MU-NLPC/Calc-aqua_rat huggingface dataset:
In how many ways, a committee of 5 members can be selected from
6 men and 5 ladies, consisting of 3 men and 2 ladies? Choose the correct option:
A) 200	B) 400	C) 300	D) 500	E) 430

Solution: Sol. (3 men out 6) and (2 ladies out of 5) are to be chosen.   Required number of ways = (6c3x5c2)   = [6x5x4/3x2x1] x [5x4/2x1] = 200.   200NSWER 200
Answer: A
If A is to be chosen at random from the set {56,85,41} and B is to be chosen at random from the set {1,2,3,4,5}, what is the probability that AB will be odd? Pick one
A) 4/15  B) 13/15  C) 56/15  D) 6/15  E) 8/15

Solution: Method-1   A13/15 will be odd when   1) A is odd and 13/15 is even, Probability of A odd is (2/3) and Probability of 13/15 even is (2/5), so Probability of Case(1) = (2/3)*(2/5) = (4/15)   2) A is even and 13/15 is odd, Probability of A even is (1/3) and Probability of 13/15 odd is (3/5), so Probability of Case(2) = (1/3)*(3/5) = (3/15)   3) A is odd and 13/15 is odd, Probability of A odd is (2/3) and Probability of 13/15 odd is (3/5), so Probability of Case(1) = (2/3)*(3/5) = (6/15)   Total Favorable Probability = (4/15)+(3/15)+(6/15) = (13/15)   Answer: option 13/15
Answer: B
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 7 seconds. What is the length of the fast train? Choices: A) 23 m B) 23 (2/9)m C) 38 (8/9)m D) 29 m E) 28 m

Solution: Relative speed = (40 - 20) km/hr =	(20 x(5/18))m/sec =	(50/9)m/sec.   Therefore Length of faster train =	((50/9)	x 7) m =	(350/9)m = 38	(8/9)	m.   38 (8/9)m
Answer: C
Johnny travels a total of one hour to and from school. On the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 21 miles per hour. How far is it to the school? Pick one.
A) 2 miles
B) 4 miles
C) 6.5 miles
D) 8 miles
E) 10 miles

Solution: Answer: C) 6.5 miles.   Average speed for round trip = 2*a*b/(a+b), where a,b are speeds   so, average speed was = 2*5*21/(5+21) = 6.5m/hr   the distance between schoolhome should be half of that. ie. 6.5 miles   Answer 6.5 miles
Answer: C
Rs. 800 becomes Rs. 956 in 3 years at a rate of S.I. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years?  Choose one:
A) 2889	B) 2798	C) 1052	D) 2789	E) 2878

Solution: S.I. = (956 - 800) = Rs. 156.   Rate = (100 * 156) / (800 * 3) = 6 1/2 %   Now rate = (6 1/2 + 4) = 10 1/2 %   New S.I. = (800 * 21/2 * 3/100) = Rs. 252   New amount = (800 + 252)   = Rs.1052.   Answer: 1052
Answer: C
If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
Choices
A) None B) I only C) II only D) III only E) I and II

Solution: given 2x/y is prime and greater than 2.   => 2x/y could be any of the following   3,5,7....   => 2x/y is odd and prime (as 2 is the only even prime number and its not in this set)   1. x = y , can't be true   if x=y , 2x/y = 2 which is not odd and prime.   2. y=1. can't be true.   if y=1,2x/y = 2x = even which is not odd & prime.   3. x and y are prime integers, need not be true.   lets say 2x/y = 3 and say y=2 prime   =>x = 6/2= 
6/2 = 3
3 prime   satisfies the given condition here.   but when 2x/y= 3 and y=5 prime   => x = 15/2 not prime   My Nonenswer is None
Answer: A
In the list 3, 4, 5, 5, 5, 5, 7, 11, 21, what fraction of the data is less than the mode?  Select the correct option:
A) 2/9 B) 1/3 C) 2/5 D) 2/3 E) 7/9

Solution: highest frequent term in the set is 5 (with frequency 4) hence   Mode = 5   two terms (3, 4) out of a total of 9 terms are less than mode of the set.   Fraction of set that are less than Mode of set = 2/9   2/9nswer: Option 2/9
Answer: A
Eleven books consisting of 4 financial management, 3 marketing management and 4 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together. Select.
A) 1/1455 B) 1/1355 C) 1/2255 D) 1/5040 E) 1/1155

Solution: Since the denominator will be 11! . And there is no way to divide 11 from numerator and denominator. Use a multiple of 11 in the denominator only answer   1/1155
Answer: E
In the year 2011, Shantanu gets a total of Rs. 3832.5 as his pocket allowance. Find his pocket allowance per day.?
Choose the correct choice from the following choices:
A) Rs. 9.5  B) Rs. 10.5  C) Rs. 12.5  D) Rs. 11.5  E) None of these

Solution: Answer   Allowance per day = 3832.5 / 365 = Rs. 10.50   Correct Option: Rs. 10.5
Answer: B
Three numbers are in the ratio 3:5:7. The largest number is 56. What is the difference between smallest and largest number? Choose the correct choice from the following
A) 20  B) 24  C) 28  D) 32  E) 36

Solution: The three numbers are 3x, 5x, and 7x.   The largest number is 56 = 7*8, so x = 8.   The smallest number is   3*8= 
  3*8 = 24
24.   56 - 24= 
56 - 24 = 32
32   The answer is 32.
Answer: D
A and B can do a piece of work in 40 days and 50 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?  Choose the correct choice from the following choices
A) 28 days B) 60 days C) 20 days D) 30 days E) 40 days

Solution: Explanation:   (28 days+B)’s 10 days work = 10[1/40+1/50]=10[5+4/200]= 9/20   28 days complete remaining work in 9/20*40= 
9/20*40 = 18
18   Total work= 10+18= 
10+18 = 28
28days   28 daysnswer: Option 28 days
Answer: A
I had 30 donuts when I left home this morning but only 9 when I came back home. What percentage of the donuts are missing?	Select the correct option.
A) 70  B) 65  C) 55  D) 75  E) 60

Solution: 30 - 9= 
30 - 9 = 21
21   21/30 or 7/10   7/10= 70/100 = 70%   70nswer is 70
Answer: A
The average salary of 20 people in the shipping department at a certain firm is $1000. The salary of 10 of the employees is $600 each and the salary of 6 of the employees is $200 each. What is the average salary of the remaining employees?  Choose the correct choice
A) $2500	B) $3200	C) $4500	D) $5000	E) $5200

Solution: total salary... 20*1000=20000   10 emp @ 600 =6000   6 emp @ 200 =1200   remaing 4 emp salary = 20000-6000-1200= 
20000-6000-1200 = 12_800
12800   average=12800/4= 
12800/4 = 3_200
3200   Answer is $3200
Answer: B
A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x ? Choose the correct choice from the following:
A) 8 B) 7 C) 6 D) 5 E) 4

Solution: Clearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.   or 137 + x = 144 o144 - 137 = 7.   Answer: 7
Answer: B
The perimeter of a triangle is 48 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?	Select.
A) 76 cm2  B) 56 cm2  C) 18 cm2  D) 98 cm2  E) 60 cm2

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle   = 2.5 * 48/2= 
2.5 * 48/2 = 60
60 cm2   Answer:60 cm2
Answer: E
For the positive numbers, n, n + 3, n + 5, n + 8, and n + 9, the mean is how much greater than the median? Options.
A) 0 B) 1 C) n+l D) n+2 E) n+3

Solution: Let’s first calculate the mean (arithmetic average).   mean = sum/quantity   mean = (n + n + 3 + n + 5 + n + 8 + n + 9)/5   mean = (5n + 25)/5   mean = n + 5   Next, we determine the median. The median is the middle value when the terms are ordered from least to greatest. The terms ordered from least to greatest are as follows:   n, n + 3, n + 5, n + 8, n + 9   The median is n + 5.   Finally we are asked how much greater the mean is than the median. To determine the difference we can subtract the smaller value (the median) from the larger value (the mean) and we get:   n + 5 – (n + 5) = n + 5 – n – 5 = 0   The answer is 0
Answer: A
If p/5 = r/2 and r = 0.75s, what is the ratio of p to r to s?
Choose the correct choice from the following choices:
A) 2 : 3 : 4  B) 8 : 12 : 9  C) 15 : 6 : 8  D) 6 : 4 : 3  E) 12 : 8 : 3

Solution: p/5=r/2, r=0.75s, what is p:r:s?   we get p/r=5/2 and r/s=3/4, so   5/3*3/2 and 2/2*3/4   15/6 and 6/8   15 : 6 : 8
Answer: C
If 522x is a 3 digit no. with as a digit x. If the no.is divisible by 6, What is the value of the digit x is?
Choose the correct answer.
A) 4 B) 6 C) 9 D) 10 E) 11

Solution: If a number is divisible by 6 , it must be divisible by both 2 and 3   In 522x, to this number be divisible by 2, the value of x must be even. So it can be 2,4 or 6 from given options   552x is divisible by 3, If sum of its digits is a multiple of 3.   5+5+2+x =12+x ,   If put x =2 , 12+2=14 not a multiple of 3   If put x =4 , 12+6=18 is a multiple of 3   If put x =6 , 12+2=14 not a multiple of 3   The value of x is 6.   6
Answer: B
10% of a number is more than 20% of 650 by 190. Find the number?
Pick.
A) 288  B) 3200  C) 800  D) 267  E) 121

Solution: (10/100) * X â€“ (20/100) * 650 = 190   1/10 X = 320   X = 3200   Answer:3200
Answer: B
Two dice are rolled. What is the probability the sum will be greater than 10?
Choose the most appropriate option
A) 1/9.	B) 1/12.	C) 5/36.	D) 1/6.	E) 1/5.

Solution: Combinations possible: (6,6) , (5,6) , (6,5) = 3   Total combinations possible:   6*6= 
  6*6 = 36
36   Answer= 3/36 = 1/12 Option 1/12..
Answer: B
If an amount of Rs 42,680 is distributed equally
amongst 22 persons, how much amount would each
person get?
Choose the correct option
A) Rs 1905	B) Rs 2000	C) Rs 745	D) Rs 1940	E) None

Solution: Required amount =42680/22= 
42680/22 = 1_940
Rs 1940   Answer Rs 1940
Answer: D
How long will it take a train travelling at 68kmph to pass an electric pole if the train is 170 m long	Select the correct option.
A) 6.99 B) 5.99 C) 8.99 D) 4.99 E) 9.99

Solution: Sol.   Speed = [ 68x5/18] m/sec =18.9 m / sec.   Time taken = (170/18.9)sec =8.99 sec.   Answer 8.99
Answer: C
A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 52 minutes. The total distance is? Choose the correct choice from the following
A) 1 km
B) 2 km
C) 3.3 km
D) 4 km
E) 5 km

Solution: C   3 km   Let the total distance be 3x km.   Then, x/3 + x/4 + x/5 = 52/60   47x/60 = 52/60 => x = 1.1   Total distance = 3 * 1.1= 
3 * 1.1 = 3.3
3.3 km.
Answer: C
A company issued 20000 shares of par value Rs. 10 each. If the total divided declared by the company is Rs.24000, find the rate of dividend paid by the company.	Choose the correct choice from the following
A) 10  B) 11  C) 12  D) 13  E) 15

Solution: Number of shares = 20000   Face value of each share = Rs.10   divided per share = 10×R/100 where R is the rate of interest   Total divided = 20000×10×R/100   20000×10×R/100=24000   ⇒R=24000/2000= 
24000/2000 = 12
12   ie, divided= 12%   Answer is 12.
Answer: C
Complete the series 6,120, 504, 1320	Select
A) 1730  B) 2730  C) 3730  D) 2830  E) 2630

Solution: 2^3-2-=6   5^3-5=120   8^3-8=504   11^3=1320   14^3=2730.   ANSWER:2730
Answer: B
If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?  Choose one
A) 120 cm2	B) 176 cm2	C) 267 cm2	D) 268 cm2	E) 976 cm2

Solution: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.   120 cm2rea of the triangle   = 1/2 * 24 * 10= 
1/2 * 24 * 10 = 120
120 cm2   120 cm2nswer: 120 cm2
Answer: A
The speed of a boat in upstream is 80 kmph and the speed of the boat downstream is 120 kmph. Find the speed of the boat in still water and the speed of the stream?  Choose the correct choice from the following:
A) 21 kmph.
B) 22 kmph.
C) 20 kmph.
D) 25 kmph.
E) 28 kmph.

Solution: Speed of the boat in still water = (80+120)/2= 
(80+120)/2 = 100
100 kmph. Speed of the stream= (120-80)/2= 
(120-80)/2 = 20
20 kmph.   Answer:20 kmph.
Answer: C
What was the day of the week on 15th May, 2006?
Choose the correct choice from the following choices:
A) Thursday B) Friday C) Saturday D) Monday E) Sunday

Solution: 28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)   Odd days in 1600 years = 0   Odd days in 400 years = 0   5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days   Jan. Feb. March April May    (31 + 28 + 31 + 30 + 15 )= 
 (31 + 28 + 31 + 30 + 15 ) = 135
135 days   135 days= (19 weeks + 2 day) 1 odd day.   Total number of odd days = (0 + 0 + 6 + 2)= 
(0 + 0 + 6 + 2) = 8
8 0 odd day.   Given day is Monday.   Answer: Option Monday
Answer: D
Of 61 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?	Choose the correct choice from the following:	A) 53	B) 55	C) 59	D) 71	E) 92

Solution: Total = 61   Thrower = 37   Rest = 61 - 37= 
61 - 37 = 24
24   Left Handed= 24/3= 
24/3 = 8
8   Right handed= 16   If all Thrower are right handed then total right handed is   37 + 16= 
  37 + 16 = 53
53   so A. 53 is the right answer
Answer: A
A company plans to gradually replace its fleet of 20 cars with newer models. At the end of every year starting with 2000 it retires 5 of its old cars and buys 6 new models.How many years did it take before the number of older cars left in the company's fleet was less than 50 percent of the fleet?
Answers
A) 6
B) 3
C) 2
D) 4
E) 5

Solution: Total fleet--20   End of year 2000 -- (retires 5 and buys 6) total fleet--21(15 old 6 new).   End of year 2001 -- (retires 5 and buys 6) total fleet--22(10 old 12 new).   Answer is 2--after 2 years the company has a total of 22 cars (10 old 12 new), the old cars are already less than 50% of its fleet.
Answer: C
A 40 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
Choose the correct option:
A) 810  B) 12  C) 13  D) 14  E) 16

Solution: Amount of salt = 4.0   Assume x gallons of water are added.   4.0 / 40 + x = 8/100   400 = 8x + 320   8x = 80   x = 10   Correct Option: 810
Answer: A
The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 24, how many more dollars, in terms of x, will it cost per person? Choose the correct option:
A) x/6
B) x/17
C) x/40
D) 3x/40
E) 3x/80

Solution: Just plugging in values   X= 240   Cost per person if we consider 10 = 24   Cost per person if we consider 24 = 10   Difference between costs is 14 dollars.   Plugging in the value of x into the answer choices, let's see which one yields a result of 14. And that is x/17.
Answer: B
Find the value of m 32519 x 9999 = m?	Pick one:  A) 724533811  B) 353654655  C) 545463251  D) 725117481  E) 325157481

Solution: 32519 x 9999 = 32519 x (10000 - 1)   = 32519 x 10000 - 32519 x 1   = 325190000 - 32519= 
325190000 - 32519 = 325_157_481
325157481   325157481
Answer: E
A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 7700. What is the share of B ?
Pick one: A) 1100 B) 800 C) 1400 D) 1200 E) None of them

Solution: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x   A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.   Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.   Hence, B's share = Rs. ( 7700 x (2/11))= Rs. 1400.   Answer is 1400
Answer: C
An ant walks an average of 600 meters in 12 minutes. A beetle walks 15% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h?	Choose the correct option:  A) 2.215.  B) 2.55  C) 2.775.  D) 3.2.  E) 3.5.

Solution: the ant walks an average of 600 meters in 12 minutes   600 meters in 1/5 hours   the beetle walks 15% less distance = 600-90= 
600-90 = 510
510 meters in 12 minutes   0.510 km in 12/60= 1/5 hours   speed = 0.510*5= 
0.510*5 = 2.55
2.55 km/h   Correct answer 2.55=2.55
Answer: B
An empty fuel tank with a capacity of 218 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added? Choose the correct choice from the following choices:  A) 122  B) 150  C) 100  D) 80  E) 50

Solution: Say there are A gallons of fuel A in the tank, then there would be 218-A gallons of fuel B.   The amount of ethanol in A gallons of fuel A is 0.12A;   The amount of ethanol in 218-A gallons of fuel B is 0.16(218-A);   Since the total amount of ethanol is 30 gallons then 0.12A+0.16(218-A)=30 --> A=122.   122nswer: 122.
Answer: A
eight mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the eight arrange themselves in line such that Frankie’s requirement is satisfied? Choose the correct choice from the following answers:
A) 22222
B) 20160
C) 8644
D) 46060
E) 40320

Solution: 8 mobsters can stand in 8! ways = 40320   in half of the cases one person will be ahead and in the other person in the other half.   thus 20160 cases.   20160
Answer: B
If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by
Choose the correct option.
A) 330  B) 340  C) 350  D) 360  E) 370

Solution: 1 11 21 .......91   2 12 22........92   3 13 23........93   . . . .. . .. . .   . . .. .. . .. .   . . .. . . .. . ...   there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column   and diff of 6 and 9 is 3 so   3*1*10+3*10*10= 
3*1*10+3*10*10 = 330
330   330NSWER:330
Answer: A
If n is an integer greater than 8, which of the following must be divisible by 8 ?
Choose the correct choice from the following answers.
A) n(n + 5)(n – 6)  B) n(n + 2)(n – 1)  C) n(n + 1)(n – 4)  D) n(n + 3)(n – 5)  E) n(n + 5)(n – 6)

Solution: If n= 9 , then (n-1) is divisible by 8 .   n(n + 2)(n – 1)
Answer: B
Tough and Tricky questions: Statistics.
Set X consists of prime numbers {3, 11, 7, A, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?  Choose the most appropriate option: A) 14 B) 16 C) 17 D) 20 E) 26

Solution: Since 11Y = Even therefore Y has to beEVENsince 11 is a odd integer (Even * Odd = Even)   Similarly, Y is the product of all integers in set X But all integers in Set X are odd except the unknown A and since X contains only prime numbers, A has to equal to 2... ( 2 is the only even prime number and the product of all prime numbers in set X has to be Even, Even * Odd = Even)   Since you know value of A you can calculate the range = Largest integer in the set minus Smallest integer in the set = 19-2= 
19-2 = 17
17   Answer is 17
Answer: C
A restaurant meal cost $34.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:
Options:	A) $40 and $42	B) $39 and $41	C) $38 and 40	D) $37 and $39	E) $36 and $37

Solution: let tip=t   meal cost=34.50   range of tip = from 10% of 34.5 to 15% of 34.5 = 3.55 to 5.325   hence range of amount paid= 34.5+T= 38.05 to 39.825   ANSWER:$38 and 40
Answer: C
The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is? Choose the correct choice from the following options:	A) 12	B) 16	C) 18	D) 19	E) 20

Solution: 3:4   Total parts = 7   = 7 parts --> 28 (7 × 4 = 28)   = 1 part ---->4 (1 × 4 = 4)   = The greater of the two number is = 4   = 4 parts ----> 16 (4 × 4 = 16)   16
Answer: B
The sum of three consecutive even numbers is 42. Find the middle number of the three?	Choose the correct choice from the following answers:
A) 14
B) 16
C) 18
D) 24
E) 34

Solution: Three consecutive even numbers (2P - 2), 2P, (2P + 2).   (2P - 2) + 2P + (2P + 2) = 42   6P = 42 => P = 7.   The middle number is: 2P = 14.   14NSWER:14
Answer: A
Mohit sold an article for Rs. 18000. Had he offered a discount of 25% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
Choose the correct choice from the following choices:
A) 12500
B) 27767
C) 16688
D) 26678
E) 19987

Solution: Let the CP be Rs. x.   Had he offered 25% discount, profit = 8%   Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 25/100(18000) = Rs. 13500   => 1.08x = 13500   => x = 12500   \12500nswer: 12500
Answer: A
An empty pool being filled with water at a constant rate takes 3hours to fill to 3/5 of its capacity.how much more time will it take to finish filling the pool?
Select the correct option.
A) 5hr 30min  B) 5hr 20min  C) 4hr 48min  D) 3 hr 12min  E) 2hr 40 min

Solution: As pool is filled to 3/5 of its capacity then 2/5 of its capacity is left to fill.   To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).   Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours = 2 hours 40 minutes.   Answer: 2hr 40 min.
Answer: E
The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 80%?  Pick one.
A) 6 B) 7 C) 9 D) 10 E) 11

Solution: We need on-time departure rate to be higher than 8/10, so it should be at least 9/11, which means that 9 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then  9-3= 
 9-3 = 6
6 subsequent flights need to depart on-time.   6nswer: 6
Answer: A
Average of 8 numbers is zero. At most how many numbers may be greater than zero  Answers
A) 0	B) 7	C) 5	D) 6	E) 10

Solution: Answer: Option 7
Answer: B
Sachin is younger than Rahul by 6 years. If the ratio of their ages is 7:9, find the age of Sachin
Choose the correct choice from the following choices:
A) 24.58	B) 14	C) 15	D) 24.9	E) 24.1

Solution: If Rahul age is x, then Sachin age is x-6,   so (x-6)/x = 7/9   => 9x-42 = 7x   => 2x = 42   => x = 21   So Sachin age is   21 - 6= 
  21 - 6 = 15
15   Answer: 15
Answer: C
Which of the following could be the sum of the reciprocals of two prime numbers?  Choose the correct answer.
A) 7/13 B) 11/12 C) 11/30 D) 23/50 E) 14/33

Solution: 10/12 it is   14/33=(1/3) + (1/11)   Answer - 14/33
Answer: E
If KING is coded as 17 and MASS is coded as 29 Then DOG is coded as	Choose the correct choice from the following answers.
A) 21 B) 20 C) 19 D) 29 E) None

Solution: KING = 11+9+14+7= 
11+9+14+7 = 41
41 i.e (4*4)+(1*1)=17   MASS = 13+1+19+19= 
13+1+19+19 = 52
52 i.e (5*5)+(2*2)=29   29OG = 4+14+7= 
4+14+7 = 25
25 i.e(2*2)+(5*5)=29   ANSWER:29
Answer: D
If 3x+y=40, 2x-y=20, for integers of x and y, y^2=? Select.
A) 2
B) 4
C) 0
D) 16
E) 3

Solution: 3x+y = 40   2x-y = 20   5x = 60   x = 12   y = 4   y^2 = 16   Answer is 16
Answer: D
Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6 Pick: A) 7/9 B) 7/5 C) 7/18 D) 4/7 E) 2/7

Solution: Clearly n(S)=6*6= 
6*6 = 36
36   Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then   E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),   (6,6)}   n(E)=14.   Hence p(e)=n(e)/n(s)=14/36=7/18   Option 7/18
Answer: C
The average of nine numbers is 15. The average of first four numbers is 11 and the average of last four numbers is 14. What is the middle number?
Choose the correct choice from the following.
A) 19	B) 20	C) 35	D) 31	E) 27

Solution: The total of nine numbers = 9X15 = 135   The total of first 4 and last 4 numbers is = 4 X 11+4 X 14 = 100   So, the middle number is  (135 - 100 )= 
 (135 - 100 ) = 35
35   35
Answer: C