MU-NLPC/Calc-aqua_rat huggingface dataset:
106 Ã— 106 + 94 Ã— 94 = ?	Options
A) 20072  B) 20062  C) 10072  D) 20172  E) 10272

Solution: Explanation :   (a + b)2 + (a âˆ’ b)2 = 2(a2 + b2)   (Reference : Basic Algebraic Formulas)   1062 + 942 = (100 + 6)2 + (100 âˆ’ 6)2 = 2(1002 + 62) = 2(10000 + 36) = 20072. 20072nswer : Option 20072
Answer: A
A train 110 m long is running with a speed of 40 km/h. In how many seconds will the train pass a man who is running at 4 km/h in the direction opposite to that in which the train is going? Choose one
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: The speed of the train relative to the man = 40 + 4= 
40 + 4 = 44
44 km/h.   44000 m/h * 1h/3600 s= (440/36) m/s   (110 m) / (440/36 m/s) = (110 * 36) / 440 = 36/4= 
36/4 = 9
9 seconds   The answer is 9.
Answer: D
A certain bag contains 100 balls â€” 50 white, 30 green, 8 yellow, 9 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?  Answers:	A) 0.9	B) 0.75	C) 0.6	D) 0.88	E) 0.5

Solution: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (50 + 30 + 8)/100 = 88/100 = 0.88.   Answer is 0.88
Answer: D
An assembly line produces 90 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately decreased so that it only produces 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?  Choose the correct choice
A) 68 B) 69 C) 70 D) 71 E) 72

Solution: The time to produce the first 60 cogs is 60/90 = 2/3 hours.   The time to produce the next 60 cogs is 60/60= 
60/60 = 1
1 hour.   The average output is 120 cogs / (5/3) hours= 72 cogs per hour.   The answer is 72.
Answer: E
A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?	Select
A) 40 Kmph	B) 52 Kmph	C) 60 Kmph	D) 76 Kmph	E) 80 Kmph

Solution: Time = 6   Distance = 540   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 540/9= 
540/9 = 60
60 Kmph   60 Kmph)
Answer: C
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is: Choose the correct choice from the following choices:
A) 32%
B) 34%
C) 42%
D) 44%
E) 54%

Solution: Explanation:   Let original length = x metres and original breadth = y metres.   Original area =xy m2New Length =120/100x=6/5x   New Breadth =120/100y=6/5y   =>New Area =6/5x∗6/5y   =>New Area =36/25xy   Area 44%ifference=36/25xy−xy   =11/25xy   Increase%=44%iffernce/Actual∗100   =11xy/25∗1/xy∗100=44%   ANSWER IS 44%
Answer: D
Pipe A can fill a tank in 10 hrs and pipe B can fill it in 8 hrs. If both the pipes are opened in the empty tank.There is an outlet pipe in 3/4 th of the tank. In how many hours will it be fill 3/4th of that tank?  Choices.
A) 3 hr B) 3.10hr C) 3.15 hr D) 3.20 hr E) 3.30 hr

Solution: Part filled A in 1 hr= (1/10)   Part filled B in 1 hr= (1/8)   Part filled by (A+B) together in 1 hr=(1/10)+(1/8)=18/80   So, The tank will be full in 80/18 hrs.   Time taken to fill Exact 3/4th of the tank = (80/18) *(3/4) = 3.20 hrs   Answer : 3.20 hr
Answer: D
If a farmer wants to plough a farm field on time, he must plough 160 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?	Choose the correct choice from the following options: A) 600 B) 490 C) 448 D) 435 E) 679

Solution: Let x be the number of days in the initial plan. Therefore, the whole field is 160â‹…x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:   160x=85(x+2)+40   75x=210   x=2.8   So the farmer planned to have the work done in 6 days, and the area of the farm field is 160(2.8)=448 hectares   correct answer 448
Answer: C
A man has Rs. 176 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? Choose the most appropriate option
A) 33 B) 60 C) 75 D) 90 E) 95

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 176   16x = 176   x = 11.   Hence, total number of notes = 3x = 33.   33nswer: Option 33
Answer: A
The number 0.8 is how much greater than 1/2 ?  Choose the correct answer:
A) ½ B) 3/10 C) 1/50 D) 1/500 E) 2/500

Solution: let x be the difference   then   .8-1/2=x   8/10-1/2=x   x= 3/10   ans 3/10
Answer: B
Find the value of x in each of the following equation:	[(17.28/x) / (3.6*0.2)] = 2  Choices
A) 12
B) 14
C) 16
D) 18
E) 20

Solution: (17.28/x) = 2*3.6*0.2  x = (17.28/1.44) = (1728/14) = 12.   12nswer is 12.
Answer: A
Which of these lines in the xy-plane does not contain any point with two negative coordinates?  Choose the correct choice:	A) y = 4x	B) y = x + 6	C) y = x^2 - 5	D) y = x^3 + 3x	E) y = 2x^4

Solution: 2x^4 is 0 when x is 0 and positive for all other values of x.   The answer is y = 2x^4.
Answer: E
During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. she stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 180 miles to her detination. What was the total distance, in miles from Maria's starting point to her destination?  Select
A) 280  B) 320  C) 360  D) 420  E) 480

Solution: Easy 480 is the answer.   3/4 ( x/2) = 180   x = 180 * 8 /3= 
180 * 8 /3 = 480
480.   Answer 480
Answer: E
Three men sit at a table. One dollar is placed in front of each of them. When a buzzer sounds, the first man to touch the money in front of him keeps the money that is in front of him, while the other two receive nothing. If none of the three men touches the money in front of them, then the amount of money doubles for the next round. After three rounds of this activity, what is the maximum amount of money that any one man could receive?  Choose the correct choice from the following answers:  A) $4  B) $5  C) $10  D) $15  E) $16

Solution: The Optimized scenario   After 1st Round - $1. Let nobody touches the amount will double in next round.   After 2nd Round - $2. Let Man A touches it and get$2 or nobody touches   After 3rd Round - $2 Let the same Man A touches it and get another$2.( $4 in case nobody touches in 2nd round).   So, after 3rd round, the maximum amount a man receives is $4.   $4nswer ($4)
Answer: A
Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 3?	Choose the correct choice from the following options:
A) 2/5	B) 2/7	C) 33/83	D) 51/250	E) 100/249

Solution: SOLUTION   The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 51/250.   Answer: 51/250
Answer: D
What is x if x + 2y = 20 and y = 5?	Pick:  A) A)10  B) B)8  C) C)6  D) D)4  E) E)2

Solution: x = 20 - 2y   x = 20 - 10.= 
20 - 10. = 10
10   10nswer : 10
Answer: A
If the price of a certain bond on May 1st was 1/2 the price of the bond on June 1st and the price of the bond on July 1st was 50% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st? Pick one
A) 50% B) 75% C) 120% D) 133 1/3% E) 160%

Solution: The price on June 1st = 12 (assume);   The price on May 1st = 1/2*12= 
1/2*12 = 6
6;   The price on July 1st= 6*1.5= 
6*1.5 = 9
9.   The average price of the bond on May 1st and July 1st= (6+9)/2 = 7.5.   The price of the bond on June 1st (12) is 8/5 times (160%) the average price of the bond on May 1st and July 1st.   Answer: 160%.
Answer: E
If x dollars is invested at 12.5 percent for one year and y dollars is invested at 9.5 percent for one year, the annual income from the 12.5 percent investment will exceed the annual income from the 8 percent investment by $60. If $2500 is the total amount invested, how much is invested at 9.5 percent?	Options
A) a. $1097.83  B) b. $1231.57  C) c. $1101.52  D) d. $1147.72  E) e. $1352.27

Solution: 2 equations with 2 unknowns   12.5x / 100 - 9.5y / 100 = 60   and   x + y = 2500   Solving these 2 equations, x =1352.27 and y = 1147.72   Answer d. $1147.72.
Answer: D
If the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c − a?
Choose the correct choice from the following answers.
A) 25  B) 60  C) 90  D) 140  E) It cannot be determined from the information given.

Solution: -(a + b = 90)   b + c=160   c-a=60   B. 60
Answer: B
Rs. 6000 is lent out in two parts. One part is lent at 2% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?	Choose the correct answer.
A) 5:11  B) 5:6  C) 5:2  D) 5:8  E) 5:2

Solution: Let the amount lent at 2% be Rs. x   Amount lent at 10% is Rs. (6000 - x)   Total interest for one year on the two sums lent   = 2/100 x + 10/100 (6000 - x) = 600 - 3x/100   => 600 - 3/100 x = 450 => x = 1875   5:11mount lent at 10% = 4125   Required ratio = 5:11   5:11nswer:5:11
Answer: A
If y/x is an integer, which of the following must also be an integer?
I. xy
II. x/y
III. x Select the correct option:
A) I alone  B) II alone  C) None of the above  D) I and III  E) III alone

Solution: Lets take X = 1/6 and Y = 2/3   Then Y/X = 4 which is an integer.   But XY = 1/6 * 2/3 = 1/9 --> Not an integer.   X/Y = 1/6 divided by 2/3 = 1/4 --> Not an integer.   X alone is 1/6. Not an integer.   Hence C. None of the above.
Answer: C
Evaluate permutation
7P7  Pick one.
A) 5010  B) 5020  C) 5030  D) 5040  E) None of these

Solution: Explanation:   nPn=n!   7P7=7*6*5∗4∗3∗2∗1=5040   Option 5040
Answer: D
The difference between a two-digit number and the number obtained by interchanging the digit is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1:2?	Choose the correct answer.
A) 7 B) 8 C) 6 D) 5 E) 2

Solution: Explanation:   Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.   Let the ten's and unit's digits be 2x and x respectively.   Then, (10 * 2x + x) - (10x + 2x) = 36   9x = 36   x = 4   Required difference = (2x + x) - (2x - x) = 2x = 8.   Answer: 8
Answer: B
In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 77 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?  Choose the correct choice from the following: A) 550 B) 245 C) 150 D) 35 E) 350

Solution: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7= 
0.2*0.7 = 0.14
0.14, or 14% of the boys in the camp are from school A and do not study science.   We are told that this number equals to 77, so 0.14*{total}= 77 --> {total} = 550.   550nswer: 550.
Answer: A
An analyst will recommend a combination of 2 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 6 stocks are possible?
-- Choose the correct option.
A) 12
B) 19
C) 60
D) 180
E) 720

Solution: 5C2 * 4C2 * 3C2 = 10*6*3= 
10*6*3 = 180
180.   Answer: 180.
Answer: D
In a certain code VOLITION is written as UMIEUKRR, MARTINET is written as LYOPJPMX. How is DESTROYS written in this code?
Select the correct option:
A) CCPPSQBW  B) CCPPSQBU  C) CCPPSQBV  D) CCPPSQBX  E) CCPPSQBZ

Solution: as per the sequence the   ans is D-1 = C   E-2 = C   S-3=P   T-4=P   R+1=S   O+2=Q   Y+3=B   S+4=W   ans is CCPPSQBW   CCPPSQBWNSWER:CCPPSQBW
Answer: A
A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 6% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.
What is the probability that a smartphone bundle that will be rejected by quality control? Pick
A) 0.25
B) .05^10
C) 1-0.94^10
D) 1-0.05^10
E) 0.95^10

Solution: Find the probability of the opposite event and subtract from 1.   The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.94^10.   P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.94^10.   Answer: 1-0.94^10.
Answer: C
If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is :
Choose the correct choice from the following:
A) 3 M^9	B) 3 M^2	C) 3 M^6	D) 3 M^1	E) 3 M^7

Solution: Explanation:   We have : ( a + b + c) / 3 = M or (a + b + c) = 3M.   Now. .   Answer: 3 M^2) 3 M^2
Answer: B
Two pipes can fill a tank in 5 hours and 10 hours. While the 3rd pipe empties the full tank in 10hours. If all the 3 pipes are open in how much time will the tank be filled?  Options
A) 6hr
B) 8hr
C) 2hr
D) 1hr
E) 5hr

Solution: Net part filled in 1 hour = 1/5 + 1/10 - 1/10 = 1/5   The tank will be full in 5 hr   Answer is 5hr
Answer: E
There are 5 candidates in an election and 3 of them are tobe elected. A voter can cast any number of votes but notmore than three. The number of ways in which he can cast his vote is
Pick.
A) 5	B) 15	C) 20	D) 25	E) 30

Solution: Solution   The voter can cast one or two or three votes. So total number of ways in which he can cast his vote =5C1 + 5C2 + 5C3 = 5 + 10 + 10= 
5 + 10 + 10 = 25
25. Answer 25
Answer: D
If $30,000 interest is invested in x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?  Pick one:
A) 10,000(x^n)
B) 30,000n(x/100)
C) 10,000(1 + x/100)^n
D) 30,000(x/100)^n
E) 10,000n(1 + x/100)

Solution: Principal * no.of years * percentage of interest   Answer : 30,000n(x/100)
Answer: B
Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?  Choose the correct choice from the following options:  A) 7 min  B) 6 min  C) 9 min  D) 10 min  E) 11 min

Solution: Due to stoppages, it covers 5 km less.   Time taken to cover 5 km =(5/50)x60 = 6 min   answer : 6 min
Answer: B
If a = (1/6)b and c = 7a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ?  Pick one
A) a + 4	B) (11/3)a	C) (13/3)a	D) (4 1/7)a	E) (7 1/4)a

Solution: Official Answer: C   The average of the three variables isa + b + c/3. However, we need to solve in terms of a, which means we must convert b and c into something in terms of a.   Were told that a =1/6b, which is equivalent to b = 6a. We can plug that in and simplify the average to:a + 6a + c/3   We also know that c = 7a, which we can plug directly into the average expression:   a + 6a + 7a/3   = 13a/3 = (13/3)a choice(13/3)a.
Answer: C
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
Choose the correct choice from the following choices
A) 180	B) 190	C) 130	D) 120	E) 140

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 1900 m   T = D/S   T = 1900/10= 
1900/10 = 190
190 Sec   Answer: Option 190
Answer: B
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?	Choose the most appropriate option
A) 23/35  B) 23/36  C) 23/33  D) 23/31  E) 23/32

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green   = (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂   = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7   = 46/70 = 23/35   23/35nswer: 23/35
Answer: A
Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?	Options
A) 270
B) 150
C) 130
D) 90
E) 210

Solution: Let x be the total number of pages in the book, then she finished 2/3*x pages.   Then she has x−2/3*x=1/3*x pages left.   2/3*x−1/3*x=90   1/3*x=90   x=270   So the book is 270 pages long.   270nswer is 270.
Answer: A
In a division, divident is 689, divisior is 36 and quotient is 19. Find the remainder.	Choose the correct option:
A) 4	B) 3	C) 2	D) 5	E) 6

Solution: Explanation:   689 = 36 x 19 + r   689 = 684 + r   r = 689 - 684= 
689 - 684 = 5
5   Answer: Option 5
Answer: D
The pages of a report are numbered consecutively from 1 to 13. If the sum of the page numbers up to and including page number x of the report is equal to one less than the sum of the page numbers following page number x, then x =	Choose the correct option:
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: sum of the first few numbers =1+2+3+4+5+6+7+8+9= 
1+2+3+4+5+6+7+8+9 = 45
45   sum of the last few= 10 +11+12+13= 
10 +11+12+13 = 46
46 page no.9 answer .9
Answer: E
A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 5 days. B can do the work alone in?
Answers:
A) 19  B) 12  C) 11  D) 30  E) 114

Solution: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.   Then, (1/x + 2/x + 3/x) = 1/5   6/x = 1/5 => x = 30   So, B takes 15 hours to finish the work.   Answer: 30
Answer: D
Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $4.25 million from its orange exports, how much money does it generate from its yearly total of exports?
Choose the correct choice from the following options
A) $21.25m  B) $25.5m  C) $106.25m  D) $127.5m  E) $153m

Solution: 2/10*1/6*(total) = 4.25   1/30*(total) = 4.25   (total) = 4.25*30= 
4.25*30 = 127.5
127.5   Answer: $127.5m.
Answer: D
A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?	Choose the correct choice from the following answers
A) 7	B) 13	C) 19	D) 10	E) None

Solution: 1/6 â€“ 1/15 = 1/10   B can do the work in 10 days   Answer: 10
Answer: D
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate got? Options
A) 55% B) 56% C) 57% D) 58% E) 59%

Solution: Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400   So, Required percentage= 11628/20400 * 100= 
11628/20400 * 100 = 57
57%   ANSWER : 57%
Answer: C
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
Pick
A) 50 m  B) 150 m  C) 200 m  D) 300 m  E) None of these

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 100)/25 = x/15 => x = 150 m.   ANSWER:150 m
Answer: B
Distances from you to Man united is written below.
CHELSEA and ARSENAL are 700 kms away
SPURS 1800 kms away
WOLVES 200 kms away
Based on the system , How far should it be to MANCITY ?	Choose the correct choice from the following: A) 1100 miles. B) 3100 miles. C) 2100 miles. D) 5100 miles. E) 4100 miles.

Solution: Solution:   2100 miles.   Each vowel equivalent to 500 and each consonant equivalent to -200   Answer 2100 miles.
Answer: C
Amar takes as much time in running 18 meters as a car takes in covering 12 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
Choose the correct option.
A) 6200 m	B) 2400 m	C) 300 m	D) 4300 m	E) 1200 m

Solution: 2400 m   2400 m   Distance covered by Amar = 18/1.2 (1.6km) = 3/8(1600) = 2400 m   Answer is 2400 m
Answer: B
The sequence of numbers a1, a2, a3, ..., an is defined by an = 1/n - 1/(n+2) for each integer n >= 1. What is the sum of the first 40 terms of this sequence?
Answers:	A) (1+1/2) + 1/40	B) (1+1/2) – 1/42	C) (1+1/2) – 1/40	D) (1+1/2) – (1/41 +1/ 42)	E) (1/41 +1/ 42)

Solution: The answer would most certainly be[D]. But the question needs a slight modification.n>=1, since the answer does consider a1 under the sum.   The sequence is :   a1 = 1-1/3   a2 = 1/2 - 1/4   a3 = 1/3 - 1/5....   We can observe that the third term in the sequence cancels the negative term in the first. A similar approach can be seen on all the terms and we would be left with 1 + 1/2 from a1 and a2 along with -1/42 and -1/41 from a40 and a39 term which could not be cancelled.   Hence the sum = (1+1/2) – (1/41 +1/ 42)   Answer : (1+1/2) – (1/41 +1/ 42)
Answer: D
A train 120 meters long passes an electric pole in 12 seconds and another train of same length traveling in opposite direction in 8 seconds. The speed of the second train is	Choose one:
A) 60 Km B) 66 Km C) 72 Km D) 62 Km E) 70 Km

Solution: speed of first train=120/12= 
120/12 = 10
10 m/s   let speed of second train be x m/s. As they are approaching each other, relative speed is (10+x) m/s.   distance between each other is  120+120= 
 120+120 = 240
240 m.   time of crossing each other is 8 sec=>240/(10+x)=8   =>x=20m/s = 20*18/5 km/hr = 72 kmph   ANSWER:72 Km
Answer: C
Jack and Jill work at a hospital with 3 other workers. For an internal review, 2 of the 5 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?  Answers:
A) 1/3
B) 1/10
C) 1/15
D) 3/8
E) 2/3

Solution: 1/5C2=1/10.   Answer: 1/10.
Answer: B
The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?
Answers.
A) 1:4 B) 2:3 C) 3:5 D) 5:6 E) 5:7

Solution: Let the present ages of the two brothers be x and 2x years respectively.   Then, (x - 5)/(2x - 5) = 1/3   3(x - 5) = (2x - 5) => x = 10   Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5   ANSWER:3:5
Answer: C
A 300 m long train crosses a platform in 36 sec while it crosses a signal pole in 18 sec. What is the length of the platform?	Choose the correct answer:	A) 286 m	B) 350 m	C) 277 m	D) 278 m	E) 300 m

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/36 = 50/3   x = 300 m.   Answer:300 m
Answer: E
Albert borrowed a total of $ 6000 from Brian and Milton. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years?  Choose the correct choice
A) 491
B) 481
C) 471
D) 441
E) 445

Solution: Let x be the amount borrowed form Brian. So amount borrowed form Milton = 6000-x.   1494 = 21/100x + 27/100(6000-x)   =>x = 2100.   Interest paid = 3*7/100*2100= 
3*7/100*2100 = 441
441.   441
Answer: D
Find the average of first 5000 natural numbers?	Choose one.
A) 2500  B) 2500.5  C) 2145.5  D) 2005.5  E) 2560

Solution: Sum of first 100 natural numbers = 5000*5001/2= 
5000*5001/2 = 12_502_500
12502500   Required average= 12502500/5000= 
12502500/5000 = 5_001/2 = around 2_500.5
2500.5   Answer is 2500.5
Answer: B
A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age five years back was?	Choices
A) 10 years  B) 12 years  C) 14 years  D) 16 years  E) 18 years

Solution: Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 5 years back (19 - 5)= 
(19 - 5) = 14
14 years.   14 years
Answer: C