MU-NLPC/Calc-aqua_rat huggingface dataset:
Set S contains exactly 10 numbers and has an average (arithmetic mean) of 6.2. If one of the numbers in Set S is increased by 6, while all other numbers remain the same, what is the new average of Set S?	Choose the most appropriate option:
A) 6.6  B) 6.7  C) 6.8  D) 6.85  E) 6.9

Solution: Old set S - Total is avg * no of elements = 6.2*10= 
6.2*10 = 62
62   If one number is increased by 6 then total increased to  62+6= 
 62+6 = 68
68   New avg - 68/10= 6.8.   Hence answer is 6.8.
Answer: C
Car A is 10 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
Choose the correct choice from the following choices
A) 1.5 B) 2.25 C) 2.75 D) 2.5 E) 3.5

Solution: Relative speed of car A is 58-50= 
58-50 = 8
8 miles per hour, to catch up 10 miles and drive 8 miles ahead so to drive 18 miles it'll need 18/8= 
18/8 = 9/4 = around 2.25
2.25 hours.   Answer: 2.25
Answer: B
If a/b = 4/3, Then (3a + 2b) / (3a - 2b) = ?	Pick one
A) 6
B) 3
C) 5
D) -1
E) None

Solution: Answer   Dividing numerator as well as denominator by b, we get   Given Exp. = (3a + 2b) / (3a - 2b) = (3a/b + 2) / (3a/b - 2)   = [ (3 x 4) / 3 + 2 ] / [ (3 x 4)/3 - 2 ]   = (4 + 2) / (4 - 2)= 
(4 + 2) / (4 - 2) = 3
3   Option: 3
Answer: B
The positive two-digit integers p and q have the same digits, but in reverse order. Which of the following must be a factor of p + q?	Choose the correct choice from the following options
A) 66
B) 9
C) 10
D) 12
E) 14

Solution: Remember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9   and when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187   66 is multiple of 11   66nswer : 66
Answer: A
P runs 20% faster than Q so P gives Q a 50 meter head start. If the race ends in a tie, how far (in meters) did P run in the race?  Answers:
A) 250	B) 300	C) 350	D) 400	E) 450

Solution: Let D be the race distance that P ran.   Let T be the time it took to complete the race.   Let V be Q's speed.   T = D/1.2V = (D-50) / V   D=1.2D-60   0.2D=60   D=300 meters.   The answer is 300.
Answer: B
A Cricketer makes a score of 134 runs in the 22nd inning and thus increases his average by 3.5. Find his average after 22nd inning.  Choose the correct answer: A) 40 B) 60.5 C) 52 D) 55 E) 36

Solution: Explanation :   Let the average after 22nd innings = x   Then average after 21th innings = (x-3.5)   Therefore 21(x-3.5) + 134 = 22x   Therefore x = 60.5   Answer : 60.5
Answer: B
Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?	Answers.
A) 7  B) 6  C) 5  D) 4  E) 3

Solution: Let rate = R% and time = R years.   Then, (1200 * R * R) / 100 = 432   12R2 = 432   R2 = 36 => R = 6.   Answer: 6
Answer: B
If x and y are three-digit integers such that x > 400 and y<700, which of the following is closest to the maximum possible value of xy ?	Select the correct option.
A) 698,301  B) 2,800  C) 45,000  D) 76,000  E) 28,000

Solution: To get the maximum possible value of xy, we need maximize the value of both x and y   max x can be = 999 (given x is a two-digit integer > 400)   max y can be = 699 (given y is a two-digit integer < 700)   xy = 999*699 = 698,301   698,301nswer (698,301)
Answer: A
A person covers a distance in 12 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes. Choose the correct choice from the following:
A) 8 m/s	B) 4 m/s	C) 15 m/s	D) 10 m/s	E) 5 m/s

Solution: Explanation:   T = 12 m   Spees = 12 kmph   = 12 x 5/18 = 10/3 m/s   Let new speed be "x"   12 x (10/3) = 5x   x = 8 m/s   8 m/snswer: Option 8 m/s
Answer: A
How many number of 4 digits can be formed with the digits 1,2,3,4,5 if repetition of digits is not allowed?  Choose the correct option:	A) 60	B) 120	C) 180	D) 240	E) 32

Solution: n = number of digits = 5   r = number of places to be filled up = 4   Required number = 5P4 = 5!/1! = 120   Answer is 120
Answer: B
You have a pair of unbiased dices. You throw them together till you get a sum of 4 or 7.
What is the probability that you get a sum of 4 before the sum of 7?	Pick.
A) 5/6  B) 4/5  C) 2/5  D) 1/8  E) 4/4

Solution: C   2/5   This problem can be solved with different approaches. Let us not go into the complicated generic stuff to avoid confusion and try to solve it with simpler means.   Let us find the results separately. There can be 4 different results that give the sum of 5 and there can be 6 different results that give the sum of 7.   Thus, the probability that we get the sum of 4 before the sum of 7 will be:   4/(4+6) = 4/10 = 2/5.
Answer: C
Marge has C candies, where C is an integer such that 20 <C< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children? Choose the correct choice from the following answers
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: If Marge divides the candies equally among 5 children, she will have 2 candies remaining.   This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47   If she divides the candies among 6 children, she will have 1 candy remaining.   this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49   ONLY 37 is common, so candies are 37 in number..   if 37 is divided in 7 kids, remainder 2= 2   2
Answer: C
A,B,and C were started a business, the total profit for one year is $56700.The profit sharing ratio is 8:9:10 (according to their investment they divide their profit).what is the profit of c?
Choose the correct choice from the following options.
A) $5670	B) $18900	C) $21000	D) $13500	E) $27000

Solution: A:B:C = 8+9+10= 
8+9+10 = 27
27; C'share= 10/27 of the total profit. c will get = 10/27*$56700=$21000.   Answer : $2100010/27* 56700= 
10/27* 56700 = 21_000
$21000.   Answer : $21000
Answer: C
A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?	Choose the correct option.
A) 9:1  B) 4:7  C) 7:1  D) 2:5  E) 5:6

Solution: Explanation:   Milk = 3/5 * 20= 
3/5 * 20 = 12
12 liters, water= 8 liters   If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.   Remaining milk = 12 - 6= 
12 - 6 = 6
6 liters   Remaining water= 8 - 4= 
8 - 4 = 4
4 liters   10 liters of pure milk are added, therefore total milk= (6 + 10)= 
(6 + 10) = 16
16 liters.   The ratio of milk and water in the new mixture= 16:4 = 4:1   If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10= 
4/5 * 10 = 8
8 liters.   Amount of water removed= 2 liters.   Remaining milk = (16 - 8)= 
(16 - 8) = 8
8 liters.   Remaining water= (4 -2)= 
(4 -2) = 2
2 liters.   The required ratio of milk and water in the final mixture obtained= (8 + 10):2 = 18:2 = 9:1.   9:1NSWER IS 9:1
Answer: A
The distance between 2 cities A and B is 1000km. A train starts from A at 11 a.m. and travels towards B at 100 km/hr. Another starts from B at 12 P.m. and travels towards A at 150 km/hr. At what time do they meet?
Choices
A) 11am.
B) 12p.m.
C) 3pm.
D) 4p.m.
E) 1p.m.

Solution: Suppose they meet x hrs after 11 a.m.   Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000   100x + 150 (x-1) = 1000   x = 4.60 = 5 hrs   They meet at 11+5 = 4 p.m.   Answer is 4p.m.
Answer: D
One third of a two digit number exceeds its one fourth by 3. What is the sum of the digits of the number?
Choose the correct option
A) seven
B) eight
C) nine
D) ten
E) eleven

Solution: Explanation:   x/3 – x/4 = 3 => x =36   3 + 6= 
3 + 6 = 9
9   nine
Answer: C
Find the one which does not belong to that group ?	Choose the correct choice from the following options:	A) 36	B) 77	C) 28	D) 99	E) 22

Solution: Explanation:   16, 36, 64 and 4 are perfect squares but not 28.   Answer:28
Answer: C
If c = (1/4)a and b = 3c, then which of the following represents the result of a^2+b^2+c^2 in terms of c	Pick: A) 26c^2 B) 15c^2 C) 25c D) 56c^2 E) 19c

Solution: a = 4c and b =3c.   a^2+b^2+c^2 = (4c)^2+(3c)^2+c^2 = 26c^2.   26c^2nswer is 26c^2
Answer: A
How many even number in the range between 15 to 100 inclusive are not divisible by 3 Pick:
A) 29  B) 30  C) 31  D) 33  E) 46

Solution: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)   For 2,   16,18...100   using AP formula, we can say 100 = 16 + (n-1) *2   or n=43.   For 6,   18,...96   using AP formula, we can say 96 = 18 + (n-1) *6   or n=14.   Hence, only divisible by 2 but not 3 = 43-14= 
43-14 = 29
29. hence, 29nswer 29
Answer: A
On a certain road, 20% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit? Pick one:	A) 10.5%	B) 12.5%	C) 15%	D) 25%	E) 30%

Solution: suppose there are X motorists.   20% of them exceeded the speed limit and received the ticket, i.e. X/5.   Again, suppose total no. of motorists who exceeded the speed limit are Y.   20% of Y exceeded the speed limit but didn't received the ticket, i.e. Y/5.   it means 4Y/5 received the ticket.   hence, 4Y/5 = X/5   or Y/X=1/4   or Y/X * 100= 1/4 * 100= 
1/4 * 100 = 25
25%   25%
Answer: D
In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 23,947. Approximately what was the percent increase? Select:
A) 45%	B) 125%	C) 145%	D) 150%	E) 169%

Solution: The percent increase is (23947-8902)/8902=15045/8902=1.69   So the approximate answer is 169%
Answer: E
If 2x = 3y = 20, then 12xy = ?	Pick.
A) 1,200 B) 800 C) 120 D) 40 E) 20

Solution: 2x = 20;x=10   3y = 20;y=20/3   Multiply: 12xy=12*10*20/3= 
12*10*20/3 = 800
800.   Answer: 800.
Answer: B
Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?  Select:
A) 10
B) 12
C) 15
D) 20
E) 5

Solution: Answer: Option B   Speed of the first train = 120/10= 
120/10 = 12
12 m/sec.   Speed of the second train= 120/5 = 8 m/sec.   Relative speed = 12 + 8= 
12 + 8 = 20
20 m/sec.   Required time= (120 + 120)/20= 
(120 + 120)/20 = 12
12 sec.
Answer: B
The fourth proportional to 12, 14 and 18 is? Choose the correct choice.
A) 21  B) 66  C) 77  D) 88  E) 12

Solution: (14*18)/12= 
(14*18)/12 = 21
21   21nswer: 21
Answer: A
Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements T.  Select the correct option: A) a) T=48 B) b) T=144 C) c) T=240 D) d) T=288 E) e) T=120

Solution: One specific boy is seated to either of end seat, lets call him b1   One specific girl is seated in the middle, lets call her g1   Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.   b1 can be seated 2 different seats : 2!   g1 is seated on the seat #4, fixed (no other alternative) : 1   the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!   2! x 1 x 5! = 240   Answer c) T=240
Answer: C
The present ages of three persons in proportions 10 : 1 : 5. Eight years ago, the sum of their ages was 56. Find their present ages (in years).  Choose one:	A) 50, 5, 25	B) 16, 28, 36	C) 16, 28, 35	D) 16, 28, 34	E) 16, 28, 33

Solution: Let their present ages be 10x, 1x and 5x years respectively.   Then, (10x - 8) + (1x - 8) + (5x - 8) = 56   16x = 80   x = 5.   Their present ages are 10x = 50 years, 1x = 5 years and 5x = 25 years respectively.   50, 5, 25nswer:50, 5, 25
Answer: A
If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 65, then the average marks of all the students is:
Options:
A) 53.33	B) 54.68	C) 55	D) 56.09	E) None of these

Solution: Explanation:   Required average = (55 × 50 + 60 × 55 + 45 × 65/55 + 60 + 45)   = (2750 + 3300 + 2925/160)   = 8975/160   = 56.09   Answer: 56.09
Answer: D
The sum of the terms of an infinite G.P is 7 and the sum of the cubes of the terms is 1,225. Find the first term of the series. Choose the most appropriate option:
A) 35/3 B) 35/2 C) 15/2 D) 9/4 E) 7/4

Solution: S a = a/ ( 1 – r ) = 7 …………. (1)   Sum to infinity of the cubes = a 3 / 1 –r 3 = 1,225   From (1) a 3 / ( 1 – r ) 3 = 7 3 = 343   Therefore, ( 1 – r ) 3 / 1 – r 3 = 1225/343,   (1+ r 2 -2r)/ ( 1 + r 2 + r ) = 25/7   7 + 7 r 2 –14r = 25 + 25 r + 25 r 2   18 r 2 +39r + 18 = 0, on solving r = -3/2 or -2/3   for an infinite G.P | r | < 1, r = - 2/3   Therefore, a / [ 1 – ( - 2/3 ) ] = 7, a = 7 * 5/3 = 35/3 35/3NSWER:35/3
Answer: A
Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed must he travel to reach A at 1 PM?  Answers:  A) 8 kmph  B) 12 kmph  C) 5 kmph  D) 6 kmph  E) 8 kmph

Solution: Let the distance travelled by x km.   Then, x - x = 2   10 15   3x - 2x = 60   x = 60 km.   Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.   10   So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.   Required speed = 60 kmph. = 12 kmph.   5   12 kmph
Answer: B
A boat crossed a lake from North to West at the speed of 5 km/h, entered a river and covered twice as much distance going upstream at 4 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.6 km/h that day, what was its approximate downstream speed?	Choose the correct choice from the following options:
A) 2  B) 3  C) 6  D) 7  E) 8

Solution: One way of solving this is:   Speed of boat on still water (lake)=5kmph   Speed upstream = 4kmph = speed in still water - speed of river => speed of river = 1kmph   =>Speed downstream = speed in still water + speed of river = 5+1= 
5+1 = 6
6kmph   Ans is 6
Answer: C
In racing over a given distance d at uniform speed, A can beat B by 20 meters, B can beat C by 5 meters, and A can beat C by 24 meters. What is the distance d in meters?	Select the correct option: A) 70 B) 80 C) 90 D) 100 E) 120

Solution: When A is at the finish line, B is 20 meters back, and C is 24 meters back.   When B runs another 20 meters to the finish line, C is 5 meters back.   So B gains 1 meter on C every 20 meters covered.   To gain a final difference of 5 meters, B runs a total of 100 meters.   The answer is 100.
Answer: D
There are 6 boxes numbered 1, 2,…,.6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is Answers.
A) 44  B) 21  C) 56  D) 52  E) 12

Solution: List down possibilities: From only 1 box all the way to all 6   If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.   If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.   If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.   If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.   If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.   If all 6 boxes have green balls, there is just 1 possibility.   Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1= 
6 + 5 + 4 + 3 + 2 + 1 = 21
21.   Ans: 21
Answer: B
The speed of a boat in still water is 40 kmph and the speed of the current is 16 kmph. Find the speed downstream and upstream?  Answers:	A) 56,24 kmph	B) 40,24 kmph	C) 29,24 kmph	D) 26,24 kmph	E) 12,24 kmph

Solution: Speed downstream = 40 + 16= 
40 + 16 = 56
56 kmph   Speed upstream= 40 - 16= 
40 - 16 = 24
24 kmph   56,24 kmphnswer: 56,24 kmph
Answer: A
There are 27 different three-digit integers that can be formed using only the digits 1, 2 and 3. If all 27 of the integers were listed, what would their sum be?  Choose the correct choice from the following answers
A) 2,704 B) 2,990 C) 5,404 D) 5,444 E) 5,994

Solution: Probably the easiest and fastest way to answer this problem is to think about the average three digit number you can create using just the digits 1,2,3, and to multiply this average number with 27.   The average three digit number is 222 (choosing an average of 1,2,3 for every single digit of the number). So  222*27= 
 222*27 = 5_994
5994.   Hence, solution 2,704 is correct.
Answer: A
The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5500. The monthly income of P is? Choose the correct option:
A) A)Rs.4078	B) B)Rs.4000	C) C)Rs.4029	D) D)Rs.4300	E) E)Rs.4020

Solution: Let P, Q and R represent their respective monthly incomes. Then, we have:   P + Q = (5050 * 2)= 
(5050 * 2) = 10_100
10100 --- (i)   Q + R= (6250 * 2)= 
(6250 * 2) = 12_500
12500 --- (ii)   P + R= (5500 * 2)= 
(5500 * 2) = 11_000
11000 --- (iii)   Adding (i), (ii) and (iii), we get:   2(P + Q + R)= 33600 = P + Q + R = 16800 --- (iv)   Subtracting (ii) from (iv), we get, P = 4300.   P's monthly income = Rs.4300.   Answer: Rs.4300
Answer: D
The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle? Choose the correct choice from the following options:
A) 5 hours 5 minutes
B) 8 hours 5 minutes
C) 7 hours 5 minutes
D) 6 hours 5 minutes
E) 3 hours 5 minutes

Solution: If L and W be the original length and width of the rectangle and its area is given by   L * W   After increase the length becomes 2 L and the width becomes 3 W. The area is then given by (2 L) * (3 W) and is known. Hence   (2 L) * (3 W) = 1800   Solve the above equation to find L* W   6 L * W = 1800   L * W = 1800 / 6= 
1800 / 6 = 300
300 square meters , area of original rectangle   Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute).   Solution   In 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill   1/5 + 1/8= 13 / 40 of a tank   Since the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving   (13/40) t = 1   t = 40 / 13 = 39/13 + 1/13 hours   = 3 hours and (1/13)*60 minutes   = 3 hours 5 minutes (rounded to the nearest minute)   correct answer 3 hours 5 minutes
Answer: E
The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is: Choose the correct choice from the following options:
A) 4.37% B) 5% C) 6% D) 8.75% E) None

Solution: Explanation: Increase in 10 years = (262500 - 175000)= 
(262500 - 175000) = 87_500
87500.   Increase%= (87500/175000 x 100)% = 50%.   Required average = (50/10)= 
(50/10) = 5
5%.   Answer: Option 5%
Answer: B
Equal weights of two alloys containing tin, copper and lead in the ratio 3:2:7 and 4:11:3 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy? Choose the correct choice from the following choices.
A) 41:81:37 B) 33:91:81 C) 17:28:27 D) 51:86:89 E) 41:86:89

Solution: Let the weight of the two alloys be w each   Required ratio =   (3w/12 +4w/18): ( 2w/12 +11w/18 ): (7w/12+3w/18)   = 17w/36 : 28w/36 : 27w/36   = 17:28: 27   ANSWER:17:28:27
Answer: C
The diameter of a garden roller is 1.2 m and it is 2 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22â„7)
Choose the correct choice from the following:  A) 40 m2  B) 44 m2  C) 48 m2  D) 37.7 m2  E) None of these

Solution: Required area covered in 5 revolutions   = 5 Ã— 2Ï€rh = 5 Ã— 2 Ã— 22â„7 Ã— 0.6 Ã— 2 = 37.7 m2   Answer 37.7 m2
Answer: D
Two trains are moving in opposite directions with speed of 90 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds  Select.
A) 56	B) 40	C) 47	D) 26	E) 25

Solution: Explanation:   Relative speed = 90+90= 
90+90 = 180
180 km/hr (Since both trains are moving in opposite directions)   Total distance= 1.1+.9= 
1.1+.9 = 2
2km   Time= 2/180 hr = 1/90 hr = 3600/90= 
3600/90 = 40
40 seconds   Answer: Option 40
Answer: B
In a caravan, in addition to 60 hens, there are 35 goats and 6 camels with some keepers. If the total number of feet be 193 more than the number of heads in the caravan, the number of keepers is
Choose the correct choice from the following choices:  A) 5  B) 10  C) 15  D) 20  E) 25

Solution: Explanation: Let number of keepers be x. Then, Total number of feet = 2 x 60 + 4 x 35 + 4 x 6 + 2x = 2x + 284. Total number of heads = 60 + 35 + 6 + x= 101 + x. Therefore (2x + 284) = (101 + x) + 193 or x = 10. Answer: 10
Answer: B
If a, b, c, d, and x are nonzero numbers, which of the following conditions must be true for (ax)^61(bx)^21(cx)^14(dx)^6>0? Choices.
A) x > 0 B) a × b > 0 C) c × d > 0 D) a × d > 0 E) a × b < 0

Solution: The question becomes a^(61) *b ^(21) *c^(14) *d^6*x^(102) >0   c^14 , d^6 , x^102 are positive no matter what the sign of c ,d and x respectively   =>a^61 *b ^21 must me positive   => a*b should be positive   Ans a × b > 0
Answer: B
A cricket player whose bowling average was 23.50 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.50. What will be the number of wickets taken by him till the last match?	Options:  A) 64  B) 72  C) 131  D) 456  E) 108

Solution: Average = Total Runs / Total wickets   Total runs after last match = 23.5w + 52   Total wickets after last match = w + 5   (23.5w + 52) / (w + 5) = 23.5 - 0.5= 
23.5 - 0.5 = 23
23   w= 126   so total wickets aftr last match = w+5 = 131   ANSWER:131
Answer: C
The list price of an article is Rs.70. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?  Select the correct option
A) 10.85%
B) 14.85%
C) 15.85%
D) 16.85%
E) 17.85%

Solution: 70*(90/100)*((100-x)/100) = 56.16   x = 10.85%   10.85%NSWER:10.85%
Answer: A
A certain galaxy is known to comprise approximately 4 x 10^10 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?  Choose the correct choice from the following answers.
A) 800 B) 1,250 C) 8,000 D) 12,000 E) 80,000

Solution: Total no. of stars on galaxy = 4 * 10^10   Of every 50 million stars, 1 is larger than sun.   1 million = 10^6 therofore, 50 million = 50 * 10^6   total no. of stars larger than sun = 4 * 10^10 / 50 * 10^6   =40 * 10^2 /5   = 800   therefore answer is 800
Answer: A
A train 125 m long passes a man, running at 20 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Choose the correct option.
A) 36 B) 50 C) 28 D) 26 E) 65

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 20) km/hr. x - 20 = 45 ==> x = 65 km/hr   Answer: 65
Answer: E