MU-NLPC/Calc-aqua_rat huggingface dataset:
4 people are sitting in a 4 seat row watching a football game. At halftime they all get up. When they return, they each randomly sit down on one of the 5 chairs. What is the likelihood that none of the 4 end up sitting in the same chair that they sat in during the first half?	Choose the correct choice from the following
A) 3/24
B) 3/4
C) 15/24
D) 18/24
E) 21/24

Solution: Originally seated A B C D   now when after they get up and when they sit back again .   1st- A has option to sit on 3 seats ( apart from his previous seat . thus he now sits on B's seat.)   2nd- Similarly B has option to sit on 3 seats ( because A has already occupied B's previous seat, thus B sits on a's seat.)   3rd- Now C has only 1 option to sit on D's seat . and similarly D also has one option to sit on C's seat.)   hence total favourable outcomes   3*3*2*1*1= 
  3*3*2*1*1 = 18
18   and total possible outcomes=4!=24   probability of the favourable outcome= 3/4. 3/4
Answer: B
Find compound interest on Rs. 7500 at 4% per year for 2 years, compounded annually.	Choose the correct option.
A) 812	B) 712	C) 412	D) 512	E) 612

Solution: Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112.   therefore, Compound Interest = Rs. (8112 - 7500) = Rs. 612.   Answer is 612.
Answer: E
For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers R are there between 6* + 2 and 6* + 6, inclusive? Choose the correct choice from the following choices:	A) None	B) One	C) Two	D) Three	E) Four

Solution: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.   Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes R in this range.   Nonenswer: None.
Answer: A
The simple interest on a sum of money will be Rs.800 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year? Choose the correct answer:	A) 2261	B) 1600	C) 1200	D) 2699	E) 2771

Solution: P --- 10 ---- 800   P --- 5 ----- 400   3P --- 5 ----- 1200   ------   => 1600   Answer: 1600
Answer: B
If y is the smallest positive integer such that 630 multiplied by y is the square of an integer, then y must be Choose the correct choice from the following
A) 20  B) 50  C) 60  D) 70  E) 140

Solution: 630 = 2*3^2*5*7= 
2*5*7 = 70
70.   The answer is 70.
Answer: D
If 15 students in a class average 80% on an English exam and 10 students average 90% on the same exam, what is the average in percent for all 25 students?  Choose the correct choice from the following answers
A) 83%
B) 83 1⁄2%
C) 84%
D) 85%
E) 86 2⁄3%

Solution: The average percentage = (15 x 80% + 10 x 90%)/25   = (15 x 80% + 10x 80% + 10x10%) / 25 ......(as 90% = 10% + 80% )   =(25x80% + 10x10%)/25   = 80% + 10x10%/25   = 80% + 4%   = 84%   ANSWER:84%80  + 4= 
80  + 4 = 84
84%   ANSWER:84%
Answer: C
A shopkeeper first raises the price of Jewellery by x% then he decreases the new price by x%. After such up down cycle, the price of a Jewellery decreased by Rs. 21025. After a second up down cycle the Jewellery was sold for Rs. 484416. What was the original price of the jewellery.2 Choices.
A) Rs. 5,26,000  B) Rs. 6,00,625  C) Rs. 525625  D) Rs. 5,00,000  E) None of these

Solution: Solution: Let the initial price = Rs. 10000P   price after first increment = 10000P + 100xP.   price after first decrement = 10000P + 100xP - (100Px+Px2) = 10000P - Px2.   Now, total decrement,   Px2 = 21025 .............. (1)   price after second increment,   10000P - Px2 + 100xP - Px3/100   price after second increment,   10000P - P2 + 100xP - P3/100 - 100xP + Px3/100 - Px2 + Px4/10000   = 10000P -2Px2+Px2/10000 = 484416 ............... (2)   on solving equation equn (1) and (2), We get   x = 20.   substituting back we get,   P = 52.5625   Therefore   Answer: Option Rs. 525625
Answer: C
The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?  Choose the correct answer.
A) 1000  B) 1500  C) 2000  D) 3000  E) 4000

Solution: Let monthly income of A = a   monthly income of B = b   monthly income of C = c   a + b = 2 × 5050 .... (Equation 1)   b + c = 2 × 6250 .... (Equation 2)   a + c = 2 × 5200 .... (4000quation 3)   (4000quation 1) + (4000quation 3) - (4000quation 2)   => a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250)   => 2a = 2(5050 + 5200 - 6250)   => a = 4000   i.e., Monthly income of A = 4000   Answer is 4000.
Answer: E
An ice cream store received shipments of ingredients on Tuesday and Wednesday. Tuesday's shipment had 6 different packages, with an average (arithmetic mean) of 9 and 2/3 pounds. Wednesday's shipment included 7 packages, weighing an average of 9 and 3/7 pounds. What was the average package weight, in pounds, of the shipments received on both days?  Choose the most appropriate option: A) 9 and 6/7 pounds B) 10 and 1/10 pounds C) 10 and 2/5 pounds D) 11 pounds E) 124/13 pounds

Solution: Solution: Average weight = Total weight/number of packages. The total weight on Tuesday was 6 * (9 and 2/3 pounds), or 58 pounds. The total weight on Wednesday was 7 * (9 and 3/7 pounds), or 66 pounds. The sum of the weights for both days is 66 + 58, or 124 pounds. The average is 124 pounds/13 packages.   Correct answer: 124/13 pounds
Answer: E
If w/x = 2/3 and w/y = 6/15, then (x + y)/y =	Choices
A) 4/5 B) 6/5 C) 7/5 D) 8/5 E) 9/5

Solution: W/X = 2/3=>x=3/2w and W/Y = 6/15=>y=15/6w   (X+Y)/Y = (3/2w+15/6w)/15/6w = 4w/(15/6W) = 8/5   Correct Option: 8/5
Answer: D
How many unique positive odd integers less than 110 are equal to the product of a positive multiple of 5 and an odd number?
Choose the most appropriate option
A) 4	B) 6	C) 11	D) 12	E) 15

Solution: The Question basically asks how many positive odd integers less than 110 are odd multiples of 5   So we have 5,15,25,35,45,.. and 105   =11   Ans 11
Answer: C
A cycle is bought for Rs.670 and sold for Rs.780, find the gain percent?  Answers.
A) 70%
B) 20%
C) 16%
D) 19%
E) 80%

Solution: Explanation:   670 ---- 110   100 ---- ? => 16%   Answer: 16%
Answer: C
John paid a sum of money for purchasing 30 pens, which he recovered in full when he sold 20 of them. What was his percentage of profit or loss per pen?	Options:
A) 50% B) 60% C) 40% D) 30% E) 45%

Solution: A   50%   If the sum he paid whilst purchasing 30 pens = A,   Then the Cost Price of each pen = A/30.   Since the amount he got whilst selling 20 pens is also = A   Then the Selling Price of each pen = A/20.   Since Selling Price > Cost Price, he made a profit.   Profit per pen = Selling Price - Cost Price = A/20 - A/30 = A/60.   Profit percentage per pen = Profit per pen / Cost per pen x 100 = (50%/60) / (50%/30) x 100 = 50%
Answer: A
A swimmer can swim in still water at 4 km/h. If the speed of the water current is 2 km/h, how many hours will the swimmer take to swim against the current for 3 km?
Pick:  A) 1.5  B) 1.75  C) 2.0  D) 2.25  E) 2.5

Solution: The swimmer can swim against the current at a speed of 4-2= 
4-2 = 2
2 km/h.   The time it will take is  3/2= 
 3/2 = 3/2 = around 1.5
1.5 hours.   The answer is 1.5.
Answer: A
Bradley owns b video game cartridges. If Bradley’s total is one-half the total owned by James and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
Choose the correct choice from the following answers:
A) (16/3)b
B) (17/4)b
C) (13/4)b
D) (19/12)b
E) (7/12)b

Solution: b = Bradley’s total   2b = James’s total   (1/4)b = (13/4)bharlie’s total   Add each total   b + 2b+ (1/4)b = 3b + (1/4)b = = (13/4b)   Answer : (13/4)b
Answer: C
If n is a prime number greater than 19, what is the remainder when n^2 is divided by 12 ?	Answers:
A) 0	B) 1	C) 2	D) 3	E) 5

Solution: There are several algebraic ways to solve this question, but the easiest way is as follows:since we cannot have two correct answers just pick a prime greater than 19, square it and see what would be the remainder upon division of it by 12.   n=23 --> n^2=529 --> remainder upon division 529 by 12 is 1.   Answer: 1.
Answer: B
Four of the five parts numbered (a) ,(b) ,(c) (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
Choose the correct answer
A) 2a2 – ab + 3b2  B) (a – b)(2a – 3b) + 4ab  C) (a – b)2 + (a2 + ab + 2b2)  D) (a + b)2 + (a2 + 2b2 – 3ab)  E) (a + b)(a – b) + (2a2 – ab + 4b2)

Solution: The other parts are equal to 34.   Answer (a + b)(a – b) + (2a2 – ab + 4b2)
Answer: E
David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?
Select
A) 75  B) 37  C) 26  D) 97  E) 27

Solution: Average = (76 + 65 + 82 + 67 + 85 )/ 5 = 375/5= 
375/5 = 75
75.   75nswer: 75
Answer: A
If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?  Choose the correct choice from the following
A) Saturday  B) Sunday  C) Monday  D) Friday  E) Thursday

Solution: The year 2004 is a leap year. So, it has 2 odd days.   But, Feb 2004 not included because we are calculating from March 2004 to March 2005.   So it has 1 odd day only.   The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.   Given that, 6th March, 2005 is Monday.   6th March, 2004 is Sunday (1 day before to 6th March, 2005).   Answer is Sunday.
Answer: B
Sum of two number is 50 & sum of three reciprocal is 1/12 so find these two numbers	Choose the correct choice from the following:
A) 30 & 29	B) 30 & 26	C) 30 & 24	D) 30 & 22	E) 30 & 20

Solution: Sol : x+y = 50 .....(1) x=50-y ....(2)   1x+1y=1121x+1y=112 ⇒y+xxy=112⇒12(y+x)=xy⇒y+xxy=112⇒12(y+x)=xy ...(3)   put (2) in (4)   ⇒⇒ 12(y+50-y)=(50-y)y   ⇒⇒ 12y+600-12y=50y-y2y2   ⇒⇒ y2y2-50y+600=0   ⇒⇒ y2y2-30y-20y+600=0   ⇒⇒ y(y-30)-20(y-30)=0   ⇒⇒ (y-20) (y-30)=0   y=20 or y=30   if y=20 then x = 30   or y=30 then x = 20   two numbers are 30 & 20   Answer:30 & 20
Answer: E
John is going with 7 friends on a trip to Paris for spring break. Airfare and hotel costs a total of $5600.00 for the group of 8 friends. How much does each person have to pay for their hotel and airfare?
Choose the correct choice.
A) $500	B) $600	C) $650	D) $680	E) $700

Solution: Answer= $700   The total cost of the trip ($5600.00) divided by 8 equals $700.00.
Answer: E
A can do a piece of work in 6days, and B can do it in 5days. If C, who can do the work in 12days, joins them, how long will they take to complete the work?	Options
A) 2days	B) 3.5days	C) 2.2days	D) 4days	E) 5.7days

Solution: A,B, and 2.2days do the work in = 6*5*12/6*5+5*12+6*12 = 360/162= 2.2 days   Answer is 2.2days
Answer: C
A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?	Choose the most appropriate option.
A) 35 days  B) 48 days  C) 64 days  D) 24 days  E) 36 days

Solution: 48 days   48 days   48 days = 1/16 – 1/24 = 1/48 => 48 days
Answer: B
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?	Pick:
A) 22
B) 287
C) 48
D) 277
E) 21

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.9= 
1.10 + 0.9 = 2
2 km= 2000 m.   Required time = 2000 * 3/125= 
2000 * 3/125 = 48
48 sec.   Answer: 48
Answer: C
How many integers n are there such that 1< 5n +5 < 60?
Choose the correct choice:
A) 5
B) 7
C) 11
D) 13
E) 12

Solution: Solution:   1< 5n + 5 < 60 is a compound inequality. Compound inequalities often need to be manipulated, and we can use the rules of algebra that we already know, to do this. Just as with equations, whatever we do to one part of a compound inequality, we must do to all parts of the compound inequality. Let’s first isolate n within the inequality.   1< 5n + 5 < 60   We first subtract 5 from all three parts of the inequality, and we obtain:   -4 < 5n < 55   Next, we divide both sides of the inequality by 5 and we get:   -4/5 < n < 11   The integers that are greater than -4/5 and less than 4 are 0, 1, 2, and 3. Thus, there are 4 integers that satisfy the inequality 1 < 5n + 5 < 25.   The answer is 11.
Answer: C
A house wife saved $4 in buying an item on sale. If she spent $28 for the item, approximately how much percent she saved in the transaction?	Choose the correct option.
A) 8% B) 13% C) 10% D) 11% E) 12%

Solution: Actual price = 28+4= 
28+4 = 32
$32   Saving= 4/32 * 100 = 13% approximately   Answer is 13%
Answer: B
From 6 positive numbers and 6 negative numbers, how many groups F of 4 numbers, yielding a positive product, can be formed?	Answers
A) 720
B) 625
C) 30
D) 960
E) 255

Solution: Potential combinations of 4 numbers that will yield positive product   ++++ 4C6   ---- 4C6   ++-- 2C6*2C6   4C6 + 4C6 + 2C6*2C6   F=15 +15 + 15*15= 
15 +15 + 15*15 = 255
255=255
Answer: E
If the first and second letters in the word DEPRESSION' were interchanged, also the third and the fourth letters, the fifth and the sixth letters and so on, which of the following would be the seventh letter from the right ?
Select:
A) H B) K C) I D) P E) U

Solution: Explanation:   The new letter sequence is EPRPSEISNO   The seventh letter from the right is P   Answer: P) P
Answer: D
One fourth of one third of two fifth of a number is 17. What will be 40% of that number Pick one:
A) 140
B) 204
C) 180
D) 200
E) 250

Solution: Explanation:   (1/4) * (1/3) * (2/5) * x = 17 then x = 17 * 30= 
17 * 30 = 510
510   40% of 510= 204   Answer: Option 204
Answer: B
If p and q are positive integers and q ≠ 1, then pq(q −5) is	Select the correct option:
A) pq^2+5pq	B) pq^2+pq	C) pq^2-pq	D) pq^2-5pq	E) pq^2

Solution: pq(q-5) = pq^2-5pq   Answer : pq^2-5pq
Answer: D
All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A? Pick:
A) 1184	B) 1151	C) 1126	D) 1130	E) 1254

Solution: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.   Quantity of water in B = 8k - 5k = 3k.   Quantity of water in container C 8  - 5= 
8  - 5 = 3
3k.   Quantity of water in container C= 8k - 3k = 5k   Container: A B C   Quantity of water: 8k 3k 5k   It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.   5k - 148 8  - 3= 
8  - 3 = 5
5k   Container: A B C   Quantity of water: 8k 3k 5k   It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.   5k - 148= 3k + 148 => 2k = 296 => k = 148   The initial quantity of water in A = 8k = 8 * 148= 
8 * 148 = 1_184
1184 liters.   1184NSWER 1184
Answer: A
A car covers a distance of 840 km in 6 ½ hours. Find its speed?	Select the correct option:	A) 104 kmph	B) 187 kmph	C) 164 kmph	D) 140 kmph	E) 106 kmph

Solution: 840/6= 
840/6 = 140
140 kmph   Answer: 140 kmph
Answer: D
The diagonals of a rhombus are 14 cm and 20 cm. Find its area? Choose the correct answer:	A) 329	B) 140	C) 150	D) 238	E) 31

Solution: 1/2 * 14 * 20= 
1/2 * 14 * 20 = 140
140   Answer: 140
Answer: B
If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.5
II. 15.3
III. 9.5 Choose the correct choice from the following answers: A) I only B) I and II only C) II only D) III only E) I and III only

Solution: Mean = 12   SD = 1.3   2 SD above mean = 12+2*1.3= 
12+2*1.3 = 14.6
14.6   2 SD below mean= 12-2*1.3= 
12-2*1.3 = 9.4
9.4   14.5 and 9.5 lies in the range of 2SD from mean   Answer: Option II only
Answer: C
Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 1/5 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity?  Select the correct option: A) 3/10 B) 7/10 C) 9/10 D) 9/20 E) 13/20

Solution: (1/2)X = (1/4)Y   (1/4)Y + (1/5)Y = (9/20)Y   The answer is 9/20.
Answer: D
A passenger sitting near the window in a train moving at 50 km/h, noticed that it took 3 sec. for the oncoming train to pass by. What was the speed of the oncoming train if the length of the oncoming train was 75 metres?
Choose the correct choice from the following.
A) a)50km/h B) b)52km/h C) c)56km/h D) d)60km/h E) e)40km/h

Solution: im getting A   3 secs to pass a 75 mts train , therefore speed = 25 meters/sec   to convert m/s to km/hrs multiply by 3.6   25*3.6= 
25*3.6 = 90
90   so its  90-50= 
 90-50 = 40
40 .   e)40km/h
Answer: E
An unbiased die is tossed .find the probability of getting a multiple of 3  Pick.
A) 1/3
B) 5/3
C) 2/3
D) 7/3
E) 3/7

Solution: Here S={1,2,3,4,5,6}   Let E be the event of getting the multiple of 3   then ,E={3,6}   P(E)=n(E)/n(S)=2/6=1/3   Option: 1/3
Answer: A
4, 6, 9, 13.50, 20.25, (...)
Choices:
A) 60  B) 60.75  C) 58  D) 31.528  E) 30.375

Solution: 4   (4Ã—3)Ã· 2 = 6   (6Ã—3)Ã· 2 = 9   (9Ã—3)Ã· 2 = 13.50   (13.50Ã—3)Ã· 2 = 20.25   (40.5Ã—3)Ã· 2 = 30.375   Answer is 30.375
Answer: E
A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
Pick one
A) 2205 B) 8786 C) 8275 D) 2872 E) 2282

Solution: 2205 = 2000(21/20)2 = 2205   2205nswer:2205
Answer: A
A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 140. The dividend from the stock is :
Choose the correct option.
A) 7.5 %
B) 8.75 %
C) 9.7 %
D) None of these
E) Cannot be determined

Solution: Solution   By investing Rs. 1552,income = Rs. 140.   By investing Rs. 97, income = Rs. (140/1552x97)= Rs.8.75   âˆ´ Dividend = 8.75%.   Answer 8.75 %
Answer: B
A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train? Pick one:
A) 52 kmph B) 14 kmph C) 54 kmph D) 58 kmph E) 24 kmph

Solution: D = 100 + 125= 
100 + 125 = 225
225   T= 15   S = 225/15 * 18/5= 
225/15 * 18/5 = 54
54 kmph   Answer: 54 kmph
Answer: C
A train passes a station platform in 36 sec and a man standing on the platform in 23 sec. If the speed of the train is 54 km/hr. What is the length of the platform? Choose one
A) 767 m	B) 240 m	C) 195 m	D) 176 m	E) 186 m

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 23= 
15 * 23 = 345
345 m.   Let the length of the platform be x m . Then,   (x + 345)/36= 15 => x = 195 m.   Answer:195 m
Answer: C
A jewelry store purchased a pair of earrings for $240 and was selling it at a price that equaled the purchase price of the earrings plus a markup that was 25 percent of the selling price. After some time a jewelry store owner decided to decrease the selling price by 20 percent. What was the jewelry store's gross profit on this sale?
Choose the correct choice from the following options:
A) $14
B) $2
C) $10
D) $16
E) $18

Solution: Sale Price(SP) = 240 + Markup(MP)   --> Mp = SP-240   and given MP=SP/4 ( 25% is 1/4th)   so SP/4= SP-240   3SP/4= 240   SP=320   Now a discount of 20% is given so NEW SP is .8 *320= 
.8 *320 = 256
256   Profit=256-240= 
256-240 = 16
16   Answer is $16
Answer: D
The difference between a 8 digit number and the number formed by reversing its digit is not a multiple of Choose the correct choice from the following:  A) 3  B) 5  C) 296297  D) 888891  E) 2666673

Solution: Another approach is to TEST a number.   Let's say the original number is 12000002   So, the REVERSED number is 20000021   The DIFFERENCE = 20000021-12000002= 
20000021-12000002 = 8_000_019
8000019   No check the answer choices   8000019 is a multiple of 3,296297,888891,2666673   5 is NOT a multiple of 8000019   Answer ; 5
Answer: B
Nitin borrowed some money at the rate of 6% p.a. for the first three years,9% p.a. for the next five years and 13% p.a. for the period beyond eight years.If the total interest paid by him at the end of eleven years is Rs. 8160,how much money did he borrow ? Choose the correct choice from the following answers: A) Rs. 8000 B) Rs. 10,000 C) Rs. 12,000 D) Data inadequate E) None

Solution: Solution   22.21   Let the sum be Rs. x.Then,   (X x6 x 3/100)+ (X x 9 x 5/100)+ (X x 13 x 3/100) 8160   18 x + 45x + 39x (8160x100)= 816000 x = 8000.   Rs. 8000nswer Rs. 8000
Answer: A
How many multiples of 4 are there between 20 and 196 ?	Select the correct option.
A) 45 B) 42 C) 52 D) 43 E) 51

Solution: It should be mentioned whether 20 and 196 are inclusive.   If 20 and 196 are inclusive, then the answer is   (196-20)/4+1= 
  (196-20)/4+1 = 45
45.   If 20 and 196 are NOT inclusive, then the answer is   (192-24)/4+1= 
  (192-24)/4+1 = 43
43.   Since OA is 43, then we have NOT inclusive case.
Answer: D
A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? Choose the most appropriate option.
A) 5/8
B) 5/9
C) 5/6
D) 5/3
E) 5/1

Solution: Two balls can be picked from nine balls in ⁹C₂ ways.   We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵ ways.   The required probability = (5 * 4)= 
(5 * 4) = 20
20/36= 5/9   Answer: 5/9
Answer: B
A coin is tossed 8 times. What is the probability of getting exactly 7 heads?  Choose the correct answer
A) 1/8  B) 1/16  C) 1/32  D) 1/64  E) 1/128

Solution: The number of possible outcomes is 2^8 = 256   There are 8 ways to get exactly 7 heads.   P(exactly 7 heads) = 8/256 = 1/32   The answer is 1/32.
Answer: C
In an election between two candidates, 20% of votes are were declares invalid. First candidate got 480 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was  Choose the correct choice from the following choices:  A) 2000 votes  B) 3000 votes  C) 3500 votes  D) 3600 votes  E) 3700 votes

Solution: (100%-20%=80%   48%-32%=16%   16%  48 -32= 
 48 -32 = 16
16%   16%= 16×30 = 480   100% =100×30 =3000 votes)   3000 votes
Answer: B
After increasing 20% in the price of a Book costs Rs.240. Find the actual cost of an article?	Choose the correct choice from the following options:
A) 100
B) 150
C) 200
D) 220
E) 250

Solution: 200P* (120/100) = 240   200P200 * (120/100)= 
200 * (120/100) = 240
240   200P= 2* 100= 
2* 100 = 200
> 200P= 200   Answer:200
Answer: C
The owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 8400 for a computer table, then what was the cost price of the computer table? Answers
A) Rs.6725 B) Rs.6727 C) Rs.6908 D) Rs.6725 E) Rs.7000

Solution: CP = SP * (100/(100 + profit%))   = 8400(100/120) = Rs.7000.   Answer: Rs.7000
Answer: E
6^5 is equal to which of the following? Pick one.
A) 7,776  B) 8,752  C) 9,660  D) 2,662  E) 1,608

Solution: A is the correct answer. We do not really need to calculate it. The last digit for 6^5 will be 6. Hence 7,776 is the correct answer
Answer: A
Set A contains all the even numbers between 42 and 90 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?	Choose the most appropriate option.
A) 300 B) 350 C) 400 D) 450 E) 500

Solution: Each term in set B is 20 more than the corresponding term in set A.   The difference of the sums = 25 * 20= 
25 * 20 = 500
500.   The answer is 500.
Answer: E