MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 99 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there?
Choose the correct choice from the following answers
A) 2 B) 4 C) 8 D) 69 E) 32

Solution: lets assign variables to all the areas in Venn Diagram of Three.   three different Units are 69OG, Cat, Snake= Total = 99   Only 69og= d=15   Only Cat = c=10   Only Snake = s   Exactly 69og and Cat= 5   Exactly 69og and Snake = x   Exactly Cat and Snake = y   all three= 3   so 99=15+10+5+3+x+y+s   we need to know total snakes= x+y+s+3 = 69   answer:69
Answer: D
A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient? Choose the correct choice from the following options.
A) 227
B) 66
C) 10
D) 99
E) 77

Solution: 400 --- 31   400 --- 3   120 --- ?   400*3 = 120*x => x =10 days   Answer: 10
Answer: C
What is the probability of rolling two six-sided dice, and getting a different number on each die?
Answers
A) 5/6  B) 1/3  C) 4/9  D) 5/9  E) 7/18

Solution: MAGOOSHOFFICIAL SOLUTION   For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.   6 x 5 = 30 possibilities out of 36 total possibilities. (For total possibilities we get 6 x 6 = 36).   30/36 = 5/6   5/6nswer: 5/6.
Answer: A
A box contain Red, Blue and Green colored balls. The number of Red balls is 80 and the number of Blue balls is 60.
The number of Green balls subtracted from the number of Red balls is the same as the number of Green balls added with the number of Blue balls. Then the number of Green balls is?  Choose the most appropriate option.
A) 80	B) green balls = 70	C) 60	D) 85	E) 140

Solution: Answer   Let the number of Green balls be x.   Then, x - 60= 80 - x   â‡’ 2x = 80+ 60= 
80+ 60 = 140
140   â‡’ 2x= 140   âˆ´ x = 70   Correct Option: green balls = 70
Answer: B
The total age of A and B is 20 years more than the total age of B and C. C is how many years younger than A.? Choose the correct choice from the following answers:
A) 20
B) 12
C) 15
D) 16
E) 10

Solution: (20+B)-(B-C)=20   20-C=20   20nswer is 20
Answer: A
A man can row with a speed of 40 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?  Select the correct option:
A) 29	B) 378	C) 20	D) 27	E) 45

Solution: M = 40   S = 5   DS = 40 + 5= 
40 + 5 = 45
45   Answer: 45
Answer: E
There are 6 ladies and 3 gents to dine at a round table. In how many ways can they seat themselves so that no two gents are seated together.
Choose the most appropriate option:
A) 8540  B) 2880  C) 8640  D) 6560  E) 8860

Solution: First arrange the ladies. This is a circular arrangment. 6 Gents can be arranged in 5! ways.   Now there are 4 spaces (space in between two ladies) and we have to seat 3 gents there.   First select 3 places out of 4 available places. can be done in 4C3 ways. Then arrange 3 gents there in 3! ways.   Total: 5!*4C3*3! = 2880   2880 is the answer.
Answer: B
A butler stole wine from a butt of sherry which contained
40% of spirit and he replaced,what he had stolen by wine
containing only 16% spirit. The butt was then of 24%
strength only. How much of the butt did he steal?
Choose the correct choice from the following options:
A) 1/3 OF THE BUTT	B) 2/3 OF THE BUTT	C) 1/4 OF THE BUTT	D) 1/8 OF THE BUTT	E) 1/9 OF THE BUTT

Solution: Wine containing 40%spirit Wine containing 16% spirit   Wine containing 24% spirit   8 16   They must be mixed in the ratio of =1:2.   Thus 1/3 of the butt of sherry was left   hence the butler drew out 2/3 of the butt.   ANSWER 2/3 OF THE BUTT
Answer: B
If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:	Choose the correct choice from the following answers
A) -10.0	B) -0.5	C) -0.4	D) -0.2	E) 10.0

Solution: (0.2)x = 2.   Taking log on both sides   log (0.2)x = log 2.   x log (0.2) = 0.3010, [since log 2 = 0.3010].   x log (2/10) = 0.3010.   x [log 2 - log 10] = 0.3010.   x [log 2 - 1] = 0.3010,[since log 10=1].   x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].   x[-0.699] = 0.3010.   x = 0.3010/-0.699.   x = -0.4306….   x = -0.4 (nearest tenth)   correct answer -0.4
Answer: C
Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Choose the most appropriate option:
A) 19  B) 19.7  C) 20  D) 21.1  E) 23

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   19.7)
Answer: B
Calculate the different number of ways 5 boys and 3 girls can sit on a bench?	Choices
A) 40120  B) 40220  C) 40420  D) 40320  E) 40325

Solution: npn = n!   8p8 = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320   40320
Answer: D
A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained? Choose the correct choice from the following choices
A) 9:1	B) 9:6	C) 9:3	D) 9:2	E) 9:9

Solution: Milk = 3/5 * 20= 
3/5 * 20 = 12
12 liters, water= 8 liters   If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.   Remaining milk = 12 - 6= 
12 - 6 = 6
6 liters   Remaining water= 8 - 4= 
8 - 4 = 4
4 liters   10 liters of pure milk are added, therefore total milk= (6 + 10)= 
(6 + 10) = 16
16 liters.   The ratio of milk and water in the new mixture= 16:4 = 4:1   If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10= 
4/5 * 10 = 8
8 liters.   Amount of water removed= 2 liters.   Remaining milk = (16 - 8)= 
(16 - 8) = 8
8 liters.   Remaining water= (4 -2)= 
(4 -2) = 2
2 liters.   The required ratio of milk and water in the final mixture obtained= (8 + 10):2 = 18:2 = 9:1.9:1nswer: 9:1
Answer: A
The radius of the wheel of a bus is 140 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is	Choose the correct choice from the following.
A) 125 B) 250 C) 300 D) 330 E) None of these

Solution: Radius of the wheel of bus = 140 cm. Then,   circumference of wheel = 2Ï€r = 280Ï€ = 880 cm   Distance covered by bus in 1 minute   = 66â„60 Ã— 1000 Ã— 100 cms   Distance covered by one revolution of wheel   = circumference of wheel   = 880 cm   âˆ´ Revolutions per minute = 6600000/60Ã—880 = 125   125nswer 125
Answer: A
The number of boys in a class is four times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
Choose one:
A) A)48
B) B)44
C) C)42
D) D)40
E) E)38

Solution: Explanation:   Let number of girls = x and number of boys = 4x.   Then, 4x + x = 5x = total number of students.   Thus, to find exact value of x, the total number of students must be divisible by 5.   Answer: 40
Answer: D
A tradesman by means of his false balance defrauds to the extent of 30%? in buying goods as well as by selling the goods. What percent does he gain on his outlay? Choose the correct choice from the following answers: A) 37 B) 69 C) 65 D) 78 E) 56

Solution: Explanation:   g% = 30 + 30 + (30*30)/100= 
30 + 30 + (30*30)/100 = 69
69%   Answer: 69
Answer: B
If there are twice as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is men who own cars?
Choose the correct choice:  A) 3⁄20  B) 11⁄60  C) 2⁄15  D) 1⁄3  E) 11⁄20

Solution: Consider a group of 100 men and 200 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car.   Half of them are men, and the other half are women, more precisely 60.   It means that there are 100 - 60= 
100 - 60 = 40
40 men who own a car, and this represents 40/300= 2/15 of the total.   Answer 2⁄15
Answer: C
In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
Choose the correct choice from the following:
A) 172000
B) 12600
C) 45920
D) 43200
E) None

Solution: Solution:   The four person who wish to sit facing forward can be seated in: 5P4 ways and 3 who wish to sit facing towards the rear can be seated in: 5P3 ways and the remaining 3 can be seated in the remaining 3 seats in 3P3 ways. Total number of ways =5P4 *5P3 *3P3 = 43200.   Answer: Option 43200
Answer: D
The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 87°, what fraction of the wheel’s area is represented by the smallest sector? Select the correct option.
A) 1/120 B) 1/100 C) 1/80 D) 1/60 E) 1/40

Solution: The largest angle is 87.   Let d be the difference between any two angles in the progression.   The sum of all the angles will be:   87 + (87-d) + (87-2d) + ... + (87-7d) = 696 - 28d   The sum of all the central angles in a circle = 360   696 - 28d = 360   d = 336/28= 
336/28 = 12
12   The smallest sector is (87-7d)= 87-7*12= 
87-7*12 = 3
3   3/360= 1/120   The answer is 1/120.
Answer: A
If the numerator of a fraction be increased by 15% and its denominator be diminished by 8% , the value of the fraction is 15/16. Find the original fraction.
Choose the most appropriate option: A) 3/4 B) 1/4 C) 1/2 D) 1 E) None of them

Solution: Let the original fraction be x/y.   Then (115%of x)/(92% of y)=15/16 => (115x/92y)=15/16   =((15/16)*(92/115))=3/4   3/4nswer is 3/4.
Answer: A
The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 21.5 years. What is the age of the new member ?  Choose the correct choice from the following options:  A) 20 years  B) 19 years  C) 22 years  D) 23 years  E) 24 years

Solution: The average age of the 5 members is 20 years   => The sum of the ages of the 5 members is 20*5= 
20*5 = 100
100 years   Once the new member joins, the average age becomes 21.5 years.   Let the age of the new member be x.   Then (110+x)/6= 21.5   => x = 19 years   Answer 19 years
Answer: B
A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?	Choose the correct choice
A) 33 B) 37 C) 40 D) 38 E) 27

Solution: Let the distance be x km ,   the speed in which he moved = v kmph   Time taken when moving at normal speed - time taken when moving 3 kmph faster = 40 minutes   ⇒xv−xv+3=4060⇒x[1v−1v+3]=23⇒x[v+3−vv(v+3)]=23⇒2v(v+3)=9x................(Equation1)   Time taken when moving 2 kmph slower - Time taken when moving at normal speed = 40 minutes   ⇒xv−2−xv=4060⇒x[1v−2−1v]=23⇒x[v−v+2v(v−2)]=23⇒x[2v(v−2)]=23⇒x[1v(v−2)]=13⇒v(v−2)=3x................(Equation2)Equation1Equation2⇒2(v+3)(v−2)=3⇒2v+6=3v−6⇒v=12Substituting this value of v in Equation 1⇒2×12×15=9x=>x=2×12×159=2×4×153=2×4×5=40Hence distance = 40 km   Answer :40
Answer: C
If an article is sold at 5% gain instead of 5% loss,the seller gets Rs 6.72 more. The C.P of the article is? Select the correct option
A) 132.82  B) 138.55  C) 148.81  D) 150.45  E) None

Solution: Sol.   100 * 10/6.72 = 148.81 answer   Answer 148.81
Answer: C
4 DICE ARE THROWN AND THE SUM OF THE NUMBERS NOTED IS 10. FIND THE PROBABILITY THAT ALL THE NUMBERS LIE BETWEEN 2 AND 5 (both inclusive)?
Pick:
A) 11/79	B) 10/79	C) 12/79	D) 13/79	E) 14/79

Solution: Sum of numbers noted on 4 dice(with six faces) to be 10 will include combinations:   ( 1,1,2,6)(1,1,3,5)(1,1,4,4)(1,1,5,3)(1,1,6,2)(1,2,1,6)(1,2,2,5)(1,2,3,4)(1,2,4,3)(1,2,5,2)(1,2,6,1)(1,3,1,5)(1,3,2,4)(1,3,3,3)(1,3,4,2)(1,3,5,1)(1,4,1,4)(1,4,2,3)(1,4,3,2)(1,4,4,1)(1,5,1,3)(1,5,2,2)(1,5,3,1)(1,6,1,2)(1,6,2,1)   (2,1,1,6)(2,1,2,5)(2,1,3,4)(2,1,4,3)(2,1,5,2)(2,1,6,1)(2,2,1,5)(2,2,2,4)(2,2,3,3)(2,2,4,2)(2,2,5,1)(2,3,1,4)(2,3,2,3)(2,3,3,2)(2,3,4,1)(2,4,1,3)(2,4,2,2)(2,4,3,1)(2,5,1,2)(2,5,2,1)(2,6,1,1)   (3,1,1,5)(3,1,2,4)(3,1,3,3)(3,1,4,2)(3,1,5,1)(3,2,1,4)(3,2,2,3)(3,2,3,2)(3,2,4,1)(3,3,1,3)(3,3,2,2)(3,3,3,1)(3,4,1,2)(3,4,2,1)(3,5,1,1)   (4,1,1,4)(4,1,2,3)(4,1,3,2)(4,1,4,1)(4,2,1,3)(4,2,2,2)(4,2,3,1)(4,3,1,2)(4,3,2,1)(4,4,1,1)   (5,1,1,3)(5,1,2,2)(5,1,3,1)(5,2,1,2)(5,2,2,1)(5,3,1,1)   (6,1,1,2)(6,1,2,1) ------- Total 79   Combinations with all the numbers lie between 2 and 5 are (2,2,2,4)(2,2,3,3)(2,2,4,2)(2,3,2,3)(2,3,3,2)(2,4,2,2)(3,2,2,3)(3,2,3,2)(3,3,2,2)(4,2,2,2) ------Total 10   So probability=10/79   ANSWER:10/79
Answer: B
If the sum of two numbers is 30 and the sum of their squares is 840, then the product of the numbers is	Options.
A) 40
B) 44
C) 80
D) 88
E) 30

Solution: Sol.   Let the numbers be x and y.   Then, (x+y) = 30 and x2 + y2 = 840.   Now, 2xy = (x+y)2 - (x2 + y2)   = (30)2 - 840= 900 - 840= 
900 - 840 = 60
60   xy= 30.   Answer 30
Answer: E
The 40 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?
Choose the correct option.
A) 4  B) 6  C) 8  D) 9  E) 10

Solution: The formula is Total = A+B+8 - sum of exactly two + 2*all three + neither   21+18+19-x-2*5=40   solving for x you get 8   Answer 8
Answer: C
If x + y = 13 and x – y = 3, then x^2 - y^2 =  Choose the correct option
A) -4
B) 4
C) 10
D) 39
E) 40

Solution: The fastest approach has already been shown. Here's one more option.   Given:   x + y = 13   x – y = 3   Add the two equations to get: 2x = 16, which means x = 8   If x = 8, we can plug that value into either equation, to conclude that y = 5   If x = 8 and y = 5, then x² - y² = 39   Answer: 39
Answer: D
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 6625, what is the length of the plot in metres?
Options.
A) 333 B) 250 C) 288 D) 276 E) 1999

Solution: Let length of plot = L meters, then breadth = L - 20 meters   and perimeter = 2[L + L - 20] = [4L - 40] meters   [4L - 40] * 26.50 = 6625   [4L - 40] = 6625 / 26.50= 
6625 / 26.50 = 250
250   4L= 290   L = 240/4= 72.5 meters.   Answer: 250
Answer: B
$400 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is
Options.
A) $100 B) $150 C) $160 D) $200 E) $250

Solution: A:(B+$160) = 2:3   A's share = 400*2/5= 
400*2/5 = 160
$160   Answer is $160
Answer: C
In how many W ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?	Choose the correct option.
A) 720  B) 864  C) 900  D) 936  E) 1,296

Solution: Total number of four letter passwords = 6*6*6*6= 
6*6*6*6 = 1_296
1296 ------(1)   Total number of passwords in which no letter repeats= 6C4*4!= 15*24= 
15*24 = 360
360------(2)   therefore required value W= (1)-(2)= 1296-360=936.936
Answer: D
It is currently 8:12 PM. At what time in the morning was it exactly 205,106 minutes ago?
Choose the correct option.
A) 9:14	B) 9:16	C) 9:42	D) 9:44	E) 9:46

Solution: Convert 205,106 minutes to hours by dividing by 60: 205,106/60 = 3,418 R26. That is 3,418 hours and 26 minutes. Convert 3,418 hours to days by dividing by 24: 3,418/24 = 142 R10. That is 142 days and 10 hours. Now, 142 days previous was 8:12 PM. Another 10 hours previous was 10:12 AM. Another 26 minutes previous was 9:46 AM (Subtract the 12 minutes of 10:12 from 26 to get 14. Then subtract 14 from 60 to get 46). 9:46
Answer: E
A sum of money becomes Rs 13,380 in 3 years and Rs 20,070 in 6 years at compound interest. The initial sum is?	Pick one
A) Rs 8927  B) Rs 8922  C) Rs 89298  D) Rs 8920  E) Rs 8921

Solution: Use the formula Amount = Principal Amount(1 + R/100)n   Where r is rate and t is time in years   =>13,380 = P(1+R/100)2 --(1)   =>20,070 = P(1+R/100)6 --(2)   => 1.5 = (1+R/100)4   => P = Rs 8920   ANSWER:Rs 8920
Answer: D
In a factory, an average of 50 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 48 sets/day . The average production per day for day last 5days is ? Select
A) 20	B) 36	C) 48	D) 38	E) 59

Solution: Production during these 5 days = Total production in a month - production in first 25 days.   = 30 x 48 - 25 x 50   = 190   ∴ Average for last 5 days = 190 / 5= 
190 / 5 = 38
38   38
Answer: D
A money lender lent a total of $1800 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1800, how much did he lend to each of the two customers?  Choose the correct choice from the following choices:  A) 700; 1100  B) 1200; 600  C) 1000; 800  D) 1200; 800  E) None of the above

Solution: The method given above is the one given in the book.   However the method I used was   (1*x*5)/100 + (1800-x)*6/100 = 1800*5.67/100   Simplifying we get x=594   Though the actual answer is 600   ANSWER:1200; 600
Answer: B
A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 28 m * 2 m * 0.75 m?	Pick: A) 28000 B) 27908 C) 78902 D) 25000 E) 27991

Solution: 28 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x   28 = 1/100 * x => x   = 28000   28000nswer: 28000
Answer: A
If 0 < M < Y, M is an odd number and Y is a prime number, which of the following can be the value of M + Y ? Options:
A) 11.	B) 13.	C) 17.	D) 10.	E) 7.

Solution: If m is odd ,implies m(odd)+y(odd/even prime)=(Even/Odd)   If Y is even, the 2 is the even prime , therefore y=2m=1 since 0<M<Y therefore M+Y =3. But 3 is not an option   which implies y is odd,   Now M(odd)+Y(odd)=Even   10 is the only option that is even=10.
Answer: D
In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-4, 1), (1, 1), (1, -3) and (-4, -3)?	Choose the correct choice from the following answers.
A) 16
B) 20
C) 24
D) 25
E) 30

Solution: Length of side 1= 4+1= 
4+1 = 5
5   Length of side 2= 3+1= 
3+1 = 4
4   Area of rectangle= 5*4= 
5*4 = 20
20   20 is the answer
Answer: B
A cistern is normally filled in 12 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?
Choose the correct choice from the following.
A) 10 hours	B) 84 hours	C) 30 hours	D) 40 hours	E) 50 hours

Solution: If leakage/hour=1/x, then 1/12 -1/x= 1/14, solving 1/x=1/84   So in 84 hours full cistern will be empty.   ANSWER:84 hours
Answer: B
By using the numbers 1, 2, 3, 5 and 7 only once, how many five digit numbers can be made that are divisible by 25?	Answers
A) 10
B) 11
C) 12
D) 13
E) 14

Solution: A number to be divisible by 25 must end with 00, 25, 50, or 75.   So, there are the following cases possible:   137-25 --> the first three digits can be arranged in 3=6 ways.   123-75 --> the first three digits can be arranged in 3=6 ways.   Total = 6 + 6= 
6 + 6 = 12
12.   Answer: 12.
Answer: C
what is the speed of a stream if a canoes rows upstream at 8km/hr and downstream at 10.5km/hr.
Choose the correct answer:
A) 1.5 kmph
B) 1.25 kmph
C) 1.35 kmph
D) 1.27 kmph
E) 1.22 kmph

Solution: Sol.   Speed of stream = 1/2(10.5 -8) kmph = 1.25 kmph.   Answer 1.25 kmph
Answer: B
The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is Choose the correct choice from the following answers.
A) 17.2 km B) 7.2 km C) 7.6 km D) 17.6 km E) 27.2 km

Solution: speed of a boat in still water = 15 km/hr   Speed of the current = 3 km/hr   Speed downstream = (15+3)= 
(15+3) = 18
18 km/hr   Distance travelled downstream in 24 minutes=(24/60)×18=(2×18)/5 = 7.2 km   Answer is 7.2 km
Answer: B
A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Choose the correct choice from the following answers
A) 111.12 m  B) 111.22 m  C) 111.19 m  D) 118.12 m  E) 311.12 m

Solution: A runs 1000 m while B runs 900 m and C runs 800 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 800)/900 = 8000/9 = 888.88 m.   B can give C = 1000 - 888.88= 
1000 - 888.88 = 111.12
111.12 m.111.12 mnswer:111.12 m
Answer: A
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?	Choose the correct choice from the following options.
A) 80 B) 89 C) 78 D) 67 E) 56

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 650)/10= 
(240 + 650)/10 = 89
89 sec.   Answer: Option 89
Answer: B
In 1 kg mixture of sand and iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10%?  Choose the correct option.
A) 1 kg  B) 200 gms  C) 800 gms  D) 1.8 kg  E) None of these

Solution: In 1 kg mixture quantity of iron = 200 gm   Let x gm sand should be added, then   10% of (1000 + x) = 200   \ x = 1000 gm = 1 kg   1 kgnswer 1 kg
Answer: A
David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 8 family members in a row for the picture?	Pick one.
A) 9!	B) 9×8!	C) 6×7!	D) 10!/2!	E) 10!

Solution: In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, 5, 6, which can be arranged in 7! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 7!*2! ways.   Total - Restriction =   = 8! - 7!*2! =   = 7!(8 - 2!) =   = 6*7!.   Answer: 6×7!.
Answer: C
A horse is tethered to one corner of a rectangular grassy field 40 m by 24 m with a rope 14 m long. Over how much area of the field can it graze?  Select:
A) 154 cm2 B) 308 m2 C) 150 m2 D) 407 m2 E) None of these

Solution: 154 cm2rea of the shaded portion   = 1⁄4 × π × (14)2 = 154 m2   154 cm2nswer 154 cm2
Answer: A
Seven friends are planning to attend a concert. If another friend also goes with them, they will get a group discount on their tickets. If the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount, how much is the discount?	Options: A) 8.5% B) 12.5% C) 16.5% D) 19.5% E) 21.5%

Solution: Let x be the original price of one ticket.   The total original cost is 7x.   The new cost is 8y, where y is the discounted price of one ticket.   7x = 8y   y = 7x/8 = 0.875x which is a discount of 12.5%.   The answer is 12.5%.7 /8= 
7 /8 = 7/8 = around 0.875
0.875x which is a discount of 12.5%.   The answer is 12.5%.
Answer: B