MU-NLPC/Calc-aqua_rat huggingface dataset:
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 99 km/hr. What is the length of the platform?
Select the correct option:
A) 440
B) 488
C) 477
D) 426
E) 422

Solution: Speed = 99 * 5/18= 
99 * 5/18 = 55/2 = around 27.5
27.5 m/sec.   Length of the train= 27.5 * 20= 
27.5 * 20 = 550
550 m.   Let the length of the platform be x m . Then,   (x + 550)/36= 27.5 => x = 440 m.   440nswer: 440
Answer: A
A certain rectangular crate measures 6 feet by 8 feet by 10 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?	Answers.
A) 4 B) 4 C) 6 D) 8 E) 10

Solution: Ans is "B".   For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. . Therefore for max vol base should be 8x10 i.e. of radius   8/2= 
  8/2 = 4
4   4
Answer: B
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?  Options:	A) 70,10 kmph	B) 78,10 kmph	C) 70,70 kmph	D) 78,10 kmph	E) 70,12 kmph

Solution: Speed of the boat in still water   = (60+80)/2= 
(60+80)/2 = 70
70 kmph. Speed of the stream= (80-60)/2= 
(80-60)/2 = 10
10 kmph.   70,10 kmphnswer:70,10 kmph
Answer: A
In filling a lot with sand, that is 40 m * 20 m * 2m the volumes of the sand filled will be?  Choose the correct option.
A) 1200 cu.m B) 2200 cu.m C) 4800 cu.m D) 1600 cu.m E) 4000 cu.m

Solution: 40 * 20 * 2= 
40 * 20 * 2 = 1_600
1600   ANSWER:1600 cu.m
Answer: D
what is the smallest integer that is multiple of 5,7,20 Answers
A) 70
B) 35
C) 200
D) 280
E) 140

Solution: It is the lcm of 5, 7 and 20 which is 140.   The answer is 140.
Answer: E
One student's mark was wrongly entered as 73 instead of 63. Due to that the average marks for the class got increased by 1/3. What is the number of students in the class? Choose the correct choice
A) 30 B) 32 C) 35 D) 40 E) 45

Solution: Let the total number of students = a   The average marks increased by 1/3 due to an increase of   73 - 63= 
  73 - 63 = 10
10 marks.   But total increase in the marks= 1/3 *x =x/3   Hence we can write as   =>x/3=10   =>x=30   30NSWER:30
Answer: A
A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 12 km, if the person completes half of the distance by walking and the other half by running?	Select the correct option:
A) 1.25	B) 1.75	C) 2.25	D) 2.75	E) 3.25

Solution: time = 6/4 + 6/8 = 18/8= 
18/8 = 9/4 = around 2.25
2.25 hours   The answer is 2.25.
Answer: C
The average age of a class is 15.8 years. The average age of boys in the class is 16.4 years while that of girls is 15.4 years. What is the ratio of boys to girls in the class?	Choose the correct choice from the following choices:
A) 1:2
B) 3:4
C) 3:5
D) 2:3
E) None of these

Solution: let x = number of girls   y = number of boys   sum of girls ages / x = 15.4   sum of boys ages / y = 16.4   The sum of the girls' ages is 15.4x, and boys' sum is 16.4y   (sum of girls ages + sum of boys ages) / (x+y)= 15.8   (15.4x + 16.4y) / (x+y) = 15.8   15.4x + 16.4y = 15.8(x+y)   15.4x + 16.4y = 15.8x + 15.8y   0.6y = 0.4x   0.6y/x = 0.4   y/x = 0.4/0.6   y/x = 2/3 which is the ratio of boys to girls   ANSWER:2:3
Answer: D
When positive integer n is divided by 3, the remainder is 1. When n is divided by 5, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 15?  Choose the correct choice from the following answers
A) 2 B) 4 C) 6 D) 8 E) 10

Solution: n = 3p + 1 = 5q + 3   n+2 = 3p + 3 = 5q + 5   n+2 is a multiple of 3 and 5, so it is a multiple of 15.   The answer is 2.
Answer: A
How many three-digit integers exist such that all their digits are
odd?
Pick:
A) 80
B) 100
C) 120
D) 125
E) 135

Solution: so last digit can be filled in 5 ways- 1,3,5,7,9   there are 5 possibilities. The answer is 5∗5∗5=125   The correct answer is 125
Answer: D
A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weights 8g/cm cube, then find the weight of the pipe.
Choose the correct choice from the following:
A) 3.696 kg  B) 3.686 kg  C) 2.696 kg  D) 2.686 kg  E) None of these

Solution: Explanation:   In this type of question, we need to subtract external radius and internal radius to get the answer using the volume formula as the pipe is hollow. Oh! line become a bit complicated, sorry for that, lets solve it.   External radius = 4 cm   Internal radius = 3 cm [because thickness of pipe is 1 cm]   Volume of iron =πr2h=22/7∗[42−32]∗21cm3   =22/7∗1∗21cm3=462cm3   Weight of iron = 462*8= 
462*8 = 3_696
3696 gm= 3.696 kg   Option 3.696 kg
Answer: A
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?  Choose the correct answer:
A) Rs. 6825
B) Rs. 6721
C) Rs. 6725.
D) Rs. 4298
E) Rs. 6729

Solution: CP = SP * (100/(100 + profit%))   = 8339(100/124) = Rs. 6725.   Answer:Rs. 6725.
Answer: C
Two cards are selected at random from 10 cards numbered 1 to 10. Find the probability that the sum is odd if two cards are drawn together.  Answers:	A) 11	B) 88	C) 77	D) 19	E) 17

Solution: Answer:77
Answer: C
A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?	Choose the most appropriate option: A) 50 kmph B) 58 kmph C) 62 kmph D) 65 kmph E) 75 kmph

Solution: Relative speed = 280/9 m / sec = ((280/9)*(18/5))= 
((280/9)*(18/5)) = 112
112 kmph.   Speed of goods train= (112 - 50)= 
(112 - 50) = 62
62 kmph.   Answer : 62 kmph.
Answer: C
The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-half of the males and one-fourth of the females in the class?	Choose one:
A) 120	B) 126	C) 132	D) 138	E) 144

Solution: 1/2*2/5 + 1/4*3/5 = 4/20 + 3/20 = 7/20   The number of degrees is  7/20 * 360= 
 7/20 * 360 = 126
126 degrees   The answer is 126.
Answer: B
On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is?  Choose the correct choice from the following:
A) 10%  B) 10.5%  C) 12%  D) 13%  E) None of these

Solution: Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30.   S.I for one year = Rs. 330.   S.I. on Rs. 330 for 1 year = Rs. 36.30   Rate = (100 * 36.30)/(330 * 1)= 
(100 * 36.30)/(330 * 1) = 11
11%   ANSWER:13%
Answer: D
Jonathan can type a 50 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?	Choose the correct choice from the following answers: A) 5 minutes B) 10 minutes C) 15 minutes D) 18 minutes E) 20 minutes

Solution: You may set up common equation like this:   job/A+job/B+job/C=job/x   Memorize this universal formula, you will need it definitely for GMAT.   and find x from this equation   In this specific case, the equation will look like this:   50/40+50/30+50/24=50/x   If you solve this equation, you get the same answer 10 minutes (10)
Answer: B
A wheel that has 6 cogs is meshed with a larger wheel of 21 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:	Choose the correct answer:
A) 9
B) 10
C) 6
D) 8
E) 7

Solution: Explanation :   Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   21:6::21:x => 21 * x = 21 * 6   => x = (21 * 6)/21   => x = 6   Answer : 6
Answer: C
What is the sum of all the multiples of 9 between 0 and 99? Select the correct option.
A) 500  B) 594  C) 450  D) 340  E) 440

Solution: The multiples of 9 between 0 and 99 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99. If these are all added together, the result is 594.   Final Answer:   594
Answer: B
Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
Choose the correct answer: A) 33 B) 27 C) 20 D) 98 E) 21

Solution: Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.   Rate of interest = (100 * 240) / (100 * 1) = 20% p.a   Answer:20
Answer: C
A can do a piece of work in 3 hours; B and C together can do it in 6 hours, while A and C together can do it in 9 hours. How long will B alone take to do it? Answers:
A) 4 9/7 hours
B) 3 5/7 hours
C) 2 4/7 hours
D) 3 8/7 hours
E) none of the above

Solution: A's 1 hour's work = 1/3 ;   (B + C)'s 1 hour's work = 1/6 ;   (B + C)'s 1 hour's work = 1/9   (A + B + C)'s 1 hour's work = (1/3 + 1/6) = 1/2   B's 1 hour's work = (1/2 - 1/9) = 7/18   B alone will take 18/7 hours to do the work.   =2 4/7   Answer = 2 4/7 hours
Answer: C
If N is a positive integer and 14N/60 is an integer, then N has how many different positive prime factors? Choose the correct answer:	A) 2	B) 3	C) 5	D) 6	E) cannot be determined

Solution: 14N/60 = (2)(7)(N)/(2)(2)(3)(5)   = (7)(N)/(2)(3)(5)   For (7)(N)/(2)(3)(5) to be an integer, N must have a 2, 3 and 5 in its prime factorization (so the 2, 3 and 5 can cancel out in the denominator).   So, for example, if N = (2)(3)(5), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)/(2)(3)(5) = 7, which is an integer.   Likewise, if N = (2)(3)(5)(7), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)(7)/(2)(3)(5) = (7)(7) = 49, which is an integer.   Also, if N = (2)(3)(5)(7)(11), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)(7)(11)/(2)(3)(5) = (7)(7)(11), which will evaluate to be an integer.   If N = (2)(3)(5)(7)(11)(13), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)(7)(11)(13)/(2)(3)(5) = (7)(7)(11)(13), which will evaluate to be an integer.   And so on....   As we can see, we can continue this line of reasoning so that N has EVERY PRIME number in its prime factorization.   cannot be determined   ANSWcannot be determinedR:cannot be determined
Answer: E
A is thrice good a workman as B and therefore is able to finish a job in 60 days less than B. Working together they can do it in? Choose one.
A) 20  B) 22 ½  C) 25  D) 30  E) 40

Solution: Explanation:   Ratio of times by A and 22 ½= 1:3   difference of time is 2 days 22 ½ takes 3 days if diff of time is 60 days 22 ½ takes 3/2 *60= 
3/2 *60 = 90
90 days   A’s 1day work is=1/30   22 ½’s 1 day work =1/90   (A+22 ½ )’s one day work is=1/90 +1/30 =2/45   together can do work in 45/2 = 22 ½ days   Answer: Option 22 ½
Answer: B
If s=(10^10)-47, what is the sum of all the digit of s?
Choices:
A) 40
B) 45
C) 50
D) 55
E) 80

Solution: Start small and check for any pattern:   10^2 - 47 = 53 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits   10^3 - 47 = 953 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits   ...extrapolate   10^10 - 47 -> number of digits = 10; number of 9s = 8; 53 will be the last 2 digits   s = 9*8 + 5 + 3= 
9*8 + 5 + 3 = 80
80.   Answer (80).
Answer: E
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
Pick one.
A) 23 m B) 23 (2/9)m C) 27 (7/9)m D) 29 m E) 28 m

Solution: Relative speed = (40 - 20) km/hr =	(20 x(5/18))m/sec =	(50/9)m/sec.   Therefore Length of faster train =	((50/9)	x 5) m =	(250/9)m = 27	(7/9)	m.   27 (7/9)m
Answer: C
If the product of all the factors of a positive integer, N, is 2 ^ 18 * 3 ^ 12, how many values can N take? Answers.
A) None B) 1 C) 2 D) 3 E) 4

Solution: Lets say   2^0 *3^0 * 2^0 * 3^1....2^0 * 3^n ...A0 >> 2^{0*(N+1)} * 3^{N(N+1)/2}   2^1 *3^0 * 2^1 * 3^1....2^1 * 3^n ...A2 >> 2^{1*(N+1)} * 3^{N(N+1)/2}   .   .   .   2^m *3^0 * 2^m * 3^1....2^m * 3^n ...AM >> 2^{M*(N+1)} * 3^[N(N+1)/2}   So product of all the factors are: A0 * A1 *...*AM = 2^{M(M+1)*(N+1)/2} * 3^{N(N+1)*(M+1)/2}   From the equation:   M(M+1)*(N+1)/2 = 18 --- X   N(N+1)*(M+1)/2 = 12 --- Y   dividing X, Y, we get M/N = 3/2   Lets say M = 3X, N = 2X   substituting the value in X OR Y we got X = 1 is the only integer satisfying   Hence the number is 2 ^ 3 * 3 ^ 2   Answer is 1
Answer: B
Ramya took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If she paid Rs.686 as interest at the end of the loan period, Find the rate of the interest?
Choose the correct choice from the following answers:
A) 5%
B) 6%
C) 4%
D) 3%
E) 7%

Solution: SI = 686   P = 1400   ==>1400*R*R/100   686=14R^2   R^2 = 49   R = 7   ANSW7%R 7%
Answer: E
In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?  Choose the correct choice from the following options:
A) 400 B) 500 C) 600 D) 530 E) 630

Solution: Explanation:   We can select one boy from 20 boys in 20 ways.   We select one girl from 25 girls in 25 ways   We select a boy and girl in 20 * 25 ways i.e., = 500 ways.   Answer: Option 500
Answer: B
The cross-section of a water channel is a trapezium in shape. If the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 990 square meters, what is the depth of the channel (in meters)?
Choices:
A) 50 B) 60 C) 70 D) 80 E) 90

Solution: 1/2 * d * (14 + 8) = 990   d = 90   The answer is 90.
Answer: E
Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?	Answers:
A) 10years B) 12 years C) 5 years D) 3 years E) 24 years

Solution: Explanation:   9261 = 8000(21/20)N   (21/20)3 = (21/20)N => N = 3 years   Answer:3 years
Answer: D
There are 6 gentlemen and 3 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are seated together.
Select.
A) 8540
B) 3640
C) 2880
D) 3880
E) 88600

Solution: First arrange the Gents. This is a circular arrangment. 6 Gents can be arranged in 5! ways.   Now there are 4 spaces (space in between two gents) and we have to seat 3 ladies there.   First select 3 places out of 4 available places. can be done in 4C3ways. Then arrange 3 ladies there in 3! ways.   Total: 5!*428803*3! = 2880   2880 is the answer.
Answer: C
A regular octagon is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of ∠OAB ?
Choose the correct choice from the following options: A) 48 degrees B) 54 degrees C) 67.5 degrees D) 84 degrees E) 108 degrees

Solution: its a regular pentagon so divide the globe by 8.   = 360/8= 
360/8 = 45
45   45 would be the angle at O.   Angles at A and B are equivalent, so   45 + 2x= 180   2x = 135   x = 67.5   Angles OAB and OBA will be 67.5 degrees each.   67.5 degrees
Answer: C
Given distinct positive integers 1, 10, 3, x, 2, and 9, which of the following could be the median?  Select the correct option:
A) 3
B) 4
C) 7
D) 8
E) 9

Solution: The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.   Arrange numbers in ascending order: 1, 2, 3, 9, 10, and x.   Now, x can not possibly be less than 3 as given that all integers are positive and distinct (and we already have 1, 2, and 3).   Next, if x is 3<x<9 then the median will be the average of 3 and x. As all answers for the median are integers, then try odd values for x:   If x=5, then median=(3+5)/2= 
(3+5)/2 = 4
4 --> OK;   Answer: B.   P.S. If x is more than 9 so 10 or more then the median will be the average of 3 and 9 so  (3+9)/2= 
 (3+9)/2 = 6
6 (the maximum median possible).
Answer: B
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 36 kmph. In how much time will the trains cross each other?	Choose the correct choice from the following choices
A) 12 sec	B) 13 sec	C) 15 sec	D) 16 sec	E) 17 sec

Solution: D   Relative speed = (54 + 36)* 5/18 = 5 * 5= 
5 * 5 = 25
25 mps.   The time required= d/s = (100 + 100 + 200)/25   = 400/25= 
400/25 = 16
16 sec.
Answer: D
The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior points respectively on them. How many triangles can be formed using these points as vertices.	Choose the correct choice:	A) 200	B) 205	C) 400	D) 410	E) 420

Solution: Total points: 3+4+5= 
3+4+5 = 12
12;   Any 3 points out of 12 but those which are collinear will form a triangle, so C312−(C33+C34+C35)=220−(1+4+10)=205C123−(C33+C43+C53)=220−(1+4+10)=205.   Answer: 205.
Answer: B
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:	Choose the correct choice:  A) 9000  B) 9400  C) 9600  D) 9800  E) 9700

Solution: Explanation:   Greatest number of 4-digits is 9999.   L.C.M. of 15, 25, 40 and 75 is 600.   On dividing 9999 by 600, the remainder is 399.   Required number  (9999 - 399)= 
 (9999 - 399) = 9_600
9600.   ANSWER IS 9600
Answer: C
find two integers, neither of which ends in a zero, and whose product is exactly 1,000	Options
A) 64 and 15,625
B) 60 and 15,625
C) 8 and 125
D) 64 and 15,635
E) 64 and 16,625

Solution: 1,000=10^3   =10x10x10   =(2x5)x(2x5)x(2x5)   =(2^3)x(5^3)   = 8x125   so the numbers are 8 and 125   ANSWER:8 and 125
Answer: C
When x is multiplied by 3, the result is 16 more than the result of subtracting x from 36. What is the value of x?
Pick one:
A) -4
B) -2
C) 11
D) 13
E) 22

Solution: The equation that can be formed is:   3x-16=36-x   or, 4x=52   or, x=13.   Answer : 13
Answer: D
After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?
Choose one:  A) Rs. 6400  B) Rs. 5600  C) Rs. 5000  D) Rs. 4800  E) None of these

Solution: Given SP = Rs. 6800   Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15) = Rs. 8000   If SP = Rs. 8000, profit = 60%   CP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs. 5000   ANSWER:Rs. 5000
Answer: C
A certain number when divided by 39 leaves a remainder 15, what is the remainder when the same number is divided by 13? Choose the correct choice from the following:
A) 7  B) 8  C) 9  D) 6  E) 2

Solution: 2xplanation:     39 + 15= 
  39 + 15 = 54
54/13= 2 (Remainder)   Answer: 2
Answer: E
What will be the reminder when (19^19+19) is divided by 20? Choose the correct choice from the following answers.
A) 18  B) 40  C) 21  D) 43  E) 28

Solution: (x^n+1) will be divisible by (x+1) only when n is odd;   (19^19+1) will be divisible by (19+1);   (19^19+1)+18 when divided by 20 will give 18 as remainder.   Correct Option : 18
Answer: A
8 liters of solution is removed from 20% milk solution and 8 liters of water is added to the solution. The resulting solution has 16% milk in it. What was the initial quantity of the 20% milk solution?	Choose the correct choice from the following:	A) 40	B) 50	C) 60	D) 70	E) 80

Solution: Allegation method.   Concentration of 40lcohol in original sol - 20%   Concentration of 40lcohol in water -- 0%   Concentration of 40lcohol in final sol -- 16%   40fter applying allegation as shown in figure they have to be mixed in 4:1 part   1 part is given as 8 ltr, so total initial volume is 5 part = 5*8= 
5*8 = 40
40 Ltrs   40NSWER:40
Answer: A
The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 8748 sq. m, the cost of fencing the field @ 25 paise per metre is  Choose the correct choice from the following choices.
A) Rs. 55.50 B) Rs. 67.50 C) Rs. 86.50 D) Rs. 94.50 E) None of these

Solution: Solution   Let length = (3x) metres and breadth = (4x) metres.   Then, 3x × 4x = 8748 ⇔ 12x2 = 8748 ⇔ x2 = 729 ⇔ x = 27.   So, length = 81 m and breadth = 108 m.   Perimeter = [2(81 + 108)] m = 378 m.   ∴ Cost of fencing = Rs. (0.25 × 378) = Rs. 94.50. Answer Rs. 94.50
Answer: D
Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temparature of the particular day is 35°C , it is equal to :  Pick.
A) 85Â°F  B) 95Â°F  C) 96Â°F  D) 97Â°F  E) None of these

Solution: Explanation:   Let F and C denotes the temparature in Fahrenheit anid Celcsius respectively.   Then, (F - 32) /(212 - 32) = (C - 0)/(100 - 0), if c = 35, then F = 95.   Answer: 95Â°F
Answer: B
In a garden, trees are planted in rows. In each row there are as many trees as the number of rows in the garden. Each tree bears as many fruits as the number of trees in each row, and each fruit has as many seeds as the number of trees in each row. If the total number of seeds from the trees in that garden is n, then : Choose the correct answer
A) n is a perfect square  B) n is an odd number  C) n is an even number  D) n is a perfect cube.  E) none

Solution: If there were 4 rows of trees, each row would have 4 trees, each tree would have 4 fruits, and each fruits would have 4 seeds. The total seeds are 4*4*4*4= 
4*4*4*4 = 256
256. 256 is a square of 16.   n is a perfect squarenswer: n is a perfect square
Answer: A
A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?  Answers
A) 7 sec	B) 6 sec	C) 4 sec	D) 2 sec	E) 9 sec

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 110 * 3/55= 
110 * 3/55 = 6
6 sec.   Answer: 6 sec
Answer: B
A, B, C, D, E, F, G, and H are all integers, listed in order of increasing size. When these numbers are arranged on a number line, the distance between any two consecutive numbers is constant. If G and H are equal to 5^12 and 5^15, respectively, what is the value of A?	Choose the correct choice from the following:
A) -24(5^12)	B) -25(5^12)	C) -24(5^6)	D) 23(5^12)	E) 24(5^12)

Solution: Ans : B   Assume that the numbers appear as shown below on the number line   A-----B-----C-----D-----E-----F-----G-----H   (5^12) (5^13)   As the values for G and H are given , we can calculate the difference between any two terms of the series .   Common Difference ,d = (5^13) - (5^12)   = (5^12) *[ 5-1 ]   = (5^12)*(4)   Also F + d = G as the terms are in equidistant and in increasing order.   So F + (5^12)*(4) = (5^12).   That is , F = (5^12) - (5^12)*(4)   = (5^12)[ 1-4]   = (5^12) (-3)   Similarly , E = F - d   = (5^12)[-3-4]   = (5^12)*(-7)   You can see a -4 getting added to the non-exponent part of the values . That is , according to the pattern , D SHOULD -25(5^12)E (5^12)*(-7-4)= (5^12)*(-11)   Following this pattern , A = (5^12)*(-25)   -25(5^12)
Answer: B
How many positive factors do 160 and 96 have in common?  Choose the most appropriate option.
A) 6	B) 12	C) 16	D) 18	E) 24

Solution: The number of common factors will be same as number of factors of the Highest Common Factor(HCF)   HCF of 160 and 96 is 32   Number of factors of 32 = 6   6nswer :6
Answer: A
An engineer undertakes a project to build a road 10 km long in 15 days and employs 30 men for the purpose. After 5 days, he finds only 2 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.  Choose the correct choice from the following
A) 15  B) 20  C) 25  D) 28  E) 30

Solution: 30 workers working already   Let x be the total men required to finish the task in next 10 days   2 km done hence remaining is 8 km   Also, work has to be completed in next 10 days (15 - 10 = 5)   We know that, proportion of men to distance is direct proportion   and, proportion of men to days is inverse proportion   Hence, X = (30 * 8 * 5) / (2 *10)   thus, X = 60   Thus, more men needed to finish the task = 60-30= 
60-30 = 30
30   Answer : 30
Answer: E