MU-NLPC/Calc-aqua_rat huggingface dataset:
Jupiter travels around the Sun at an approximate speed of 7.8 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles)  Choices
A) 40,500	B) 42,600	C) 44,700	D) 46,800	E) 48,900

Solution: The speed is 7.8 miles/s. Then 7.8/0.6= 
7.8/0.6 = 13
13 km/s   13*3600= 46,800 kph   The answer is 46,800.
Answer: D
A train running at the speed of 90 km/hr crosses a pole in 12 seconds. Find the length of the train?  Options
A) 150 B) 872 C) 287 D) 288 E) 300

Solution: Speed = 90*(5/18) m/sec = 75/3 m/sec   Length of Train (Distance) = Speed * Time     (75/3) * 12= 
  (75/3) * 12 = 300
300 meter   Answer:300
Answer: E
A dishonest dealer professes to sell goods at the cost price but uses a weight of 852 grams per kg, what is his percent? Choose the correct choice from the following options.
A) 22%	B) 25%	C) 17.37%	D) 99%	E) 12%

Solution: 852 --- 148   100 --- ? => 17.37%   Answer: 17.37%
Answer: C
In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is: Choose one
A) 20 B) 30 C) 32 D) 34 E) 46

Solution: Number = (35 * 12)= 
(35 * 12) = 420
420   Correct quotient= 420/21= 
420/21 = 20
20   20)
Answer: A
A certain kind of necklace is made from 9 yellow, 6 blue, and 3 silver beads. What is the maximum number of these necklaces that can be made from 63 beads of each color ?
Select the correct option:  A) 7  B) 6  C) 5  D) 4  E) 3

Solution: 7tleast 9 yellow breads are needed to make a necklace, so irrespective of the combinations of blue and silver beads, the number of necklaces that can be formed will be   63/9= 
63/9 = 7
7   7nswer:- 7
Answer: A
The number of positive integers valued pairs (x, y) satisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is
Choose the correct choice from the following answers
A) 59	B) 57	C) 55	D) 58	E) 60

Solution: We are asked to find integer solutions for x,y.   There is no need to apply Euclidian algorithm here, we can get particular solutions simply by plugging in some values.   As y reaches 3 we get:   y’ = 3 and x’ = 13. We need only to solve for x.   General solution for x will be:   x = x’ + bn = 13 + 17n   Hence lower limit for n is n ≥ 0.   Now we’ll find upper limit using given restriction x ≤ 1000. Plugging in general solution we’ll get:   13 + 17n ≤ 1000   17n ≤ 987   n ≤ 58   And our list of possible values of n has following representation:   0, 1,2, 3, ….. , 58   Total number of elements is 59.   59NSWER:59
Answer: A
A man's speed with the current is 20 kmph and speed of the current is 3 kmph. The Man's speed against the current will be  Choose one.
A) 11 kmph B) 12 kmph C) 14 kmph D) 17 kmph E) None of these

Solution: Explanation:   If you solved this question yourself, then trust me you have a all very clear with the basics of this chapter.   If not then lets solve this together.   Speed with current is 20,   speed of the man + It is speed of the current   Speed in still water = 20 - 3= 
20 - 3 = 17
17   Now speed against the current will be   speed of the man - speed of the current= 17 - 3= 
17 - 3 = 14
14 kmph   Option 14 kmph
Answer: C
Fifteen runners from four different countries are competing in a tournament. Each country holds a qualifying heat to determine who its fastest runner is. These four runners then run a final race for first, second, and third place. If no country has more than one more runner than any other country, how many arrangements of prize winners are there?	Select:
A) 24	B) 384	C) 455	D) 1248	E) 2730

Solution: 1. We have runners by countries: 4 4 4 3   2. We choose 3 countries for all 3 "wining" places. 4 possibility: 4 4 4 and 3 times 4 4 3   3. Now we can choose any person from each country and take into account different positions (3!)   So, we get: (4*4*4)*3! + 3*(4*4*3)*3! = 3!*4*4*(4+3*3) = 1248 (1248)
Answer: D
A train of length 250 metres takes 45 seconds to cross a tunnel of length 350metres. What is the speed of the train in km/hr?	Choose the correct answer:	A) 10 km/hr.	B) 240 km/hr.	C) 30 km/hr.	D) 24 km/hr.	E) None

Solution: Sol.   Speed = [250 + 350/ 45] m/sec = [600 / 45 * 18/5] km/hr = 24 km/hr.   Answer 24 km/hr.
Answer: D
10 books are placed at random in a shelf. The probability that a pair of books will always be together is
Choices:	A) 1/6	B) 1/9	C) 1/5	D) 1/6	E) 1/3

Solution: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!   Required probability = 1/5   Answer: 1/5
Answer: C
Two trains 140 m and 180 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? Answers:	A) 11.52 sec	B) 10.1 sec	C) 10.6 sec	D) 10.8 sec	E) 10.2 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other   = 140 + 180= 
140 + 180 = 320
320 m.   Required time= 320 * 9/250= 
320 * 9/250 = 288/25 = around 11.52
11.52 sec.   11.52 secnswer:11.52 sec
Answer: A
One woman and one man can build a wall together in half an hour, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them two hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?	Choose the correct choice from the following options: A) 5/7 B) 1 C) 10/7 D) 6/13 E) 22/7

Solution: Solution:Let work done by man, women and girl per hour be m,w,g respectively.   Then, m+w = 2/1-->(1) , w + 2= 
+ 2 = 2
2/1-->(2) and m + g=1/2-->(3).   No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g   From (1) and (2), m=2g and from (3) g=1/6,m=1/3 and w=5/3.   So, n = 1/(13/6) = 6/13   Option, 6/13
Answer: D
Add: + 47 and -27 Choices:
A) -30	B) +30	C) 0	D) 27	E) 47

Solution: The absolute values of +47 and -27 are 47 and 27 respectively; and their difference = 47 – 27 = 30.   (+47) + (-27) = +30   ANSWER :+30
Answer: B
If the population of a certain country increases at the rate of one person every 25 seconds, by how many persons does the population increase in 1 hour? Pick one:  A) 100  B) 120  C) 144  D) 180  E) 160

Solution: Answer = 2.4 * 60= 
2.4 * 60 = 144
144   Answer is 144
Answer: C
A man speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man speed against the current is  Choose the correct choice from the following answers:
A) 7 km/hr [B] [C] [D]
B) 8 km/hr
C) 9 km/hr
D) 6 km/hr
E) 10 km/hr

Solution: Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.   Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.   answer :10 km/hr
Answer: E
A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct? Choose the correct choice from the following choices
A) 10 min past 7pm on wednesday
B) 20 min past 7pm on wednesday
C) 20 min past 9pm on wednesday
D) 26 min past 7pm on wednesday
E) 20 min past 4pm on wednesday

Solution: This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours.   To show the correct time, it has to gain 5 min.   So the correct time will be shown on wednesday at 7:20 PM   Answer: 20 min past 7pm on wednesday
Answer: B
Pipes A and B can fill a tank in 10 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in	Select the correct option.
A) 1 13/17 hours  B) 2 8/11 hours  C) 3 9/17 hours  D) 5 5/11 hours  E) None

Solution: Solution   Net part filled in 1 hour	= (1/10 + 1/6 -1/12)   = 11/60.   Therefore, the tank will be full in 60/11 hrs.	â€¹=â€º 5 5/11 hrs.   Answer 5 5/11 hours
Answer: D
In 2005, 25 percent of the math department’s 60 students were female, and in 2007, 35 percent of the math department’s 65 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department? Choose the correct choice from the following choices.
A) 15%	B) 51.7%	C) 62.5%	D) 115%	E) 160%

Solution: Female students in 2005 = 25% of 60 = 15   Female students in 2007 = 35% of 65 = 22.75   Percentage increase = [(22.75- 15)/15] *100 % = 51.7%   Correct Option: 51.7%
Answer: B
The integer x is divisible by both 4 and 6. Which of the following must be an integer?  Choose the correct choice
A) x/12	B) x/9	C) x/25	D) x/24	E) x/16

Solution: Prime factorization of 4 = 2^2   Prime factorization of 6= 2*3   LCM of 4 and 6 = 2^2 * 3 = 12   Therefore x/12 must be an integer   x/12nswer x/12
Answer: A
IBM and KTC quote for a tender. On the tender opening day, IBM realizes that their quotations are in the ratio 7:4 and hence decreases its price during negotiations to make it Rs 1 Lakh lower than KTC's quoted price. KTC realizes that the final quotes of the two were in the ratio 3:4. What was the price at which IBM won the bid? Choose the correct choice from the following choices.
A) Rs. 7 lakh	B) Rs. 3 lakh	C) Rs. 4 lakh	D) Rs. 1.5 lakh	E) None of these

Solution: Explanation :   IBM initially quoted Rs 7x lakh. KTC quoted 4x lakh.   IBM's final quote = (4x−1) Lakh.   Thus, (4x−1)/4=3/4   i.e x=1.   Hence, IBM's bid winning price = Rs 3 Lakh.   Answer : Rs. 3 lakh
Answer: B
If 25% of a number is subtracted from a second number, the second number reduces to its four-sixth. What is the ratio of the first number to the second number ?
Choose the correct choice from the following choices:
A) 5:3	B) 4:3	C) 6:3	D) 3:4	E) 5:4

Solution: Explanation:   Let the numbers be p & q   q-p/4 = 4q/6   => q-4q/6 = p/4   => 2q/6 = p/4   => p/q = 4/3   Answer 4:3
Answer: B
A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 63 liters of drink A to convert it to drink B? Choose the correct choice from the following answers.
A) 7  B) 14  C) 21  D) 28  E) 35

Solution: In 63 liters of drink A, there are 36 liters of milk and 27 liters of juice.   With 36 liters of milk, we need a total of 48 liters of juice to make drink B.   We need to add 21 liters of juice.   The answer is 21.
Answer: C
What is the next number of the following sequence
7, 0, 1, 8, 5, 12, 9, 26, 3, 2, 23, ?  Choices.
A) 28
B) 29
C) 30
D) 31
E) 32

Solution: 7,0,1,8,5,12,9,26,3,2,23,X   (7,0,1,8),(5,12,9,26),(3,2,23,X)   7+0+1= 
7+0+1 = 8
8   5+12+9= 
5+12+9 = 26
26   3+2+23=X => X=28   28NSWER:28
Answer: A
Meena wrote all the numbers from 1 to 69,999 inclusive. How many digits did she write in total? Select the correct option:  A) 278,889  B) 308,889  C) 338,889  D) 368,889  E) 398,889

Solution: 1-9=>1*9 digits   10-99=>2*90= 
2*90 = 180
180 (numbers between 10-99 is 90 where each has 2 digits)   100-999=>3*900= 
3*900 = 2_700
2700   1000-9999=>4*9000 = 36,000   10000-69999=>5*60,000 = 300,000   The answer is 338,889   The answer is 338,889.
Answer: C
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. What is the probability of having 3 man in committee ?
Choices.
A) 10/36
B) 11/72
C) 12/72
D) 28/36
E) 36/90

Solution: We may have (3 men and 2 women) = (7C3 x 6C2) = 525   or (4 men and 1 woman) = (7C4 x 6C1) = 210   or (5 men only) = (7C5) = 21   Required ways = 756   Probability of having 3 man in committee = 525 / 756 =28/36   ans - 28/36
Answer: D
If the average of 37, 69, 47 and x is 46.5, what is x?
Pick one:
A) 37 B) 41 C) 50 D) 59 E) 33

Solution: x=33 because:   (37+69+47+x)/4=46.5   (37+69+47+x)/4*4=46.5*4   (37+69+47+x)=186   (37+69+47+x)-153=186-153= 
186-153 = 33
33   Therefore, the answer is 33, 33.
Answer: E
What is the ratio F of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
Select the correct option
A) 1/4
B) 3/8
C) 1/2
D) 3/5
E) 2

Solution: Let X be the side of the cube. Therefore X^2*6= surface area.   the rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.   6X^2/10X^2 = 3/5 F.   Answer = 3/5
Answer: D
8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 81. How much wine did the cask hold originally?
Options
A) 18 litres	B) 24 litres	C) 32 litres	D) 42 litres	E) 52 litres

Solution: Let the quantity of the wine in the cask originally be x litres.   Then, quantity of wine left in cask after 4 operations = x(1-8/x)^4 litres.   therefore, (x(1-8/x)^4)/x=16/81   =>(1-8/x)^4=(2/3)^4   =>x-8/x=2/3   =>3x-24=2x   =>x=24 litres.   ANSWER:24 litres
Answer: B
A box measuring 49 inches long by 42 inches wide by 14 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
Choose the correct choice from the following answers:  A) 78  B) 82  C) 84  D) 86  E) 88

Solution: least number of cubes will be required when the cubes that could fit in are biggest.   7 is the biggest number that could divide all three, 49, 42 and 14.   Thus side of cube must be 7, and total number of cubes = 49/7 * 42/7*14/7= 
49/7 * 42/7*14/7 = 84
84   Ans 84.
Answer: C
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 10 sec. What is the length of the fast train?	Choose the correct choice from the following answers
A) 27 7/6 B) 27 7/5 C) 27 7/2 D) 500/9 E) 27 7/1

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 10= 500/9   = 27 7/9 m.   Answer:500/9
Answer: D
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?	Pick:
A) 270
B) 277
C) 187
D) 257
E) 271

Solution: Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 27 sec= 27 * 10= 
27 * 10 = 270
270 m.   The length of the faster train= 270 m.   270nswer: 270
Answer: A
If you divide 7^102 by 5, which remainder do you get?  Choose the correct choice from the following choices.
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: The units digit of 7^1 is 7.   The units digit of 7^2 is 9.   The units digit of 7^3 is 3.   The units digit of 7^4 is 1.   The units digit of 7^5 is 7.   etc...   The units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}   The remainder of 102/4 is 2.   So the units digit of 7^102 is 9.   The remainder of 7^102 / 5 is 4.   The answer is 4.
Answer: E
Set A: {1, 3, 4, 6, 9, 12, 15}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?  Choose the correct choice from the following answers:
A) 3/14 B) 2/7 C) 9/14 D) 5/7 E) 11/14

Solution: Probability of an event = (# of favorable outcomes) / (total # of outcomes).   There are 5 numbers you can choose from (3, 6, 9, 12, 15) so that the sum to be divisible by 3 and there are total of 7 numbers so P=C35C37=27P=C53C73=27.   Answer: 2/7.
Answer: B
A sum of Rs.2000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Choose the correct choice from the following answers:	A) 2888	B) 3120	C) 2877	D) 2999	E) 1300

Solution: Let A be the amount received at the end of the three years.   A = 2000[1 + 10/100][1 + 20/100][1 + 25/100]   A = (2000 * 11 * 6 * 5)/(10 * 5 * 4)   A = Rs.3300   So the interest = 3300 - 2000 = Rs.1300   Answer: 1300
Answer: E
How many two digit numbers of distinct digits can be formed by using digits 3, 4, 5, 6,7 and 8 such that the numbers are divisible by 9?  Select the correct option
A) 3  B) 4  C) 5  D) 6  E) 8

Solution: CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9   Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition   If sum of Digits = 9, No. = 36, 45, 54, 63 --- 4 Cases   Answer: option 4
Answer: B
A train 150 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post? Choose one:
A) 11 s B) 10 s C) 7 s D) 12 s E) None of these

Solution: We know from the formula Time = Distance/ Speed   Thus, Time = 150/ 54 x 5/18   or, Time = 10 sec.   ANSWER:10 s
Answer: B
Rahul went to a shop and bought things worth Rs. 55, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Choose the correct choice from the following answers:	A) A)19.7	B) B)19.9	C) C)21.9	D) D)40.9	E) E)49.7

Solution: Total cost of the items he purchased = Rs.55   Given that out of this Rs.55, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (55−30/100−x)6/100 = 30/100   ⇒ 6(55 −0.3 −x) = 30   ⇒ (55 − 0.3 − x) = 5   ⇒ x = 55 − 0.3 − 5 = 49.7   49.7)
Answer: E
A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced? Choose the correct option:
A) 6 hours 12 minutes  B) 5 hours 33 minutes  C) 8 hours 15 minutes  D) 7 hours 12 minutes  E) None

Solution: Explanation :   Time = 80*4 / 60 = 5 hours 33 mins   Answer â€“ 5 hours 33 minutes
Answer: B
When their father died, he left an Estate containing many assets, and a few expenses to his 6 children equally. His assets included: Investments, ($305,000), Life Insurance ($104,000), an old car (sold for $1900), an older house (sold for $75,000). His expenses included: Nursing Home Expenses ($6500) and Funeral Costs ($9300). How much would each child inherit?  Choose the correct choice from the following answers.
A) 80983 B) 79001 C) 75452 D) 76767 E) 78350

Solution: In order to determine the total that each child would inherit, you must add all the assests and subtract all the expenses, and then divide by 6   305000 + 104000 + 1900 + 75000 - 6500 -9300= 
305000 + 104000 + 1900 + 75000 - 6500 -9300 = 470_100
470100   470100 divided by 6 equals 78350   The correct answer is 78350
Answer: E
The price of the jewel, passing through three hands, rises on the whole by 56%. If the first and the second sellers 20% and 25% profit respectively find the percentage profit earned by the third seller.  Pick
A) 20  B) 4  C) 5  D) 2  E) 30

Solution: Let the original price of the jewel be $ p and let the profit earned by the third seller be x% Then, (100+x)% of 125% of 120% of P =156% Of P ((100+X)/100*125/100*120/100*P)=(156/100*P)   ==> (100+X)=(156*100*100)/(125*120)= 
(156*100*100)/(125*120) = 104
104=>X=4%   Answer 4)
Answer: B
A sum of money at simple interest amounts to Rs. 835 in 3 years and to Rs. 854 in 4 years. The sum is:  Choose the correct answer:
A) s. 650 B) s. 690 C) s. 698 D) s. 700 E) s. 718

Solution: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.   S.I. for 3 years = Rs.(39 x 3) = Rs. 117.   Principal = Rs. (835 - 117) = Rs. 718.   Answer: Option s. 718
Answer: E
. A car covers a distance of 390 km in 4 hours. Find its speed?	Answers.
A) 104
B) 55
C) 66
D) 98
E) 100

Solution: 390/4 = 98 kmph   Answer: 98
Answer: D
If 40% of (x-y) = 20% of (x+y), then what percent of x is y?  Choose the correct choice from the following answers
A) 50.5%
B) 44.4%
C) 22.2%
D) 33.3%
E) 25%

Solution: 40% of (x-y) = 20% of (x+y)   40/100 (x-y) = 20/100 (x+y)   x = 3y   Required percentage = y/x *100 = y/3y * 100 = 33.3%   Answer is 33.3%
Answer: D
Set X consists of all two-digit primes and set Y consists of all positive even multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set?
Choose the correct choice
A) 87  B) 89  C) 90  D) 92  E) 95

Solution: Set X = {11, 13, 17,............., 83, 89, 97}   Set Y = {10, 20, 30,..............., 70, 80, 90}   Combining two sets, say Set Z   Set Z = { 10,11, 13, 17, 20,30,..................., 70, 80, 83, 89, 90, 97}   Range = Max Value - Min Value   Range (Z) = 97 - 10= 
97 - 10 = 87
87   O87 87 is the answer.
Answer: A
Prints a page 60 pg per min .If the printed for 1 hours except 10 min.Where there
was an paper jam,how many page did it print Select the correct option
A) 10,880
B) 12,880
C) 3,000
D) 8,880
E) 18,880

Solution: 60 pages ------->1 min   1 hrs except 10 mints means=1*60= 
1*60 = 60
60-10= 
60-10 = 50
50 mints   i.e.,50*60=3,000 pages printed.   ANSWER:3,000
Answer: C
A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost? Choices:  A) 10 2/8  B) 10 2/9  C) 10 2/3  D) 10 2/2  E) 10 2/5

Solution: 2/10 + 4/15 + x/20 = 1   x = 32/3 = 10 2/3   Answer: 10 2/3
Answer: C
The probability is 1/2 that a certain coin turns up heads on any given toss. If the coin is tossed six times, what is the probability that the coin turns up tails on at least one of the tosses?  Choose the correct choice from the following answers:	A) 15/16	B) 21/32	C) 31/32	D) 63/64	E) 51/64

Solution: P(6 heads)= 1/2*1/2*1/2*1/2*1/2*1/2=1/64.   P(at least one tail)=1-1/64=63/64.   The answer is 63/64.
Answer: D
A batsman in his 15th inning makes a score of 75 and their by increasing his average by 3. What is his average after the 15th inning? Pick one.
A) 31 B) 32 C) 33 D) 34 E) 35

Solution: 14x + 75 = 15(x + 3)   x = 30 + 3= 
30 + 3 = 33
33   Answer:33
Answer: C
Which of the following equations represents a line that is perpendicular to the line described by the equation 2x + 3y = 12?  Pick:
A) 4x + 2y = 5	B) 5x + y = 7	C) 3x - 2y = 8	D) 4x - 3y = 9	E) x + y = 10

Solution: Perpendicular lines have slopes which are negative reciprocals of each other.   The line 2x + 3y = 12 in slope-intercept form is y = -(2/3)x + 4   The slope of this line is -2/3.   The slope of a perpendicular line is 3/2.   3x - 2y = 8 in slope-intercept form is y = (3/2)x - 4   The answer is 3x - 2y = 8.
Answer: C
Manoj, Nayan and Ajit together started a software company. It was agreed that Manoj would invest Rs. 6500 for 6 months, Nayan, Rs. 8400 for 5 months and Ajit Rs. 10,000 for 3 months. Manoj wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of Nayan in the profit ?
Choose the correct option.
A) 2330 B) 2660 C) 3000 D) none of the above E) Cannot be determined

Solution: Explanation :   Manoj is a working member and for that, he receive 5% of the profit   = 5% of 7400 = 5*7400/100= 
5*7400/100 = 370
370   Remaining amount= 7400-370= 
7400-370 = 7_030
7030   Ratio of their investments= 6500*6 : 8400*5 : 10000*3   = 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20   = 13 : 14 : 10   Share of Nayan in the profit = 7030 * (14/37) = 190*14= 
190*14 = 2_660
2660   Answer : 2660
Answer: B
A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability R that the 2 apples selected will include the spoiled one?  Choose the correct option
A) a. 1/5	B) b. 3/10	C) c. 2/5	D) d. 1/2	E) e. 3/5

Solution: there can be two ways in which one can select a spoiled apple and a good apple.   1. you pick the spoiled one first and the good one later..   Prob of picking bad one = 1/5 (one bad apple)   Prob of picking a good one from the remaining 4 good apples (4/4 =1)   therefore the total prob for case 1 = i/5 * 1 = 1/5   Total prob R= porb1 + prob2 = 1/5+1/5 = 2/5.c. 2/5
Answer: C