MU-NLPC/Calc-aqua_rat huggingface dataset:
The perimeter of a semi circle is 198 cm then the radius is?  Choose the correct choice from the following choices:
A) 22 B) 28 C) 98 D) 38.5 E) 13

Solution: 36/7 r = 198   => r   = 38.5   Answer: 38.5
Answer: D
. A boy has six trousers and 8 shirts. In how many different ways can he select a trouser and a shirt? Choose the correct answer:
A) 9
B) 18
C) 27
D) 36
E) 48

Solution: Explanation:   The boy can select one trouser in six ways.   The boy can select one shirt in 8 ways.   The number of ways in which he can select one trouser and one shirt is   6 * 8= 
  6 * 8 = 48
48 ways.   Answer: Option 48
Answer: E
(0.8)(power 3) - (0.5)(power 3)/ (0.8)(power 2) + 0.40 + (0.5)(power 2) is: Choose the correct choice from the following choices.
A) 0.6	B) 0.5	C) 0.35	D) 0.3	E) None of them

Solution: Given expression   = (0.8) (power 3) - (0.5)(power 3) / (0.8)(power 2) + (0.8 x 0.5) + (0.5)(power 2)   = a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)   = (a - b)   = (0.8- 0.5)= 
(0.8- 0.5) = 0.3
0.30   Answer is 0.3.
Answer: D
If the value of a piece of plaza decreases by 10% while the new tax rate on the plaza represent 110% of the original tax rate, what is the effect on the taxes?	Choices:	A) a - taxes increase by 10%	B) b- taxes increase by 1%	C) c- there is no change in taxes	D) d- taxes decrease by 1%	E) c- taxes decrease by 10%

Solution: Cansider the value of plaza = 100, Original tax rate 10%, hence tax value = 100*10% = 10.   Decreased value of plaza = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9   10-9.9 = decrease by 1%.   Answer d- taxes decrease by 1%.
Answer: D
A dealer marks his goods 20% above cost price. He then allows some discount on it and makes a profit of 8%. The rate of discount is:  Choose the correct answer:
A) 16 %
B) 22 %
C) 25 %
D) 10 %
E) 15 %

Solution: Explanation:   C.P = Rs. 100   Marked Price = Rs. 120,   S.P = Rs. 108   10 %iscount = (12/120 × 100)% = 10%   ANSWER:10 %
Answer: D
A solution of cough syrup has 15% alcohol. Another solution has 5% alcohol. How many litres of the second solution must be added to 20 litres of the first solution to make a solution of 10% alcohol? Options
A) 10	B) 5	C) 15	D) 20	E) 25

Solution: Hence both the types should be added in the ratio of 1 : 1 to obtain the required strength.   Hence 20 litres of first type should be added to the 20 litres of the second type to get the desired solution.   ANSWER:20
Answer: D
A librarian has a set of nine books, including four different books about Abraham Lincoln. The librarian wants to put the nine books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other five books. How many different arrangements of the nine books are possible?  Pick one.
A) (9!)/(4!)
B) (4!)(5!)
C) (4!)(6!)
D) (4!)(9!)
E) (4!)(5!)(9!)

Solution: You can club the four Lincoln books as one, which leaves us with five other books plus this one to think about. So, these six items can be arranged in 6! ways, and since the four books can be moved around among themselves with each combination giving us a new overall combination, we have an additional 4! ways. Therefore, the answer would be 6!*4!, which is (4!)(6!).
Answer: C
Which of the following is a prime number ??
Pick: A) 33 B) 81 C) 89 D) 93 E) 10

Solution: 89   89   89learly, 89 is a prime number.
Answer: C
The perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 55, then how long is the base of isosceles triangle? Choose the correct answer
A) 5  B) 10  C) 15  D) 20  E) 25

Solution: The base of the isosceles triangle is 55-20-20= 
55-20-20 = 15
15 units   The answer is 15.
Answer: C
One fourth of one third of two fifth of a number is 15. What will be40% of that number
Choose the correct option
A) 140  B) 150  C) 180  D) 200  E) 300

Solution: Explanation:   (1/4) * (1/3) * (2/5) * x = 15 then x = 15 * 30= 
15 * 30 = 450
450   40% of 450= 180   Option 180
Answer: C
Pipe A fills a tank of capacity 800 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?  Choose the correct choice from the following
A) 48 minutes	B) 14 minutes	C) 39 minutes	D) 40 minutes 20 seconds	E) None of these

Solution: In one cycle they fill 40+30-20= 
40+30-20 = 50
50 liters   800= 50*n => n = 16   here n = number of cycles.   total time = 16*3= 
16*3 = 48
48 as in one cycle there are 3 minutes.   thus 48 minutes   48 minutesNSWER:48 minutes
Answer: A
What was the day of the week on, 16th July, 1776?
Choose the most appropriate option:
A) Saturday
B) Monday
C) Tuesday
D) Friday
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 + 2 days)   Total number of odd days = (0 + 2)= 
(0 + 2) = 2
2.   Required day was 'Tuesday'.   Answer is Tuesday.
Answer: C
Each of the positive integers a and c is a four-digit integer. If each of the digits 0 through 9 appears in one of these three integers, what is the maximum possible value of the sum of a and c? Options:	A) 18695	B) 18325	C) 18365	D) 18395	E) 18485

Solution: According to the stem we should use the digits 0 through 9 to construct 2 four-digit integers, so that their sum is as big as possible.   To maximize the sum, maximize the thousands digits of a and c, so make them 9 and 8.   Next, maximize hundreds digits. Make them 7 and 6 .   Next maximize 10's digit place by 5 and 4   Use the remaining digits (3,and 2) for units digits.   So, a would be 9753,and c would be 8642.   9753 + 8642= 
9753 + 8642 = 18_395
18395   Answer: 18395.
Answer: D
In a series of consecutive numbers, 26 is the eighth smallest number and 25 is the tenth largest number. What is the range of the series? Pick one.
A) 32 B) 30 C) 31 D) 16 E) 14

Solution: Imp:All are consecutive odd numbers.   26 is the 8th smallest ,there are 7 numbers smaller then 26 ,smallest number :  26-14= 
  26-14 = 12
12   25 is the 10th largest ,so there are 9 numbers larger then 25, largest number: 25+18= 
 25+18 = 43
43   Range:43-12= 
43-12 = 31
31   Ans : 31
Answer: C
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions. Choose the correct choice from the following options
A) 252 m	B) 704 m	C) 352 m	D) 808 m	E) None of these

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.   = 500 * 2 * 22/7 * 22.4= 
500 * 2 * 22/7 * 22.4 = 70_400
70400 cm= 704 m   ANSWER:704 m
Answer: B
Best friends Sprite and Icey have are playing a game of marbles. They invite 16 of their friends to play with them. There are 36 marbles in the bag. If all 18 people are playing, how many marbles does each person get?  Pick.
A) 3  B) 2  C) 5  D) 6  E) 7

Solution: Answer= 2   36 / 18= 
36 / 18 = 2
2   Answer= 2
Answer: B
If a 3-digit integer is selected at random from the integers 100 through 199, inclusive, what is the probability that the second digit is two greater than the first digit and the third digit is less than the second digit?  Choose the correct choice from the following.
A) 1/100	B) 3/100	C) 2/103	D) 2/150	E) 1/50

Solution: Hundreds digit has to be 1 . So tens digit needs to be 2 greater than 1   1+2= 
1+2 = 3
3   The tens digit is 3, and the units digit must be less than the tens digit so the units digit must be less than 3   0, 1, and 2 are all less than 3   140, 141, and 142 are all acceptable numbers giving us 3 possible numbers   Total numbers between 100 and 199= (199-100)+1= 
(199-100)+1 = 100
100   Probability= 3/100   Answer 3/100
Answer: B
Find the odd man out
31, 37, 41, 45, 55, 58, 61, 67  Options
A) 31
B) 41
C) 67
D) 58
E) 61

Solution: as 58 is only odd number.   ANSWER:58
Answer: D
The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?	Answers
A) 16 2/3% loss
B) 16 2/8% loss
C) 16 3/3% loss
D) 36 2/3% loss
E) 56 2/3% loss

Solution: 15 CP = 18 SP   18 --- 3 CP loss   100 --- ? => 16 2/3% loss   16 2/3% lossnswer:16 2/3% loss
Answer: A
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?  Choose the correct choice from the following: A) 227 B) 350 C) 881 D) 277 E) 271

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x = 350 m.   Answer: 350
Answer: B
A straight pipe 1 yard in length was marked off in halves and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?  Choose the correct choice from the following choices.
A) 1/6 and 1/4 only
B) 1/6 and 1/3 only
C) 1/6, 1/4, and 1/3
D) 1/12, 1/6 and 1/4
E) 1/12, 1/6, and 1/3

Solution: Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:   Here 2th : 0/2, 1/2, 2/2   and 3rd : 0/3, 1/3, 2/3, 3/3   Now with understood common denominator 6 write the numbers : for 2th : 0,3,6 and for 3rd : 0,2,4,6   Now comine : 0,2,3,4,6   Now find the cut with denominator 6 (Substracrt adjacent terms : 1/3, 1/6, 1/6, 1/3 i.e. 1/3 and 1/6 after removing duplicates.   answer : 1/6 and 1/3 only
Answer: B
In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?	Choose the correct choice:
A) 5	B) 4	C) 3	D) 2	E) 0

Solution: = 147,000   = 147 x 1000   = (3) x (7 x 7) x (2x2x2) x (5x5x5)   = 2^3 x 3^1 x 5^3 x 7^2   red = 7^2 = 49   ANSWER:2
Answer: D
Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?	Choose the correct choice from the following choices.
A) 187
B) 400
C) 168
D) 286
E) 268

Solution: 441 = P(21/20)2   P = 400   Answer: 400
Answer: B
Two water pumps, working simultaneously at their respective constant rates, took exactly five hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?	Choose the correct choice
A) 5  B) 16/3  C) 11/2  D) 6  E) 25/3

Solution: Let x be the rate of the slower pump. Then 1.5x is the rate of the faster pump.   Both pumps together can fill 1/5 of the pool each hour.   2.5x = 1/5   x = 1/12.5   1.5x = 3/25 so the faster pump could fill the pool in 25/3 hours.   The answer is 25/3.
Answer: E
The speed of a boat in upstream is 120 kmph and the speed of the boat downstream is 154 kmph. Find the speed of the boat in still water and the speed of the stream?  Select:
A) 17	B) 99	C) 88	D) 66	E) 23

Solution: Speed of the boat in still water = (120+154)/2= 
(120+154)/2 = 137
137 kmph. Speed of the stream= (154-120)/2= 
(154-120)/2 = 17
17 kmph. 17nswer:17
Answer: A
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 7 minutes, then the area of the park (in sq. m) is:
Choose the correct choice from the following choices:
A) 153601
B) 153600
C) 153602
D) 117600
E) 153604

Solution: Perimeter = Distance covered in 7 min. =(12000/60) x 7m = 1400 m.   Let length = 3x metres and breadth = 2x metres.   Then, 2(3x + 2x) = 1400 or x = 140.   Length = 420 m and Breadth = 280 m.   Area = (420 x 280) m2 = 117600 m2.   Answer: 117600
Answer: D
The sequence a1, a2, … , an, … is such that an=2an−1−x for all positive integers n ≥ 2 and for certain number x. If a5=99 and a3=27, what is the value of x? Choose the correct choice from the following choices.
A) 3 B) 9 C) 18 D) 36 E) 45

Solution: a5= 2*a4 - x = 99   a4 = 2*a3 - x = 2*27 - x   therefore;   a5 = 2*(54 - x ) -x = 99   108 - 3*x = 99   therefore X = 3   This the answer is "3"
Answer: A
The combined age of husband and wife on their 20th wedding anniversary was twice than it was at the time of wedding. If the husband is 3 years older than his wife. How old was he at the time of his marriage?
Choose one.
A) 21.5 years B) 21.9 years C) 31.5 years D) 21.7 years E) 61.5 years

Solution: Explanation:   Let the ages of husband and wife at the time of their 20th wedding anniversary be X years and Y years respectively and X > Y.   Their combined age = (X + Y) years.   The ages of both husband and wife at the time of wedding will be (X – 20) years and (Y – 20) years respectively.   Their combined age = (X – 20) + (Y – 20)   = (X + Y – 40) Years   By first information, we have   (X + Y) = 2( X + Y – 40)   X + Y = 2X + 2Y - 80   Therefore, X + Y = 80-------A   and by second information, we have   X – Y =3 ----------------------B   Solving A and B, we get X = 41.5 years   Therefore, the age of husband at the time of their 20th wedding anniversary X = 41.5 years   Age at the time of marriage = 41.5 years – 20 years = 21.5 years.   21.5 yearsNSWER:21.5 years
Answer: A
The length of a rectangle is three - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?  Select
A) 240 sq.units	B) 140 sq.units	C) 120 sq.units	D) 130 sq.units	E) 150 sq.units

Solution: Given that the area of the square = 1600 sq.units   => Side of square = √1600 = 40 units   The radius of the circle = side of the square = 35 units Length of the rectangle = 3/5 * 40= 
3/5 * 40 = 24
24units   Given that breadth= 10 units   240 sq.unitsrea of the rectangle = lb = 24* 10= 
24* 10 = 240
240 sq.units   240 sq.unitsnswer:240 sq.units
Answer: A
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
Pick one:
A) 227 B) 299 C) 285 D) 161 E) 212

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (15)   = 285 cm2   Answer: 285
Answer: C
We have 7 people and 4 chairs. In how many ways chairs can be occupy?	Choices
A) 840 B) 720 C) 650 D) 914 E) 796

Solution: no. of ways they can be occupy = 7*6*5*4= 
7*6*5*4 = 840
840   840nswer is 840
Answer: A
A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?  Pick one.
A) 2  B) 5  C) 9  D) 7  E) 9

Solution: Quantity of milk in the mixture = 90/100 (70) = 63 litres.   After adding water, milk would form 87 1/2% of the mixture.   Hence, if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63 => x = 72   Hence 72 - 70= 
72 - 70 = 2
2 litres of water must be added.   2nswer: 2
Answer: A
The function f is defined for all positive integers r by the following rule. f(r) is the number of positive integers each of which is less than r and has no positive factor in common with r other than 1. If x is any prime, number then f(x)=	Choose the correct option
A) (x+1)/2
B) x-2
C) x-1
D) (x-1)/2
E) 2

Solution: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.   This question for instance basically asks: how many positive integers are less than given prime number x which have no common factor with p except 1.   Well as x is a prime, all positive numbers less than x have no common factors with x (except common factor 1). So there would be x-1 such numbers (as we are looking number of integers less than x).   For example: if x=6 how many numbers are less than 6 having no common factors with 6: 1, 2, 3, 4, 5, --> 6-1=5.   Answer: x-1.
Answer: C
What is the solution of the following simultaneous equations?
x + y + z = 6, x + 2y + 3z = 14 and x + 3y + z = 10  Pick
A) 3
B) 7
C) 8
D) 1
E) 2

Solution: x + y + z = 6 .... (i)   x + 2y + 3z = 14 .... (ii)   x + 3y + z = 10   From (i), we get z = 6 - x - y   Substitute it in (ii) and (iii)   We have from (ii)   x + 2y + 18 - 3x - 3y = 14 or 2x + y   + 2  + 18 - 3  - 3= 
  + 2  + 18 - 3  - 3 = 14
14 or 2x + y= 4   Similarily, from (iii)   x + 3y + 6 - x - y = 10 or 2y = 4 or y = 2   On solving, we get y = 2, x = 1, z = 3.   3nswer:3
Answer: A
If 9 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?	Select the correct option
A) 127 B) 237 C) 387 D) 400 E) 481

Solution: Explanation:   Let the required no of hectares be x. Then   Men --- Hectares---400ays   9---------80---------24   36---------x---------30   More men, More hectares (400irect proportion)   More days, More hectares (400irect proportion)   x=36/9*30/24*80= 
36/9*30/24*80 = 400
400   Answer: 400
Answer: D
When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 12-inch boxes. If the university pays $0.50 for every box, and if the university needs 2.4 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?  Select the correct option:
A) $250 B) $275 C) $510 D) $1,250 E) $2,550

Solution: The volume of each box is 20*20*12= 
20*20*12 = 4_800
4800 cubic inches.   Number of boxes= 2,400,000/4800 = 500 boxes   Total cost = 500×$0.5=$250   The answer is $250.
Answer: A
Erica is four times as old as Blair. Nicole is three years older than Erica.
The sum of their ages is 21. How old is Erica?  Choose the correct choice: A) 8 B) 18 C) 19 D) 22 E) 29

Solution: The problem concerns three ages. Let x equal Blair’s age. Blair’s age: x   Represent the amounts using the same variable. Erica’s age: 4x   Nicole’s age: 4x 3   Write an equation showing the sum equal to 21. x 4x 4x 3 21   Solve the equation. x 4x 4x 3 21   The variable x is equal to 2, but that 9x 3 21   doesn’t answer the question posed in the 9x 18   problem. The problem asks you to find   Erica’s age, which is equal to 4x, or 4(2). x 2   Answer: Erica is 8 years old.   Check: Blair is 2, Erica is 8, and Nicole is 11. The ages total 21.   correct answer 8
Answer: A
What is the lowest positive integer that is divisible by each of the integers 1 through 10 inclusive?  Choose the correct answer:
A) 420
B) 840
C) 1260
D) 2520
E) 5020

Solution: We have to find the LCM of 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, and 2*5.   The LCM is 1*2^3*3^2*5*7= 2520   The answer is 2520.
Answer: D
Simplify: 1605 x 1605
Choose the correct option
A) 2576025	B) 2567025	C) 2657025	D) 2756025	E) None of them

Solution: = 1605 x 1605 = (1605)^2 = (1600 + 5)^2 = (1600)^2 + (5)^2 + 2 x 1600 x 5   = 2560000 + 25 + 16000= 
2560000 + 25 + 16000 = 2_576_025
2576025.   2576025nswer is 2576025.
Answer: A
Which of the following is a quadratic equation? Choose the correct choice: A) x1/2 + 2x + 3 = 0 B) x - 1)(x + 4) = x2 + 1 C) x4 - 3x + 5 = 0 D) (2x + 1)(3x - 4) = 2x2 + 3 E) None of these

Solution: Sol.(d) Equations in options (a) and (c) are not quadratic equations as in (a) max. power of x is fractional and in (c), it is not 2 in any of the terms.   For option (b), (x – 1)(x +4) = x2 + 1   or x2 + 4x - x + 4 = x2 + 1   or 3x - 5 = 0   which is not a quadratic equations but a linear.   For option (d), (2x + 1)(3x – 4) = 2x2 + 3   or 6x2 - 8x + 3x - 4 = 2x2 + 3   or 4x2 - 5x - 7 = 0   which is clearly a quadratic equation.   Answer (2x + 1)(3x - 4) = 2x2 + 3
Answer: D
Two trains having length of 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions (on parallel tracks). The time which they take to cross each other, is	Choose one:  A) 10.8 s  B) 12 s  C) 9.8 s  D) 8 s  E) 7 s

Solution: Explanation:   Distance = 140+160= 
140+160 = 300
300 m   Relative speed= 60+40= 
60+40 = 100
100 km/hr= (100×10)/36 m/s   Time = distance/speed = 300 / (100×10)/36 = 300×36 / 1000 = 3×36/10 = 10.8 s   10.8 snswer: Option 10.8 s
Answer: A
A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
Answers
A) 100 m  B) 150 m  C) 190 m  D) 200 m  E) 220 m

Solution: Explanation:   Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr   Distance covered in 6 minutes =1/60X6km=1/10km=100m   Distance between the thief and policeman = (200 – 100) m = 100 m.   100 mNSWER IS 100 m
Answer: A
Suppose you flip a fair coin six times. What is the probability that, in six flips, you get at least one head?
Choose the most appropriate option.
A) 5/8  B) 13/16  C) 15/16  D) 31/32  E) 63/64

Solution: Best way of solving an "at least 1" type of question is to compute "1 - probability of flipping 0 heads"   probability of flipping either a head or a tail = 1/2   probability of flipping 6 tails in a row (1/2)^6   probability of flipping at least 1 head = 1 - (1/2)^6 = 63/64 (answer 63/64)
Answer: E
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 9 can be used only once? Choose the correct choice from the following options
A) 20
B) 150
C) 225
D) 304
E) 320

Solution: 4 options for the first digit: 2, 4, 6, 8;   5 options for the second digit: 1, 3, 5, 7, 9;   4 options for the third digit: 2, 3, 5, 7;   4 options for the fourth digit: 0, 3, 6, 9.   Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320   Numbers with two 9-s, 9X9X 4*1*4*1=16.   Thus there are 320-16= 
320-16 = 304
304 such numbers.   Answer: 304.
Answer: D
P and Q can complete a work in 80 days and 48 days respectively. P alone started the work and Q joined him after 16 days till the completion of the work. How long did the work last? Choose one
A) 5 days
B) 10 days
C) 14 days
D) 22 days
E) 40 days

Solution: 40 daysxplanation :   Work done by P in 1 day = 1/80   Work done by Q in 1 day = 1/48   Work done by P in 16 days = 16 Ã— (1/80) = 1/5   Remaining work = 1 â€“ 1/5 = 4/5   Work done by P and Q in 1 day = 1/80 + 1/48=1/30   Number of days P and Q take to complete the remaining work = (4/5) / (1/30)= 
(4/5) / (1/30) = 24
24   Total days= 16 + 24= 
16 + 24 = 40
40   Answer : Option 40 days
Answer: E
A man sitting in a train which is travelling at 100 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed? Choose the correct choice.
A) 52 kmph.
B) 62 kmph.
C) 12 kmph.
D) 80 kmph.
E) None

Solution: Solution   Relative Speed	= (280 / 9)m/sec   = (280/9 x 18/5)   = 112 kmph.   Speed of the train	= (112 - 100)= 
(112 - 100) = 12
12 kmph.   Answer 12 kmph.
Answer: C
Two trains, each 100 m long, moving in opposite directions, cross other in 12 sec. If one is moving twice as fast the other, then the speed of the faster train is? Choose one.
A) 26 km/hr
B) 40 km/hr
C) 60 km/hr
D) 77 km/hr
E) 46 km/hr

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/12 = 3x => x = 50/9.   So, speed of the faster train = 100/9 = 100/9 * 18/5= 
100/9 * 18/5 = 40
40 km/hr.   Answer:40 km/hr
Answer: B