) 240 D) 250 E) 260

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, x + 300 / 36= 15   x + 300 = 540   x = 240 m.   Answer: Option 240
Answer: C
For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.0?	Choose the correct choice from the following answers.
A) 12.6.
B) 14.4.
C) 15.8.
D) 16.2.
E) 16.4.

Solution: [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.0   = 6*0 + 2*7.2 + 8 - 6.0   = 0 +14.4 +2   16.4   Answer 16.4.
Answer: E
If the sum of a number and its square is 182, what is the number?
Choose the correct choice.
A) 13  B) 15  C) 17  D) 19  E) 21

Solution: Sol.   Let the numbers be x.   Then, x + x2 = 182   ⇔ x2 + x - 182 = 0   ⇔ (x+14)(x-13) = 0   ⇔ x = 13.   13nswer 13
Answer: A
A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
Choose the correct choice from the following answers.
A) 20029	B) 20000	C) 20289	D) 20027	E) 20026

Solution: Let the total worth of the stock be Rs. x.   The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50   The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50   Total SP = 11x/50 + 38x/50 = 49x/50   Overall loss = x - 49x/50 = x/50   x/50 = 400 => x = 20000   Answer: 20000
Answer: B
A bag contains 6 white and 4 black balls. 2 balls are drawn at random.
Find the probability that they are of same color.  Choose the correct answer:
A) 7/15
B) 8/15
C) 6/15
D) 3/5
E) 8/5

Solution: let S be the sample space   Then n(S)=no of ways of drawing 2 balls out of   (6+4)= 
  (6+4) = 10
10C2=(10*9)/(2*1)= 
(10*9)/(2*1) = 45
45   Let E=event of getting both balls of same color   Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)   =(6C2+4C2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6= 
15+6 = 21
21   P(E)=n(E)/n(S)=21/45=7/15   answer option 7/15)7/15
Answer: A
How many different 4-digit numbers can be written using the digits 1 to 8 without repetition such that the number always contains the digit 2? Answers:
A) 360
B) 560
C) 760
D) 840
E) 1260

Solution: The most restrictive case. We should have a two.   No repetition. Numbers range from 1 to 8.   = 1*7*6*5= 
1*7*6*5 = 210
210 ways we can write if '2' is in the first position.= 4*(210)= 
4*(210) = 840
840 ways.   Another method.   Without restriction for 8 digits- 8*7*6*5= 1680 Ways we can write.   Without restriction for 7 digits- 7*6*5*4 = 840 Ways.   With restriction = 1680 - 840= 
1680 - 840 = 840
840 Ways.   ANSWER:840
Answer: D
Six years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages Select
A) A)21  B) B)34  C) C)45  D) D)25  E) E)26

Solution: Explanation:   Let the present age of P and Q be 3x and 4x respectively.   Six years ago, P was half of Q in age   => 2(3x – 6) = (4x – 6)   => 6x – 12 = 4x – 6   => 2x =6   => x = 3   7x=7*3= 
7*3 = 21
21   21nswer: Option 21
Answer: A
I sold a book at a profit of 10%. Had I sold it for $100 more, 15% would have been gained. Find the cost price?
Choose the correct choice from the following.
A) $2000 B) $2500 C) $3000 D) $3120 E) $1540

Solution: 115% of cost - 110% of cost = $100   5% of cost = $100   cost = 100*100/5= 
100*100/5 = 2_000
$2000   $2000nswer is $2000
Answer: A
Persons A and B. Person A picks a random no. from 1 to 1000.Then person B picks a random no. from 1 to 1000. What is the probability of B getting no. greater then what A has picked.
Pick one:  A) 0.3995  B) 0.4995  C) 0.5995  D) 0.6995  E) 0.7995

Solution: Probability of A choosing 1 and 0.4995 greater = (1/1000)*(999/1000);   Probability of A choosing 2 and 0.4995 greater = (1/1000)*(998/1000);   Probability of A choosing 3 and 0.4995 greater = (1/1000)*(997/1000); ...;   Probability of A choosing 998 and 0.4995 greater = (1/1000)*(2/1000);   Probability of A choosing 999 and 0.4995 greater = (1/1000)*(1/1000);   Total = (1/1000)*(1/1000)*(999+998+997+...+2+1) = (1/1000)*(1/1000)*(999*1000/2)= 
(1/1000)*(1/1000)*(999*1000/2) = 999/2_000 = around 0.4995
0.4995   ANSWER:0.4995
Answer: B
In a Shop, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? Choices
A) 70%  B) 50%  C) 100%  D) 60%  E) 55%

Solution: CP.= Rs. 100. => Profit = Rs. 320, S.P. = Rs. 420.   New C.P. = 125% of Rs. 100 = Rs. 125   New S.P. = Rs. 420.   Profit = Rs. (420 - 125) = Rs. 295.   Req = (295/420*100) == > 70%   70%NSWER 70%
Answer: A
What is the square root of 625, divided by 5?	Choose one: A) 9 B) 36 C) 5 D) 6 E) 1

Solution: Square root is a number times itself   Square root of 625=25, 25/5=5   (5)5
Answer: C
In a senior secondary school, 80 students play hockey or football. The number that play football is 5 more than twice the number that play hockey. If the 15 students play both games and every student in the school playsat least one game, find:
The number of students that play football?  Pick one:
A) 10	B) 15	C) 20	D) 30	E) 35

Solution: number who play hockey ---- x   number who play football -- 2x+5   x + 2x+5 = 80   x = 25   so 25 play hockey, 55 play football, and 15 play both   Answer is 15
Answer: B
The average of first 10 prime numbers is?  Choose the correct option:
A) 12.5 B) 12.4 C) 12.9 D) 12.3 E) 12.1

Solution: Sum of 10 prime no. = 129   Average = 129/10= 
129/10 = 129/10 = around 12.9
12.9   Answer: 12.9
Answer: C
Sandy had $210 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her?  Options.
A) $240 B) $300 C) $360 D) $420 E) $480

Solution: Let the money Sandy took for shopping be x.   0.7x = 210   x = 300   The answer is $300.
Answer: B
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.65 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Choose the correct choice from the following: A) 65 sec B) 55 sec C) 48 sec D) 33 sec E) 42 sec

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.65= 
1.10 + 0.65 = 1.75
1.75 km= 1750 m.   Required time = 1750 * 3/125= 
1750 * 3/125 = 42
42 sec.   Answer:42 sec
Answer: E