MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the following expressions CANNOT be equal to 0 when x^2 − 8x = 15?	Options.
A) x^2 − 3x B) x^2 − 3x -10 C) x^2 − 4x +5 D) x^2 − 4x - 5 E) x^2 − 2x - 3

Solution: x^2 − 8x = 15   x^2 − 8x - 15= 0   x=3 or x=5   All other choices result in a possibility of 0 when you plug in 3 or 5 for x   Except x^2 − 4x +5   Answer is x^2 − 4x +5
Answer: C
Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 18% vinegar, dressing P comprises what percentage of the new dressing?	Choose the correct choice from the following options:	A) 20%	B) 30%	C) 40%	D) 50%	E) 60%

Solution: Let x be the percentage of dressing P in the new dressing.   0.3x + 0.1(1-x) = 0.18   0.2x = 0.08   x = 0.4 = 40%   The answer is 40%.
Answer: C
A man can row upstream at 20 kmph and downstream at 28 kmph, and then find the speed of the man in still water? Choose the correct choice from the following answers.
A) 24
B) 37
C) 30
D) 27
E) 18

Solution: US = 20   DS = 28   M = (28 + 20)/2= 
(28 + 20)/2 = 24
24   24nswer:24
Answer: A
Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ?  Choose the correct choice from the following.
A) 2^1/2  B) 3^1/3  C) 4^1/4  D) 6^1/6  E) 12^1/12

Solution: 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12   Multiply each number raised to the power of 12   So,   2^1/2 = 2^6 = 64   3^1/3 = 3^4 = 81   4^1/4 = 4^3 = 64   6^1/6 = 6^2 = 36   12^1/12 = 12^1 = 12   So, the greatest is 3^1/3   ANSWER:3^1/3
Answer: B
Susan, John, Daisy, Tim and Kim need to be seated in 5 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?  Choose the correct choice from the following choices.
A) 360
B) 120
C) 80
D) 240
E) 60

Solution: Total # of arrangement of 5 people is 5!.   In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).   So, # of arrangements to satisfy the given condition is 5!/2=60.   Answer: 60.
Answer: E
If a / b is an integer, which of the following statements must be true?  Pick one:  A) q is an integer  B) a = nb where n is an integer  C) both a and b are integers  D) b / a is an integer  E) either a or b is negative

Solution: Let a = 1/4; b = 1/8 --> a/b = 2   a = nb where n is an integer --> 1/4 = 2*(1/8) --> Correct   Answer: a = nb where n is an integer
Answer: B
Boy sells a book for Rs. 450 he gets a loss of 10%, find CP of the book?	Choose the correct answer:
A) Rs.350 B) Rs.400 C) Rs.500 D) Rs.550 E) Rs.620

Solution: Find cost price   Let C.P. of book = x and S.P. = Rs. 450   S.P. of book = C.P. – (10% of C.P.)   S.P. = x – (0.10x)   450 = 0.9 x   x i.e cost price = Rs.500   Rs.500
Answer: C
there are two kind of professional in a company software & personal. If the personal are 15% of the total .a party is going .in a party if 50% of the total professional left and all are software then what is the ratio of the software professional left to total software professional.	Choose the correct choice from the following answers.
A) 7:15 B) 7:16 C) 7:17 D) 7:18 E) 7:19

Solution: let there are 100 professionals.   15 are personal 85 are software   in party 50% left means 50 professionals are there and all are software.   85-50= 
85-50 = 35
35 have gone then ratio   35:85   7:17   ANSWER:7:17
Answer: C
The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
Choices.
A) 1008 B) 1015 C) 1022 D) 1032 E) None of these

Solution: EXPLANATION   Required number = (L.C.M. of 12,16, 18, 21, 28) + 7   = 1008 + 7= 
1008 + 7 = 1_015
1015   Answer 1015
Answer: B
A library branch originally contained 18365 volumes, 30% of which were fiction novels. 1/3 of the volumes were transferred to another location and 1/3 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?	Choose the most appropriate option:
A) 2.5%	B) 17.67%	C) 28.3%	D) 45.2%	E) 73.6%

Solution: Fiction Novels = 5,509   Transferred to another location = 6,121   Transferred fiction novels = 2,040   Non Transferred Fiction Novels = 3,469   Percent of the remaining collection was fiction novels = 3469/(18365 - 6121 ) * 100 => 28.332...%   Hence answer will be (28.3%)
Answer: C
A drink vendor has 40 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?
Options.
A) 35  B) 37  C) 42  D) 50  E) 69

Solution: The number of liters in each can = HCF of 40, 144 and 368 = 8 liters.   Number of cans of Maaza = 40/8= 
40/8 = 5
5   Number of cans of Pepsi= 144/8= 
144/8 = 18
18   Number of cans of Sprite= 368/8= 
368/8 = 46
46   The total number of cans required= 5 + 18 + 46= 
5 + 18 + 46 = 69
69 cans.   ANSW69R:69
Answer: E
Find the third proportional to 4 and 16?
Choose the correct choice:	A) 80	B) 12	C) 64	D) 78	E) 72

Solution: Formula = Third proportional = (b × b)/a   A = 4 and B = 16   (16 × 16)/ 4 = 256/4= 
256/4 = 64
64   64
Answer: C
A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long? Choose the most appropriate option:
A) 38 sec
B) 35 sec
C) 44 sec
D) 40 sec
E) none of these

Solution: Speed = 45 km/hr = 45 × (5/18) m/s   = 150/12 = 50/4 = 25/2 m/s   Total distance = length of the train + length of the platform   = 360 + 140= 
360 + 140 = 500
500 meter   Time taken to cross the platform= 500/(25/2) = 500 × 2/25 = 40 seconds   ANSWER:40 sec
Answer: D
A tank fills in the sequence of 10, 20, 40, 80.... (Means 10 litres in 1 hr, 20 litres in 2nd so on.). If at the 4th hour the tank is 1/4 full .When will it be full?
Choose the correct choice
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: At the 4th hour, it ll fill 80 litres   80 litres is 1/4th of a tank...then the full tank can have  80 * 4= 
 80 * 4 = 320
320 litres   Given series 10, 20 ,40 ,80, (ie) each litre is double of previous litres   so at the 5th hour tank filled ll be   80 * 2= 
  80 * 2 = 160
160liters   At the 6th hr it ll fill the full tank (ie) 160 * 2= 320   So the tank ll be full at 6th hr   ANSWER:6
Answer: D
A can do a piece of work in 24 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work? Choose one.
A) 9
B) 77
C) 66
D) 55
E) 12

Solution: 8/24 + 6/x = 1   X =9 days   9nswer:9
Answer: A
When tossing two coins once, what is the probability of heads on both the coins?	Choose one.
A) 2/8 B) 4/5 C) 3/7 D) 6/7 E) 1/4

Solution: 1/4xplanation :   Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)   Hence, total number of outcomes possible when two coins are tossed, n(S) = 2 × 2 = 4   1/4 = event of getting heads on both the coins = {HH}   Hence, n(1/4) = 1   P(1/4)=n(1/4)/n(S)=1/4   Answer:1/4
Answer: E
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?	Choose the correct option:
A) 4:7	B) 4:3	C) 4:11	D) 4:9	E) 4:13

Solution: Let us name the trains A and B.   Then, (A's speed) : (4:3's speed)   = √b : √a = √16 : √9 = 4:3   Answer: 4:3
Answer: B
Twenty four years ago,a father was three times as old as his son.Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is :
Choose the correct answer.
A) 144 B) 76 C) 108 D) 105 E) 86

Solution: Let the present ages of the father and son be 2x and x years respectively.   then,(2x-24)=3 (x-24)   x=48.   Required sum =(2x+x)=3x=144 years.   144nswer is 144
Answer: A
A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?	Choose the correct choice from the following answers:
A) 66 1/4 % B) 66 9/3 % C) 66 2/3 % D) 66 1/5 % E) 66 1/3 %

Solution: The total number of mangoes bought by the shopkeeper be 15.   If he buys 5 a rupee, his 66 2/3 %P = 3   He selling at 3 a rupee, his SP = 5   Profit = SP - 66 2/3 %P = 5 - 3= 
5 - 3 = 2
2   Profit Percent= 2/3 * 100 = 66 2/3 %   Answer:66 2/3 %
Answer: C
In a theater, the first row has 14 seats and each row has 3 more seats than previous row. If the last row has 50 seats, what is the total number of seats in the theater?	Answers:
A) 404  B) 408  C) 412  D) 416  E) 420

Solution: The number of seats in the theater is   14 + (14+3) + ...+ (14+36)=   13(14) + 3(1+2+...+12)=   13(14) + 3(12)(13)/2=   13(14+18) = 13(32) = 416   The answer is 416.
Answer: D
Solution A is 10% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution? Choose the correct choice:
A) 6:4	B) 6:14	C) 3:4	D) 4:6	E) 3:7

Solution: Forget the volumes for the time being.   You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use   w1/w2 = (A2 - Aavg)/(Aavg - A1)   w1/w2 = (80 - 50)/(50 - 10) = 3/4   So the volume of the two solutions will be equal. Answer has to be 3:4.   3:4
Answer: C
Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains 2 pounds of timothy, how many acres can be planted with 640 pounds of the seed mixture?
Choose the correct choice from the following answers.
A) 12	B) 16	C) 20	D) 24	E) 120

Solution: If the mixture contains 2 pounds of timothy, the mixture must be 40 pounds.   Thus we need 40 pounds of mixture per acre.   640 / 40= 
640 / 40 = 16
16 acres   The answer is 16.
Answer: B
Which of the following fractions E has a decimal equivalent that is a terminating decimal? Pick one:
A) 10/189
B) 15/196
C) 16/225
D) 25/144
E) 39/128

Solution: The fraction E will terminate if and only if the denominator has prime divisors only 2 and 5 or both.   A. 10/189 = 10/(3*3*3*7) Non-term.   B. 15/196 = 15/(2*2*7*7) Non-term.   C. 16/225 = 16/(5*5*3*3) Non-term.   D. 25/144 = 25/(2*2*2*7) Non-term.   E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.
Answer: E
Claudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select?  Choose the correct answer:  A) 54  B) 72  C) 96  D) 144  E) 432

Solution: 2 candles from 4 candles: 4C2: 6   8 flowers from 9 flowers: 9C8 : 9   So total grouping     9*6= 
  9*6 = 54
54.   54nswer is 54.
Answer: A
A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?	Pick one.
A) 58% B) 50% C) 20% D) 30% E) 70%

Solution: L.C.M of 15 and 12 = 60   CP of 60 articles = Rs. 100 (25 * 4)   SP of 60 articles = Rs. 150 (30 * 5)   Profit percentage = (150 - 100)/100 * 100= 
(150 - 100)/100 * 100 = 50
50%   Answer:50%
Answer: B
Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
Choose the correct choice from the following options
A) 12 min	B) 6 min	C) 4 min	D) 8 min	E) 10 min

Solution: 1/8 + 1/24 = 1/6   6 * 2= 
6 * 2 = 12
12   12 minNSWER 12 min
Answer: A
The average of 11 results is 60. If the average of first six results is 58 and that of the last six is 63, find the sixth result.  Options.
A) 22
B) 44
C) 66
D) 72
E) NOne

Solution: Sol.   Sixth result = (58 x 6 + 63 x 6 - 60 x 11) = 6   Answer 66
Answer: C
A can do a piece of work in 4 hours; B and C together can do it in 2 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?  Choose the correct choice
A) 12 B) 9 C) 8 D) 6 E) 4

Solution: A's 1 hour's work = 1/4 ;   (B + C)'s 1 hour's work = 1/2 ;   (A + C)'s 1 hour's work = 1/2 .   (A + B + C)'s 1 hour's work = ( 1/4+ 1/2) =3/4 .   B's 1 hour's work = ( 3/4 - 1/2 ) = 1/4.   Therefore A alone will take 4 hours to do the work.   4
Answer: E
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: Choose the correct choice from the following options:
A) 45 km/hr  B) 50 km/hr  C) 54 km/hr  D) 55 km/hr  E) 57 km/hr

Solution: Speed of the train relative to man =125/10 m/sec   =25/2 m/sec.   =25	/2x18/5km/hr   = 45 km/hr.   Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.   x - 5 = 45 x =50 km/hr.   Answer:50 km/hr
Answer: B
A kindergarten class is going to a play with some teachers. Tickets cost 5 dollars for children and 12 dollars for adults
Number of tickets sold amount to 163 dollars.
How many teachers and children went to the play? Choose the correct choice from the following options:
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: First, make sure you understand the problem. What the problem is really asking is the following:   How many adult tickets were sold? How many children tickets were sold?   Guess and check!   Pretend that 3 children tickets were sold. Then, 17 adult tickets were sold   Total cost = 3 × 5 + 17 × 12 = 15 + 204= 
15 + 204 = 219
219   The total is too high. Pretend that 14 children tickets were sold. Then, 6 adult tickets were sold   Total cost= 14 × 5 + 6 × 12 = 70 + 72= 
70 + 72 = 142
142   The total is a little too low now. Pretend that 12 children tickets were sold. Then, 8 adult tickets were sold   Total cost= 12 × 5 + 8 × 12 = 60 + 96= 
60 + 96 = 156
156   As you can see, it is going higher again and it is getting closer to 163. May be 11 tickets for children and 9 tickets for adults will work   Total cost= 11 × 5 + 9 × 12 = 55 + 108= 
55 + 108 = 163
163   Here we go! 11 children and 9 teachers went to the play   Answer 9
Answer: B
How many words can be formed from the letters of the word SIGNATURE so that the vowels always come together?  Choose the most appropriate option:
A) 720
B) 1440
C) 3600
D) 2880
E) None of these

Solution: The word SIGNATURE consists of nine letters comprising four vowels (A, E, I and U) and five consonants (G, N, R, T and S). When the four vowels are considered as one letter, we have six letters which can be arranged in 6P6 ways i.e 6! ways. Note that the four vowels can be arranged in 4! ways.   Hence required number of words   = 6! × 4! = 720 × 24   = 17280   Answer None of these
Answer: E
By selling a watch for Rs.480/-, a man loses 20% what is that watch cost price?  Choices:  A) s. 600/-  B) s. 700/-  C) s. 800/-  D) s. 850/-  E) s. 900/-

Solution: 80 % ------> 480 (80 * 6 = 480)   100 % ------>600 (100 * 6 = 600)   Cost price = Rs. 600/-   s. 600/-)
Answer: A
A CAN FINISH A WORK IN 15 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?  Choose the correct choice from the following answers
A) 5  B) 5 1/2  C) 6  D) 8  E) NONE OF THESE

Solution: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3   NOW, 1/18 WORK IS DONE BY A IN 1 DAY   1/3 WORK IS DONE BY A IN  (15*1/3)= 
 (15*1/3) = 5
5 DAYS.   CORRECT OPTION:5
Answer: A
Pipe A can fill the tank in 50 minutes and pipe B in 40min and pipe C can empty the tank in 2 hours. How long it will take to fill the tank if three of the pipes are operating together?
Choose the correct answer:	A) 22.22	B) 27.27	C) 29.35	D) 31.2	E) 35.6

Solution: Pipe A fills 1/50th of the tank in a minute and pipe B, 1/40th. Pipe C empties in 120min(2 hours)   (1/50)+(1/40)-(1/120)=(1/x)   22/600=1/x => x=600/22 => x=27.27 minutes   Answer: 27.27
Answer: B
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?	Select the correct option
A) 19 B) 50 C) 72 D) 25 E) 28

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr   = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.   Answer: 50
Answer: B
A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year? Select the correct option:
A) 59002 B) 59001 C) 59008 D) 59000 E) 59004

Solution: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.   Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.   Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   Income of A = Twice the income of B   (2500 + 18000 + P) = 2(P)   P = 20500   Total profit = 2P + 18000   = 2*20500 + 18000= 
2*20500 + 18000 = 59_000
59000   Answer: 59000
Answer: D
If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z>(x − 1)/(y + 2)
II. z>(x − 1)/(y + 2)
III. z>(x + 1)/(y - 2)	Choose the most appropriate option:
A) I only	B) I and II	C) II and III	D) II only	E) I and III

Solution: x < y --> Let x = 2 and y = 3 --> z = 2/3   I. z>(x − 1)/(y + 2) --> 2/3 > 1/5 --> True   II. z>(x − 1)/(y + 2) --> 2/3 < 1/5 --> True   III. z>(x + 1)/(y - 2) --> 2/3 > 3/1 --> False   Answer: I and II
Answer: B
The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
Select:	A) 65	B) 44	C) 18	D) 16	E) 14

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 324/3= 
324/3 = 108
108 sq m   l b= 108 i.e., l * l/3 = 108   l2 = 324 => l = 18.   Answer:18
Answer: C
Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction? Choose the most appropriate option
A) 90	B) 27	C) 21 sec	D) 92	E) 62

Solution: Let the length of each train be x m.   (x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5)= 
(750 * 18) / (30 * 5) = 90
90 sec.   90nswer: 90
Answer: A
Three years ago, Arjun’s age was double of Ajith’s age. Seven years hence, the sum of their united ages will be 83 years. The age of Arjun today is ?  Select
A) 47 years B) 45 years C) 35 years D) 24 years E) None of these

Solution: Let us consider Arjun’s age to be X,   X - 3 = 2 (Y - 3) or X - 2Y = - 3 ...(i)   (X + 7) + (Y + 7) = 83 or X + Y = 69 ...(ii)   Therefore, Y= 24, X = 45.   The age of X today = 45 years   ANSWER:45 years
Answer: B
If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 3)?
Select:
A) 3
B) P + 2
C) p – 2
D) 3p – 1
E) 2p + 1

Solution: The number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is  (5-1)-1= 
 (5-1)-1 = 3
3: 2, 3, and 4.   Thus, the number of integers between pq and p(q+3)=pq+3p is (pq+3p-pq)-1=3p-1.   Answer: 3p – 1.
Answer: D
A river 4m deep and 40 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is?
Choose the correct option.
A) 10666	B) 11678	C) 12345	D) 10678	E) 19099

Solution: (4000 * 4 * 40)/60   = 10666 M3   10666nswer:10666
Answer: A
If D||D', D:2x - y = 1 and D':(a - 1)x + 2y = x - 2, then find the value of a.
Choose the most appropriate option:
A) -3
B) -2
C) -1
D) 0
E) 1

Solution: D:2x−y=1, D’:(a−1)x+2y=x−2   D:2x−y=1, D′:(a−1)x+2y=x−2   D∥D′⇒mD=m′   DD∥D′⇒mD=mD′   2x−y=1→y=2x−1→mD=22x−y=1→y=2x−1→mD=2   (a−1)x+2y=x−2→2y=x(1−a+1)−2→2y=x(2−a)−2→(a−1)x+2y=x−2→2y=x(1−a+1)−2→2y=x(2−a)−2→   y=x×(2−a)2−1→m′D=(2−a)2y=x×(2−a)2−1→mD′=(2−a)2   mD=m′D→(2−a)2=2→2−a=4→a=−2   ANSWER : -2 -2
Answer: B
How much greater is the value of 3x + 5 than the value of 3x − 7?  Options:	A) 8	B) 10	C) 12	D) 14	E) 16

Solution: Explanation: The easiest way to do this is to pick a number for x. Let’s say x = 3.   3(3) + 5   = 9 + 5= 
9 + 5 = 14
14   3(3) − 7= 9 − 7   = 2   The correct answer is 14 − 2 = 12.   Answer : (12)
Answer: C
Arun bought a computer with 15% discount on the labeled price. He sold the computer for $2880 with 20% profit on the labeled price. At what price did he buy the computer?
Choose the correct choice from the following options:
A) $2440	B) $2420	C) $2410	D) $2310	E) $2040

Solution: SP = 2880   Arun sold the computer with 20% profit on the Labeled Price   ⇒2880=(120×Labeled Price) / 100   ⇒Labeled Price=(2880×100)/120=28800/12=96004=2400   Arun bought a computer with 15% discount on the labeled price   => CP = (Labeled Price×85) / 100=(2400×85) / 100=24×85=2040   ANSW$2040R:$2040
Answer: E
The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is: Options
A) 30/7 B) 30/98 C) 60/147 D) 50/294 E) 52/294

Solution: Required fraction = L.C.M of 6/7, 5/14, 10/21   = (L.C.M of 6, 5, 10) / (H.C.F of 7, 14, 21) = 30/7   30/7NSWER:30/7
Answer: A
If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 37.5 miles ahead of Joe?  Choose the correct choice from the following answers:
A) 15
B) 60
C) 180
D) 90
E) 105

Solution: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.   Teena covers 55 miles in 60 mins.   Joe covers 40 miles in 60 mins   So teena gains 15 miles every 60 mins   Teena need to cover 7.5 +37.5 miles.   Teena can cover 7.5 miles in 30 mins   Teena will cover 37.5 miles in 150 mins   So answer 30+150= 
30+150 = 180
180 mins. (ANSWER 180)
Answer: C
If the area of a circle is 81pi square feet, find its circumference.
Choices:
A) 15 B) 16 C) 17 D) 18 E) 19

Solution: The area is given by pi * r *r. Hence   pi* r *r = 81 pi   r * r = 81 * hence r = 81 feet   The circumference is given by   2 * pi * r = 2 * pi *9 = 18 pi feet   correct answer 18
Answer: D
A person can row at 9 kmph and still water. He takes 3 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?	Choose the correct choice from the following answers
A) 32
B) 28
C) 29
D) 54
E) 16

Solution: Let the distance between A and B be x km.   Total time = x/(9 + 1) + x/(9 - 1) = 3.5   => x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x   = 16 km.   Answer:16
Answer: E
Of the c students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?  Choose the correct choice from the following answers.
A) c + w- x- y  B) c - w- x- y  C) z- w - x + y  D) w + x + y- z  E) w - x - y - z

Solution: {Total} = {French} + {German} - {Both} + {Neither}   c = x + y - w + {Neither}   {Neither} = c + w - x - y.   c + w- x- ynswer: c + w- x- y.
Answer: A
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 27. What is the difference between the two digits of that number?	Options:	A) 3	B) 5	C) 6	D) 8	E) 9

Solution: Sol.   Let the ten’s digit be x and unit’s digit be y,   Then, (10x + y) - (10y + x) = 27 ⇔ 9 (x - y) = 27   ⇔ x - y = 3   3nswer 3
Answer: A
The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 47 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons? Choose the correct answer:
A) 55 B) 56 C) 57 D) 58 E) 59

Solution: 20x + 47 = 21(x – 5)   X=58   ANSWER:58
Answer: D