MU-NLPC/Calc-aqua_rat huggingface dataset:
Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.153 per kg, the price of the third variety per kg will be	Select:
A) Rs.169.50  B) Rs.1700  C) Rs. 175.50  D) Rs. 180  E) None

Solution: Solution   Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50   So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.   x-153/22.50 = 1 =› x - 153 = 22.50 =› x=175.50.   Hence, price of the third variety = Rs.175.50 per kg.   Answer Rs. 175.50
Answer: C
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? Pick one:  A) 276 m  B) 167 m  C) 245 metrs  D) 167 m  E) 178 m

Solution: Speed = [45 X 5/18] m/sec   = [25/2] m/sec Time   = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30   = 25/2 => 2(130 + x) = 750 => x   = 245 m.   Answer:245 metrs
Answer: C
A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among five colors produced enough color codes to identify all but 6 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)
Choose the correct choice.
A) 14
B) 15
C) 16
D) 17
E) 18

Solution: 5162 = 10   The number of test subjects is  10 + 6= 
 10 + 6 = 16
16   The answer is 16.
Answer: C
n a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?  Choose the correct answer
A) 2 hrs
B) 3 hrs
C) 1 hr
D) 4 hrs
E) 5 hrs

Solution: Let the duration of the flight be x hours. Then,   600/x - 600/(x + 1/2) = 200   x(2x + 1) = 3 2x2 + x - 3  (2  + 1)= 
 (2  + 1) = 3
3 2x2 + x - 3= 0   (2x + 3)(x - 1) = 0   x = 1 hr.   ANSWER 1 hr
Answer: C
Shepherd Gopal had a curious aptitude for mathematics and he was known around where he lived as the 'Counting Shepherd.
A man passing throughthe meadow one dat saw Gopal grazing a number of sheep and in the course of a short conversation asked him how many of the grazing sheep were his own. Gopal's reply absolutely baffled him, which was as follows:
If you divide my sheep into two different parts, the difference between yhe two numbers will be the same as the difference between their squares. Now figure it out for yourself the number of sheep I own.'
Can you say just how many sheep Gopal had?	Pick one:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 1   Shepherd Gopal had one sheep only.
Answer: A
A train 120 meters long completely crosses a 480 meters long bridge in 55 seconds. What is the speed of the train is?
Select.
A) 32  B) 545  C) 39  D) 40  E) 09

Solution: S = (120 + 480)/45 = 600/55 * 18/5 = 39   Answer: 39
Answer: C
On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? Choose the correct choice from the following choices.
A) 2.04%  B) 6.12%  C) 8%  D) 8.25%  E) 10%

Solution: Per quarter, interest = 2%   So for a year, interest = 8%   8.25%ue to quarter cumulation, effective yield (YTM) would be slight higher than 8%   Answer = 8.25% =ANSWER:8.25%
Answer: D
What is the ratio between perimeters of two squares one having 2 times the diagonal then the other? Choose the correct choice from the following choices
A) 3: 8  B) 3: 6  C) 3: 7  D) 2: 1  E) 3: 3

Solution: d = 2d d = d   a√2 = 2d a√2 = d   a = 2d/√2 a = d/√2 => 2: 1   Answer:2: 1
Answer: D
A train passes through a telegraph post in 9 seconds moving with a speed of 54 km per hour. The length of the train is	Choose the correct choice from the following choices:
A) 135 metres  B) 145 metres  C) 125 metres  D) 155 metres  E) None of these

Solution: We know from the formula Distance = Speed x time   Thus, Distance = 54 x 5/18 x 9   or, Distance =135 meters.   135 metresNSWER:135 metres
Answer: A
The total cost of 100 paper plates and 200 paper cups is $4.00 At the same rates what is the total cost of 20 of the plates and 40 of the cups?	Pick.
A) $.80 B) $1.00 C) $1.20 D) $1.50 E) $1.60

Solution: U dont need to go through all this   What u have with u is   100 P + 200 C = $4.00   Just divide the equation by 5 and you will get what u are looking for   20P + 40 C = $0.80   Therefore O$.80 is $.80
Answer: A
A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?  Choose the correct choice from the following answers.
A) 20002  B) 20000  C) 20007  D) 200018  E) 20012

Solution: Let the total worth of the stock be Rs. x.   The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50   The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50   Total SP = 11x/50 + 38x/50 = 49x/50   Overall loss = x - 49x/50 = x/50   x/50 = 400 => x = 20000   Answer:20000
Answer: B
A bullet train passes a station platform in 36 seconds and a man standing on the platform in 23 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform? Choose one.
A) 240 m
B) 220 m
C) 195 m
D) 224 m
E) 239 m

Solution: A   195 M   Speed = 54 x 5/18 = 15 m/s   Length of the bullet train = (15 x 23)m = 345 m.   Let the length of the platform be x metres.   Then, (x + 345)/36 = 15   --> x + 345 = 540   x = 195m. 195 m
Answer: C
If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a × b × c < a^3
II. a + b + c > a^3
III. 5b < bc
Select the correct option:	A) I only	B) II only	C) III only	D) II and III	E) I, II, and III

Solution: Given:   1) a is even prime. The only even prime number known is 2, so a must be equal to 2.   2) a,b,c are consecutive such that a<b<c. So, b must be 3 and c must be 4.   So, we know that a=2, b=3 and c=4.   Substituting the above values in the three equations,   I. abc<a^3 24<8.="" a+b+c="" false.="" ii.="" simplifies="" to="" which="">a^3   which simplifies to 9>8. True.   III. 5b<bc   which simplifies to 15<12. False.   The only option correct is II, so the answer is II only.</a^3>
Answer: B
If X is to be chosen at random from the integers between 1 to 5, inclusive, and Y is to be chosen at random from the integers between 7 and 10, inclusive, what is the probability that X + Y will be even?  Choose the correct choice from the following answers:  A) 1/2  B) 2/3  C) 3/4  D) 4/5  E) 5/6

Solution: X+Y will be even if X and Y are both even or both odd.   P(X and Y are both even) = 2/5*2/4 = 1/5   P(X and Y are both odd) = 3/5*2/4 = 3/10   P(X+Y is even) = 1/5 + 3/10 = 1/2   The answer is 1/2.
Answer: A
In a cricket match, five batsmen A, B, C, D and E scored an average of 36 runs. D Scored 5 more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them. How many runs did E score ?  Choose the correct choice from the following choices:	A) 62	B) 45	C) 28	D) 20	E) 24

Solution: a+b+c+d+e=36*5= 
36*5 = 180
180   b+c=107   a=x   e=x-8   d=x-3   now 3x-11+107=180   3x=84   x=28   e's score=28-8= 
28-8 = 20
20   ANSWER:20
Answer: D
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? Choices:
A) 5.78
B) 5.28
C) 5.76
D) 5.16
E) 5.19

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2= 
2.88 * 2 = 5.76
5.76   Answer:5.76
Answer: C
Nicole cycles at a constant rate of 24 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
Choose the correct choice from the following.
A) x/4 B) x/3 C) x/2 D) x E) 4x/3

Solution: In x minutes, Jessica travels (x/60)*30 = x/2 miles   The time it takes Nicole to travel x/2 miles is (x/2) / 24 = x/48 hours = 5x/4 minutes   Jessica needs to wait 5x/4 - x = x/4 minutes.   The answer is x/4.
Answer: A
X can do a piece of work in 40days. He works at it for 8days and then Y finished it in 28 days. How long will Y take to complete the work?  Options:  A) 10  B) 12  C) 15  D) 18  E) 35

Solution: Work done by X in 8days = 8*1/40 = 1/5   Remaining work = 1 - 1/5 = 4/5   4/5 work is done by Y in 28 days   Whole work will be done by Y in  28*5/4= 
 28*5/4 = 35
35 days   Answer is 35
Answer: E
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options.
A) 277	B) 237	C) 245	D) 376	E) 368

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time   = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 =   25/2   ==> 2(130 + X) = 750 ==> X   = 245 m.   Answer:245
Answer: C
Each factor of 220 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 55?  Choose the correct choice from the following answers:  A) 1/16  B) 5/42  C) 1/8  D) 3/16  E) 1/4

Solution: the # of factors 220 has is 12 ;   so out of 12 factors only three are multiples of 55: 55, 110 and 220, itself;   So, the probability is 3/12=1/4.   Answer: 1/4.
Answer: E
Equal weights of two alloys containing tin, copper and lead in the ratio 3:2:5 and 4:5:3 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy?
Pick one:
A) 41:81:37
B) 33:91:81
C) 17:28:27
D) 38:37:45
E) 41:86:89

Solution: Let the weight of the two alloys be w each   Required ratio =   (3w/10 +4w/12): ( 2w/10+5w/12 ): (5w/10+3w/12)   = 38w/60 : 37w/60 : 45w/60   = 38:37:45   ANSWER:38:37:45
Answer: D
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? Choose the correct choice from the following choices:
A) 76 sec
B) 16 sec
C) 48 sec
D) 17 sec
E) 54 sec

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 sec
Answer: C
What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit? Select
A) 17
B) 19
C) 20
D) 21
E) 18

Solution: C   20   Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1.   Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.   Number of such number =14   Required percentage = (14/70 x 100)% = 20%.
Answer: C
if the annual rate of simple interest increases from 10% to 12.5% .Then a man’s yearly income from an investment increases by Rs.1250. His principle amount is:	Choose the correct choice from the following answers:
A) Rs,45000	B) Rs.50,000	C) Rs. 60,000	D) Rs.65,000	E) Rs.75,000

Solution: Let the sum be Rs.x Then, (x*25/2*1/100) – (x*10*1/100)= 1250   25x-20x = 250000 ;   x=50000   ANSWER:Rs.50,000
Answer: B
An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Select the correct option.
A) 33 1/7%  B) 33 1/6%  C) 33 1/3%  D) 38 1/3%  E) 33 2/3%

Solution: 675 ---- 225   100 ---- ? => 33 1/3%   Answer:33 1/3%
Answer: C
A train 600 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Choose the most appropriate option.
A) 298 m
B) 268 m
C) 700 m
D) 267 m
E) 181 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (600 + x)/60 = 65/3   x = 700 m.   Answer: 700 m
Answer: C
If 213 × 16 = 3408, then 0.16 × 2.13 is equal to : Choose one
A) 0.3408 B) 3.408 C) 34.08 D) 340.8 E) None of these

Solution: Solution   0.16 × 2.13 = (16/100x 213/100)= (16x 213/10000) = 3408/10000 = 0.3408. 0.3408nswer 0.3408
Answer: A
Which of the following is a parallelogram:- Choices:
A) 130,50,130,50(angle in deg)
B) 120,30,130,20(angle in deg)
C) 90,90,90,90(angle in deg)
D) a & c
E) none

Solution: sum of adjacent angles is 180 degrees.   so, a&c   ANSWER:a & c
Answer: D
Antony, Ben, and Charles each try independently to win a carnival game. If their individual probabilities for success are 2/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?	Choose the correct choice from the following options.
A) 3/140 B) 1/280 C) 3/280 D) 3/35 E) 68/280

Solution: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 2/5*3/8*5/7 + 2/5*5/8*2/7 + 3/5*3/8*2/7 = 68/280.   Answer: 68/280.
Answer: E
The cost of 8 pens and 4 pencils is Rs.200and the cost of 2pens and 2 pencils is Rs.48. Find the cost of each pen? Choose the correct choice:
A) Rs.32
B) Rs.36
C) Rs.42
D) Rs.26
E) Rs.104

Solution: Let the cost of each pen and pencil be 'p' and 'q' respectively.   8p + 4q = 200 --- (1)   2p + 2q = 48   4p + 4q = 96 --- (2)   (1) - (2) => 4p = 104   => p = 26   ANSWER:Rs.26
Answer: D
If a function f is defined by f(x)= 1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 3/2 then b= ?
Options:	A) -3	B) 1/3	C) -1/3	D) 3	E) -12

Solution: Given that f(x) = 1/x and f(a) = -1/2, then f(a) =1/a=-1/2 ===> a=-2, then backsolve using the answer choices:   f(ab) = f(-2b) = 1/6   A) -3 ===> f(-2*-3) = f(6) = 1/6   B) 1/3 ===> f((-2*1/3) = f(-2/3) = 1/(-2/3) = -3/2   -1/3) -1/3 ===> f(-2*-1/3) = f(2/3) = 1/(2/3) = 3/2 WINS   D) 3 ===> f(-2*3) = f(-6) = -1/6   E) -12 ===> f(-2*-12) = f(24) = 1/-24 = -1/24   Answer: -1/3
Answer: C
A man took a loan from a bank at the rate of 12% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was :	Choose the correct choice from the following answers.
A) Rs. 2000
B) Rs. 10,000
C) Rs. 15,000
D) Rs. 20,000
E) None

Solution: Solution   Principal = Rs.(100x5400/12x3)= Rs. 15000.   Answer Rs. 15,000
Answer: C
5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
Choose one.
A) 2999
B) 2788
C) 4400
D) 2999
E) 2989

Solution: X * (95/100) * (85/100) = 3553   X = 4400   Answer: 4400
Answer: C
Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Choose the correct choice from the following answers
A) 5/7 B) 5/4 C) 5/1 D) 5/6 E) 5/3

Solution: P(at least one graduate) = 1 - P(no graduates)   = 1 - ⁶C₃/¹⁰C₃   = 1 - (6 * 5 * 4)/(10 * 9 * 8)   = 5/6   Answer:5/6
Answer: D
Photography changed drastically _________ introduced in the market. Options.
A) when polariod  B) when polariod  C) when polariod  D) as polaroid  E) 1312

Solution: Explanation:   There is no adequation information is given about details of subsequent changes. So "when" is the right word. Option a. "As" inditates reason.   Answer:as polaroid
Answer: D
What was the day of the week on, 19th July, 1776? Choose the most appropriate option.
A) Friday  B) Wednesday  C) Monday  D) Saturday  E) SUNDAY

Solution: 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)   Counting of odd days :   1600 years have 0 odd day.   100 years have 5 odd days.   75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.   1775 years have (0 + 5 + 2)= 
(0 + 5 + 2) = 7
7 odd days= 0 odd day.   Jan Feb Mar Apr May Jun Jul   31 + 29 + 31 + 30 + 31 + 30 + 16= 
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198
198 days= (28 weeks + 5 days)   Total number of odd days = (0 + 5)= 
(0 + 5) = 5
5.   Required day was 'Friday'.   Fridaynswer:Friday
Answer: A
If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? Pick
A) 157.56 B) 157.51 C) 157.5 D) 157.59 E) 157.52

Solution: (3500*1.5*3)/100 => 157.50.Answer: O157.5
Answer: C
1,000^2 + 1,001^2 +1,002^2 + 1,003^2 =	Choices:
A) 6,030,053
B) 6,030,054
C) 6,030,055
D) 6,030,056
E) 6,012,012

Solution: Interesting problem.   I think key is to notice that all the given answer choices differs in last two digits. Therefore, our entire focus should be to figure out how the given terms contribute to last two digits of total.   1000^2 -> 00   1001^1 -> 01   .   .   1005^3 -> 14   Total -> *55   Answer 6,012,012.
Answer: E
If it takes a tub 2 minutes to drain 5/7 of its content, how much more time will it take for the tub to be empty?
Select the correct option
A) 48 seconds B) 1 minute, 12 seconds C) 1 minute, 50 seconds D) 2 minutes, 14 seconds E) 4 minutes, 12 seconds

Solution: If 5/7 of tub's content is drained 2/7 th of tub still needs to be drained.   If it takes 2 minutes to drain 5/7 th of tub it takes 2*(7/5) minutes to drain the entire tub and 2*(7/5)*(2/7) min to drain 2/7 th of the tub which is 4/5 minutes or 48 minutes   So answer is 48 seconds
Answer: A
the sum of all two digit numbers divisible by 5 is Choose the correct choice from the following options
A) 945	B) 3487	C) 28	D) 279	E) 1287

Solution: Required numbers are 10,15,20,25,...,95   This is an A.P. in which a=10,d=5 and l=95.   Let the number of terms in it be n.Then t=95   So a+(n-1)d=95.   10+(n-1)*5=95,then n=18.   Required sum=n/2(a+l)=18/2(10+95)=945.   945nswer: 945) 945
Answer: A
A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is? Choose the correct choice from the following choices.
A) 11  B) 21  C) 88  D) 77  E) 61

Solution: 20 15 5   25 20 8   500 + 300 + 40= 
500 + 300 + 40 = 840
840/40= 
840/40 = 21
21   Answer: 21
Answer: B
Two cars cover the same distance at the speed of 50 and 66 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. Pick:
A) 212 km B) 214 km C) 188 km D) 216 km E) 204 km

Solution: 50(x + 1) = 66x   X = 3.125   60 * 3.125 = 188 km   ANSWER:188 km
Answer: C
Suppose 7 students are staying in a hall in a hostel and they are allotted 7 beds. Among them, Parvin does not want a bed next to Anju because Anju snores. Then, in how many ways can you allot the beds?  Options.
A) 2388
B) 2088
C) 3600
D) 2028
E) 1911

Solution: Let the beds be numbered 1 to 7.Case 1 : Suppose Anju is allotted bed number 1.   Then, Parvin cannot be allotted bed number 2.   So Parvin can be allotted a bed in 5 ways.   After alloting a bed to Parvin, the remaining 5 students can be allotted beds in 5! ways.   So, in this case the beds can be allotted in 5´5!ways = 600 ways.   Case 2 : Anju is allotted bed number 7.   Then, Parvin cannot be allotted bed number 6   As in Case 1, the beds can be allotted in 600 ways.   Case 3 : Anju is allotted one of the beds numbered 2,3,4,5 or 6.   Parvin cannot be allotted the beds on the right hand side and left hand side of Anju’s bed. For example, if Anju is allotted bed number 2, beds numbered 1 or 3 cannot be allotted to Parvin.   Therefore, Parvin can be allotted a bed in 4 ways in all these cases.   After allotting a bed to Parvin, the other 5 can be allotted a bed in 5! ways.   Therefore, in each of these cases, the beds can be allotted in 4´ 5! = 480 ways.   The beds can be allotted in (2x 600 + 5 x 480)ways = (1200 + 2400)= 
(1200 + 2400) = 3_600
3600 ways   Answer: 3600
Answer: C
Weights of two friends Ram and Shyam are in the ratio 1:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased?
Pick
A) 19% B) 10% C) 21% D) 16% E) None

Solution: Solution:   given ratio of Ram and Shayam's weight = 1:5   Hence, (x-15)/(15-10) = 1/5   Or, x = 16%.   Answer: Option 16%
Answer: D
The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.80 per metre.	Pick:
A) 2399
B) 6336
C) 2999
D) 5808
E) 2888

Solution: Explanation:   Area = (13.86 x 10000) sq.m = 138600 sq.m   Circumference =   Cost of fencing = Rs. (1320 x 4.80) = Rs. 6336.   Answer: 6336) 6336
Answer: B
How long will a boy take to run round a square field of side 50 meters, if he runs at the rate of 10km/hr?	Pick one
A) 52sec B) 45sec C) 72sec D) 25sec E) 39sec

Solution: Speed = 10 km/hr = 10*5/18 = 25/9 m/sec   Distance = 50*4= 
50*4 = 200
200m   Time taken= 200*9/25= 
200*9/25 = 72
72sec   Answer is 72sec
Answer: C
A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?	Choose the most appropriate option:
A) 700  B) 1000  C) 1300  D) 1600  E) 2000

Solution: Profit=Revenue-Cost   2007:   -1000=R1-C1   2008:   0=(1+2X%)R1-(1+X%)C1   2009:   P3=(1+2 X%)^2*R1-(1+X%)^2*C1   we've already known that R3=1.44R1, so (1+2 X%)^2=1.44, X=10   we put X=10 back to the equation of 2008:   0=1.2R1-1.1C1, and we have 1.2R1=1.1C1, which we could combine with the equation of 2007.   Then we have 13001=12000, R1-11000   Finally, take 13001 and R1 into the equation of 2009 and we got P3=15840-14520= 
15840-14520 = 1_320
1320 ;Answer: 1300
Answer: C
The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Choices.
A) 235	B) 288	C) 245	D) 776	E) 232

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> 2(140 + X) = 750 ==> X   = 235 m.   235nswer:235
Answer: A
A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose? Choose the correct choice from the following answers: A) 120 B) 335 C) 784 D) 217 E) 210

Solution: Let x be the number he chose, then   2*x*138=102   2x=240   x=120   correct answer 120
Answer: A
The average of five numbers is 27. If one number is excluded, the average becomes 21. The excluded number is?  Answers.
A) 48  B) 49  C) 50  D) 51  E) 52

Solution: Excluded number = (27 * 5) - (21 * 4)   = 135 - 84= 
135 - 84 = 51
51.   Answer: 51
Answer: D
Julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Julie 's savings by the end of the year from these monthly savings were four times the amount she spent per month, what should be the fraction of her salary that she spent each month?	Pick:
A) 5/3
B) 3/9
C) 3/2
D) 3/5
E) 3/4

Solution: Let Julie 's monthly savings = S   Julie 's monthly pay = P   Julie 's monthly expenditure = P-S   Julie 's savings by the end of the year from these monthly savings were Four times the amount she spent per month   12S = 4*(P-S)   =>3S = P-S   => P = 4S   Julie's monthly expenditure = P-S = 4S-S = 3S   fraction of her salary that Julie spent each month = 3S / 4S=P-S/P = 3/4. Answer is 3/4
Answer: E
A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 539, what was his profit?  Select.
A) s. 64 B) s. 99 C) s.72 D) s.75 E) s.90

Solution: C.P. = Rs. (100/122.5)x539   = Rs. (1000/1225)x539   = Rs. 440   Profit = Rs. (539 - 440) = Rs. 99.   Answer:s. 99
Answer: B
A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 24 cm. What is the length of the wire?
Pick one
A) 6 cm
B) 4 cm
C) 8 cm
D) 3 cm
E) 9 cm

Solution: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.   π(24)^2 * h = (4/3)π (12)^3 => h   = 4 cm   Answer:4 cm
Answer: B