MU-NLPC/Calc-aqua_rat huggingface dataset:
If y exceeds x by 10%, then x is less than y by?
Select the correct option.
A) 1/3% B) 1/5% C) 1/7% D) 1/9% E) 1/11%

Solution: X=100	y=110   110------10   100-------? => 9 1/11%   Answer:1/11%
Answer: E
150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration E of the acid in the mixture? Choose the correct choice from the following.
A) 1/2
B) 1/3
C) 1/4
D) 1/6
E) 1/5

Solution: Do not need any computation   30%-----------21%---------12%   if volume of both sol. were equal the concentration E would be 21%=1/5, but 12% is more than 3 times   only possibility is 1/6   1/6
Answer: D
David walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 4 hours 20 minutes. He would have gained 2 hours by driving both ways. How long would it have taken for him to walk both ways.  Choose the correct answer
A) 5 h 20 min B) 4 h 15 min C) 6 h D) 7 h E) 6 h 20 min

Solution: 1.Walking to to a viewpoint+Driving back=4 hours 20 minutes   2.Driving to a viewpoint+Driving back=4 hours 20 minutes - 2 hours=2 hours 20 minutes, thereforeone way driving=2 hours 20 minutes/2 =1 hours 10 minutes.   3. From 1.one way driving=4 hours 20 minutes-1 hours 10 minutes=3 hours 10 minutes.   4.Walking to to a viewpoint+Walking back=3 hours 10 minutes+3 hours 10 minutes=6 hours 20 minutes.   Answer: 6 h 20 min
Answer: E
Two trains each 150 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?	Options
A) 7.8 sec
B) 7.2 sec
C) 8.2 sec
D) 6.2 sec
E) 9.2 sec

Solution: D = 150 m + 150 m = 300 m   RS = 80 + 70= 
80 + 70 = 150
150 * 5/18= 125/3   T = 300 * 3/125= 
300 * 3/125 = 36/5 = around 7.2
7.2 sec   ANSWER:7.2 sec
Answer: B
A bag contains 4 white balls, 4 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? Choose the correct choice from the following options.
A) 1/2 B) 1/5 C) 3/8 D) 5/11 E) 2/7

Solution: The probability for each ball to be drawn third is equal.   Then the probability a red ball is drawn third is 2/10 = 1/5.   The answer is 1/5.
Answer: B
If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?	Choose the correct answer:
A) 245  B) 278  C) 364  D) 378  E) 389

Solution: A particular players is never chosen, it means that 11 players are selected out of 14 players.   => Required number of ways = 1436411   = 14!/11!x3! = 364   364
Answer: C
Tim and Tom are workers in a department that has a total of 5 employees. Their boss decides that two workers from the department will be picked at random to participate in a company interview. What is the probability that both Jim and John are chosen?  Choose the correct option:
A) 3/10 B) 1/10 C) 7/10 D) 4/11 E) 2/11

Solution: Probability = 2c2/5c2   = 1/10   Answer 1/10
Answer: B
The population of a town increases 25% and 40% respectively in two consecutive years. After the growth the present population of the town is 1750. Then what is the population of the town 2 years ago?
Choose one:
A) A)750	B) B)800	C) C)850	D) D)900	E) E)950

Solution: Explanation:   Formula: (After =100 denominator   Ago = 100 numerator)   1750 * 100/125 * 100/140= 
1750 * 100/125 * 100/140 = 1_000
1000   Answer: Option 800
Answer: B
Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 15% if no discount was offered? Choose the correct choice.
A) 17608
B) 17606
C) 17604
D) 18400
E) 117601

Solution: Price at which the TV set is bought = Rs. 12,500   Discount offered = 20%   Marked Price = 12500 * 100/80 = Rs. 15625   The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000   The price at which the TV should be sold to get a profit of 15% if no discount was offered = 16000 * 115/100 = Rs. 18400.Answer: 18400
Answer: D
A certain number when divided by 899 leaves the remainder 63. Find the remainder when the same number is divided by 29.	Choose the most appropriate option:  A) 5  B) 4  C) 1  D) 0  E) Can not be determined

Solution: Sol.(a) Number = 899Q + 63, where Q is quotient   = 31 × 29 Q + (58 + 5) = 29 [ 31Q + 2] + 5   ∴ Remainder = 5 5nswer 5
Answer: A
If 2 cards are selected (with replacement) at random from the deck of 52 cards then what is the probability that one of the selected cards will be a king or a queen, and the other card will be a jack? A deck of cards has a total of 52 cards, consisting of 4 suits: spades (black), hearts (red), diamonds (red), and clubs (black). In each suit, there are 13 cards including 1 king, 1 queen, and 1 jack.  Options.
A) 3/16	B) 3/32	C) 3/64	D) 4/169	E) 8/169

Solution: P(1 king or queen, and 1 jack) = 2(8/52*4/52) = 2(2/169) = 4/169   The answer is 4/169.
Answer: D
A fruit seller sells mangoes at the rate of Rs.16 per kg and thereby loses 12%. At what price per kg, he should have sold them to make a profit of 20%?  Select the correct option.
A) Rs.21.81
B) Rs.12
C) Rs.12.25
D) Rs.12.31
E) None

Solution: Solution   88 : 16 = 120 : x   x= (16Ã—120/88)   = Rs.21.81   Hence, S.p per Kg	= Rs.21.81   Rs.21.81nswer Rs.21.81
Answer: A
If 90% of A = 30% of B and B = C% of A,then the value of C is ?  Choose the correct choice from the following answers:
A) 900
B) 800
C) 600
D) 300
E) None

Solution: Answer   ∵ 90A/100 = 30B/100 = (30/100) x AC/100   ∴ C = 100 x (100/30) x (90/100) = 300   Correct Option: 300
Answer: D
The sum of three consecutive numbers is 63. The greatest among these three number is:	Choose the correct choice from the following choices
A) 26  B) 28  C) 29  D) 22  E) 31

Solution: Let the numbers be x, x + 1 and x + 2   Then,   x + (x + 1) + (x + 2) = 63   3x =60   x = 20   Greatest number, (x + 2) = 22.   ANSWER:22
Answer: D
There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?	Choose the correct option:
A) Rs.3928
B) Rs.3920
C) Rs.3972
D) Rs.3979
E) Rs.3962

Solution: Let P = Rs. 100. Then, S.I. Rs. 60 and T   = 6 years.   R = (100 * 60)/(100 * 6)= 
(100 * 60)/(100 * 6) = 10
10% p.a.   Now, P= Rs. 12000, T = 3 years and R   = 10% p.a.   C.I. = [12000 * {(1 + 10/100)3 - 1}]   = 12000 * 331/1000   = Rs.3972   Answer:Rs.3972
Answer: C
Total dinning bill for 9 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share  Choose the correct choice from the following.
A) $30.14	B) 45.14	C) 34.66	D) 26.96	E) 33.16

Solution: 211*15= 
211*15 = 3_165
3165/100= 
3165/100 = 633/20 = around 31.65
31.65   211+31.65= 
211+31.65 = 242.65
242.65   242.65/9=26.96   ANSWER:26.96
Answer: D
Find the fourth proportional to 2.8 , 3.4 and 5.2?	Choose the correct choice from the following choices
A) 5.98	B) 6.14	C) 6.29	D) 6.31	E) 5.64

Solution: Formula = fourth proportion =(b x c)/a   a=2.8 , b=3.4 and c=5.2   (3.4 x 5.2)/2.8=6.31   6.31
Answer: D
Johnny bought six peanut butter cans at an average price (arithmetic mean) of 37.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 31¢, then what is the average price, in cents, of the two returned peanut butter cans?
Choose the correct choice from the following choices
A) 5.5	B) 11	C) 47.5	D) 50.5	E) 67.5

Solution: Total price of six cans = 6*37.5= 
6*37.5 = 225
225   Total price of 4 cans= 4*31= 
4*31 = 124
124   Total rice of two cans= 225 - 124= 
225 - 124 = 101
101   Average price of two cans= 101/2= 
101/2 = 101/2 = around 50.5
50.5 c   Another way to do it is this:   Assume that the four leftover cans were of 31c each. The avg was 37.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans.   So cost of the two cans= 2*37.5 + 4*6.5= 
2*37.5 + 4*6.5 = 101
101   Avg cost of the two cans= 101/2= 
101/2 = 101/2 = around 50.5
50.5c   Answer (50.5)
Answer: D
The age of a man is three times the sum of the ages of his two sons. Five years hence, his age will be double of the some of the ages of his sons. The father’s present age is : Choose the correct choice from the following answers.
A) 29 years  B) 36 years  C) 42 years  D) 45 years  E) None

Solution: Sol.   Let the sum of present ages of the two sons be x years.   Then, faher’s present age = 3x years.   ∴ (3x + 5) = 2 (x + 10) ⇔ 3x + 5 = 2x + 20 ⇔ x = 15.   Hence, father’s present age = 45 years.   Answer 45 years
Answer: D
The temperature in Winnipeg, Manitoba was 4 degrees Fahrenheit. At 8 pm the temperature was was -10 degrees Fahrenheit. What is the difference between the temperatures?  Choose the correct choice from the following options.
A) 6  B) -14  C) 14  D) -6  E) 0

Solution: Addition of positive and negative integers   4+-10=   answer is -6)-6
Answer: D
A man's age is 125% of what it was 10 years ago, but 83 X 1/3% of what it will be after 10years. What is his present age?
Select
A) 20  B) 60  C) 50  D) 70  E) 80

Solution: 50   50   Let the age before 10 years =x Then,   125x/100=x+10   ⇒125x=100x+1000   ⇒x=1000/25= 
1000/25 = 40
40   Present age=x+10=40+10= 
40+10 = 50
50
Answer: C
A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 25600.
Choose the correct choice from the following answers:
A) Rs. 25600
B) Rs. 8500
C) Rs. 7200
D) Rs. 8000
E) None of these

Solution: Explanation:   A = 2B and B = 5C   => A : B = 2 and B : C = 5 : 1   => A : B : C = 10 : 5 : 1   Ratio of capitals of A, B and C = 10 : 5 : 1   B's share = Rs.[(5/16) × 25600] = Rs. 8000   Answer: Option Rs. 8000
Answer: D
A caterer ordered 225 ice-cream bars and 125 sundaes. If the total price was $200.00 and the price of each ice-cream bar was $0.60, what was the price of each sundae? Choose the correct choice from the following:	A) $0.52	B) $0.80	C) $1.00	D) $1.20	E) $1.60

Solution: Let price of a sundae = S   Price of ice cream bar = .6 $   225 * .6 + 125*S = 200   => 125*S = 65   => S = 0.52   $0.52nswer $0.52
Answer: A
The average of the two-digit numbers, which remain the same when the digits interchange their positions, is? Choose the correct choice:
A) 76
B) 88
C) 55
D) 86
E) 26

Solution: Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99)/9   = [(11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55]/9   = [(4 * 110) + 55]/9 = 495/9= 
495/9 = 55
55.   Answer: 55
Answer: C
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?	Choose one
A) 270 m  B) 189 m  C) 278 m  D) 279 m  E) 917 m

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.   270 mnswer:270 m
Answer: A
If the positive integer x is divisible by 3, 8, and 12, then which of the following must x be divisible by?
I. 24
II. 26
III. 48 Pick.
A) IIonly
B) I only
C) I and II only
D) II and III only
E) I, II, and III

Solution: LCM of 3, 8, 12 = 24   Answer = 24   Answer : I only
Answer: B
Three unbiased coins are tossed. What is the probability of getting at most two heads? Choose the correct choice.
A) 9/7  B) 7/8  C) 1/2  D) 5/4  E) 3/8

Solution: Explanation:   Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}   Let E = event of getting at most two heads.   Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.   P(E)=n(E)/n(S)=7/8   Answer:7/8
Answer: B
The division of a whole number N by 10 gives a quotient of 15 and a remainder of 2. Find N.  Select the correct option:	A) 152	B) 197	C) 597	D) 997	E) 297

Solution: 152ccording to the division process of whole numbers, N can be written, using multiplication, as follows   N = quotient *divisor + remainder = 15* 10 + 2= 
15* 10 + 2 = 152
152 correc answer 152
Answer: A
A salesman sold twice as much pears in the afternoon than in the morning. If he sold $510 kilograms of pears that day, how many kilograms did he sell in the afternoon?	Pick.
A) 120	B) 180	C) 340	D) 280	E) 320

Solution: 3x=510   x=170   Therefore, the salesman sold 170kg in the morning and 2⋅170=340 kg in the afternoon. So answer is 340.
Answer: C
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
Choose the correct answer:
A) 125/128 B) 115/122 C) 125/126 D) 125/122 E) 125/112

Solution: Required probability = 1 - 1/126   = 125/126   Answer:125/126
Answer: C
A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?  Answers
A) 772
B) 369
C) 277
D) 270
E) 782

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 26 sec.   Let the length of the train be x meters.   Then, (x + 250)/26 = 20   x = 270 m.   Answer: 270
Answer: D
Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequent day of the week, she eats a number of croissants equal to the sum of the croissants eaten on the two previous days, with the exception that if she eats more than four croissants on any particular day, the next day she will eat only one croissant. At the end of the week (which runs from Monday through Sunday), the cycle resets, and Marina goes back to eating one croissant on Monday, two on Tuesday, and so forth. If a particular month begins on a Saturday, how many croissants will Marina eat on the 30th of that month? Choose the correct choice from the following answers:
A) 1
B) 2
C) 3
D) 5
E) 6

Solution: She eat as follow   Mon - 1   Tue - 2   Wed - 3   Thr - 5   Fri - 1(since she had more than 4 previous day)   sat - 6   sunday - 1 (since she had more than 4 previous day)   so 30th day of month she will have 1.   1nswer is 1
Answer: A
The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by?  Pick:
A) 33 1/3%
B) 33 1/9%
C) 33 1/3%
D) 32 1/3%
E) 33 1/2%

Solution: 100   75   -------   75 ------- 25   100 ------ ? => 33 1/3%   33 1/3%nswer:33 1/3%
Answer: A
In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount Q in 1996 as they paid in 1995? Pick one:
A) 33 1⁄3% B) 40% C) 50% D) 66 2⁄3% E) 100%

Solution: water rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount in 1996 as they paid in 1995, water use should decrease in the same ratio   Q=150-> 100 means 1/3 rd= 33(1/3) %=33 1⁄3%
Answer: A
If 2x + y = 7 and x + 2y = 5, then 7xy/3 =?
Choose the correct choice:
A) A) 1
B) B) 2
C) C) 7
D) D) 18/5
E) E) 4

Solution: 2*(x+2y = 5) equals 2x+4y=10   2x+4y=10   - 2x + y= 7   = 3y=3   Therefore Y = 1   Plug and solve...   2x + 1 = 7   2x=6   x=3   (7*3*1)/3   = 21/3= 
21/3 = 7
7   7
Answer: C
Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?	Choose the correct choice from the following choices.
A) 9680 B) 4280 C) 2789 D) 7892 E) 2792

Solution: (8000*3*2)/100= 
(8000*3*2)/100 = 480
480   9200   --------   9680   9680nswer:9680
Answer: A
The ages of two person differ by 20 years. If 10 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively	Choose the correct choice from the following answers:
A) 30, 10  B) 25, 5  C) 29, 9  D) 35, 15  E) 20,10

Solution: Let their ages be x and (x + 20) years.   Then, 5(x - 10) = (x + 20 - 10)   => 4x = 60   =>x =15   Their present ages are 35 years and 15 year.   ANSWER:35, 15
Answer: D
Sum of ages of two friends is 28 while difference is 4 then their ages are	Select the correct option:  A) 20 years, 8 years  B) 10 years, 18 years  C) 24 years, 4 years  D) 18 years, 16 years  E) None

Solution: 24,4   ANSWER:24 years, 4 years
Answer: C
2^3,5^2,6^1 Find largest Value?
Options
A) 2
B) 3
C) 1
D) 10
E) 25

Solution: 25xplanation:   2^3=2*2*2= 
2*2*2 = 8
8   5^2=5*5= 
5*5 = 25
25   6^1=6*1= 
6*1 = 6
6   Hence 5^2 is the largest one   Answer:25
Answer: E
WHEN A PERSON SELLS TWO ITEMS $900 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURES A LOSS OR GAIN OF: Choose one:  A) 4% loss  B) no loss no gain  C) 1% loss  D) 2% gain  E) 5% gain

Solution: When two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%.   4% lossnswer : 4% loss
Answer: A
A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue? Choose the correct option
A) 15/56  B) 41/56  C) 13/28  D) 15/28  E) 5/14

Solution: The required probability = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.   Ways to select 6 out of total 8 = 8C6   Ways to select 4 out of 5 white balls = 5C4   Ways to select 2 out of 3 blue balls = 3C2   Thus the required probability = (5C4*3C2)/8C6 = 15/28.   15/28 is thus the correct answer.
Answer: D
There are 3 teams each with 7 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?	Choose the correct choice from the following
A) 50
B) 23
C) 147
D) 28
E) 45

Solution: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 49 possibilities (7*7) since each team has 7 players. So there are a total of 147 possibilities (49*3). I hope this method is easier for you to understand.
Answer: C
If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is? Choose the correct choice from the following answers
A) 16  B) 127  C) 12  D) 18  E) 25

Solution: Given that, cost price of 50 article is equal to selling price of 40 articles.   Let cost price of one article = Rs. 1   Selling price of 40 articles = Rs. 50   But Cost price of 40 articles = Rs. 40   Therefore, the trader made profit.\Percentage of profit = 10/40 * 100= 
10/40 * 100 = 25
25%   Answer: 25
Answer: E
A farmer is planting a row consisting of 4 unique apple trees and 3 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?	Choose the correct answer.
A) 512  B) 576  C) 1,024  D) 288  E) 10,080

Solution: 2 possible arrangements are possible   AOAOAOAO   OAOAOAOA   2 unique type of trees are present consisting of 4 trees each   4 apple trees can be arranged in 4! ways   3 orange trees can be arranged in 4! ways   as 2 arrangements are possible   total arrangements = 2 *4! * 3! = 288   correct answer option 288
Answer: D
How many pieces of 75 cm can be cut from a rope 52.5 meters long?  Choices
A) 30 B) 40 C) 60 D) None E) Cannot be determined

Solution: Explanation :   Total pieces of 75 cm that can be cut from a rope of 52.5 meters long is   = (52.5 meters)/(75 cm)   = (52.5 meters)/(0.75 meters)   = 70   Answer : None
Answer: D
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 6 boys when No boy gets more than one prize?  Choose the correct choice from the following options:
A) 112	B) 114	C) 117	D) 120	E) 127

Solution: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 6 ways. The second in 5 ways and the third in 4 ways. But fundamental principle, (6 x 5 x 4) ways = 120 ways   120
Answer: D
An investment receives 20% annual interest compounded semi-annually for 2 years. If its final value is $29,200, approximately what was the initial investment?	Choose the correct choice from the following answers
A) $ 17,000 B) $ 18,000 C) $ 19,000 D) $ 20,000 E) $ 21,000

Solution: At the same time the key concept to keep in mind is that interest compound annually, semestral and so on are simply % increase or decrease, one after another.   Similarly, we have 100 and we have a discount of 20% and then 10 % . We have , of course, 80 and after this 10% of 80.   Here is the same.   here we have 20% 2 times per year so: 10% or 1.1 for two years. 1.141.14or 1.1 four times.   if we have the original amount X and the final amount 29,200. We need only to divide 29,200/1.1the result again 1.1 for four times.the result is 19943 We have approximately.   $ 20,000 is the answer.
Answer: D
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?	Select: A) 766 min B) 656 min C) 144 min D) 877 min E) 555 min

Solution: Let the slower pipe alone fill the tank in x min.   Then, faster pipe will fill it in x/3 min.   1/x + 3/x = 1/36   4/x = 1/36 => x = 144 min.Answer:144 min
Answer: C
Three candidates contested an election and received 1136, 7636 and 21628 votes respectively. What percentage of the total votes did the winning candidate got  Choose the correct choice from the following choices
A) 55%  B) 56%  C) 57%  D) 71.1%  E) 59%

Solution: Explanation:   Total number of votes polled = (1136 + 7636 + 21628)= 
(1136 + 7636 + 21628) = 30_400
30400   So, Required percentage= 21628/30400 * 100 = 71.1%   Answer: Option 71.1%
Answer: D
In how many ways can 10 books be arranged on a shelf such that a particular pair of books should always be together?	Options
A) 9!  B) 2!  C) 3! * 2!  D) 9! * 2!  E) 9! * 5!

Solution: We have a total of 10 books.   Given that a particular pair of books should always be together. Hence, just tie these two books together and consider as a single book.   Hence we can take total number of books as 9. These 9 books can be arranged in 9P9 =9!=9! ways.   We had tied two books together. These books can be arranged among themselves in 2P2 =2!=2! ways.   Hence, required number of ways   =9!×2!   ANSWER 9! * 2! 9! * 2!
Answer: D
A retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price t of the machine?	Choose one:	A) 81	B) 100	C) 120	D) 135	E) 160

Solution: Since the wholesale price was $90 and the profit was 20% of the wholesale price ([.2][90] = $18), the retail price would have to be above $108, but not that much greater than that.   Let's start by TESTing Answer C: $120....   If.....   Retail Price t= $120   10% discount off = $120 - (.1)(120) = 120 - 12= 
120 - 12 = 108
108   20% profit on wholesale price= 90 + (.2)(90) = 90 + 18= 
90 + 18 = 108
108   These two numbers MAT120H, so this MUST be the answer!   Final Answer:   [Reveal]Spoiler:   120
Answer: C
P and Q be centers of two circle having radius 200cms. These circle intersect each other at some point A and B. Length of PQ is 250 cms. What will the angle AQP be?
Answers
A) between 0 to 45 B) between 0 to 30 C) between 0 to 60 D) between 0 to 75 E) between 0 to 100

Solution: since if we draw the figure, then AP= 200 , AQ=200 and PQ=250   triangle property of 45- 45 - 90 is that H=L * root(2)   H= hypo and L= Leg.therefore H/L= root(2)   here H=250 and L=200 and H/L= 250/200= 
250/200 = 5/4 = around 1.25
1.25   and the value of root(2)== 1.44   so H/L= approx root(2).   Therefore the angle between H and L = near about 44 degree   so the ans will be 0 to 45.   between 0 to 45NSWER:between 0 to 45
Answer: A