MU-NLPC/Calc-aqua_rat huggingface dataset:
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?
Answers.
A) 23/35  B) 23/31  C) 23/19  D) 23/13  E) 23/10

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
A is the average (arithmetic mean) of the first 7 positive multiples of 8 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n?	Choose one:	A) 10	B) 12	C) 16	D) 24	E) 32

Solution: If A^2 - B^2 = 0, then let's assume that A = B.   A must equal the 4th positive multiple of 4, thus A = 32, which also equals B.   B is the second positive multiple of n, thus n = 32/2= 
32/2 = 16
16.   The answer is 16.
Answer: C
In a race of length Lmetres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N) Pick
A) L(L-N) / L-M	B) M-N	C) L-N	D) (N-M)L / L-M	E) M+

Solution: the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:   L = 100   M = 10   N =20.   So basically, L beat G by 10 meters. Now whatever options comes close to the figure 10 is the right ans..   looking the the opion C to E, one can make out that they are incorrect, leaving us with just two options..A and B.   Out of which, i choose (N-M)L / L-M.
Answer: D
Lory spent 2⁄5 of her money on new clothes and then deposited 1⁄2 of what remained into her savings account. If she then had $21 left, how much did she have at the start? Choices:
A) $30	B) $35	C) $70	D) $105	E) $210

Solution: Lory spent 2⁄5 of her money on new clothes but if you see 21 is half of 3/5 money so 210 is too huge to be correct..   solution..   let the money be x..   2/5 is used...   1/2 of remaining 3/5 is put in savings account and remaining half is 21..   so 1/2 * 3/5 *x=21..   x=21*2*5/3=70..   $70
Answer: C
The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.  Select
A) 22
B) 35
C) 25
D) 99
E) 21

Solution: Let the number of students who wrote the exam be x.   Total marks of students = 80 x.   Total marks of (x - 5) students = 90(x - 5)   80x - (5 * 20) = 90(x - 5)   350 = 10x => x = 35.Answer: 35
Answer: B
Dhoni spent 20 percent of his earning last month on rent and 5 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did Dhoni have left over?
Choose the correct choice
A) 61%	B) 62%	C) 65%	D) 64%	E) 50%

Solution: Say Dhoni's earning last month was $100.   Dhoni spent 20 percent of his earning last month on rent --> $20 on rent;   5 percent less than what he spent on rent to purchase a new dishwasher --> $20*0.95= 
20*0.95 = 19
$19 on the dishwasher.   Left over amount   100 - (20 + 19)= 
  100 - (20 + 19) = 61
$61   61%nswer: 61%
Answer: A
If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number D of integers that can be negative?
Options: A) 2 B) 3 C) 4 D) 5 E) 6

Solution: Minimuum should be 1   Maximum should be 4:   1 out of a or b to make the multiplication negative   3 out of c, d, e or f to make the multiplication negative.   Negative+Negative<0   Answer:C   maximum will be 5..   you dont require both the multiplicatin to be negative for entire equation to be negative...   any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers...   actually by writing minimum required as 1 out of 6,you are actually meaning 5 out of 6 also possible as you will see D=5 or 1 will give you same equation..   ans 5
Answer: D
In the first M games of a team's season, the ratio of the team's wins to its losses was 3:1. In the subsequent N games, the ratio of the team´s wins to losses was 2:3. If M:N = 4:5, what was the ratio of the team's wins to its losses for all M+N games? Answers
A) 7:8 B) 9:2 C) 1:2 D) 5:4 E) 3:2

Solution: M = 4/9 of total games   N = 5/9 of total games   Wins = 3/4*4/9 + 2/5*5/9 = 3/9 + 2/9 = 5/9   Losses = 1 - 5/9 = 4/9   The ratio of wins to losses is 5:4.   The answer is 5:4.
Answer: D
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) 754 m
B) 704 m
C) 708 m
D) 706 m
E) 204 m

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
What will be in the next series
1, 7, 8, 49, 56, 57, 343, ...	Choose the correct choice
A) 223 B) 344 C) 677 D) 297 E) 1291

Solution: Ans: 344   1 = 1   7 = 1 x 7   8 = 1 x 7 + 1   49 = 7 x 7 + 1   50 = 7 x 7 + 1   56 = 8 x 7   57 = 8 x 7 + 1   343 = 49 x 7   Next term should be 49 x 7 + 1 = 344   Ans:344
Answer: B
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 83.5°, what fraction of the wheel’s area is represented by the smallest sector?	Choose the correct choice from the following options
A) 1/80 B) 3/100 C) 7/240 D) 11/480 E) 13/720

Solution: The largest angle is 83.5.   Let d be the difference between any two angles in the progression.   The sum of all the angles will be:   83.5 + (83.5-d) + (83.5-2d) + ... + (83.5-7d) = 668 - 28d   The sum of all the central angles in a circle = 360   668 - 28d = 360   d = 308/28= 
308/28 = 11
11   The smallest sector is (83.5-7d)= 83.5-7*11= 
83.5-7*11 = 6.5
6.5   The fraction of the area covered is 6.5/360= 13/720.   The answer is 13/720.
Answer: E
Machine X can complete a job in half the time it takes Machine Y to complete the same job, and Machine Z takes 50% longer than Machine X to complete the job. If all three machines always work at their respective, constant rates, what is the ratio B of the amount of time it will take Machines X and Z to complete the job to the ratio of the amount of time it will take Machines Y and Z to complete the job?	Choose the correct choice from the following options:
A) 5 to 1	B) 10 to 7	C) 1 to 5	D) 7 to 10	E) 9 to 10

Solution: Solutioning this exercise can be facilitated by using a R T W (rate time work) table:   We translate the exercise into the table:   R T W   X t/2 1   Y t 1   Z (t/2*3/2 =3t/4) 1   From this table we find the rates   Rx = 2/t   Ry = 1/t   Rz = 4/3t   The Q is what is the ratio of (Tx + Ty) / (Ty + Tz)   Rx + Ry = 2/t + 4/3t = 6/3t+4/3t = 10/3t   Ry+Rz = 1/t + 4/3t = 3/3t + 4/3t = 7/3t   The (10/3t)/(7/3t) = 10/7 then the work ratios is 10 to 7   Since Time Ratio B is the inverse of work, the the answer is 7 to 10   CORRECT ANSWER 7 to 10
Answer: D
Which of the following CAN be the least common multiple of two positive integers 2 and 8?
Choose one.
A) 7	B) 5	C) 8	D) 4	E) 2

Solution: L8M of 2, 8 is 8   Answer : 8
Answer: C
The average age of three boys is 15 years. If their ages are in the ratio 3:5:7, the age of the youngest boy is :
Choose the correct choice:
A) 9  B) 8  C) 7  D) 6  E) 5

Solution: Explanation:   3x+5x+7x3=15⇒15x=15×33x+5x+7x3=15⇒15x=15×3 or x = 3   9ge of youngest = 3x = 9 years   9nswer:\9
Answer: A
How many unique positive odd integers less than 60 are equal to the product of a positive multiple of 5 and an odd number?	Options:
A) 4 B) 6 C) 11 D) 12 E) 15

Solution: the odd numbers less than 60 are 1,3,5,...59   some of them are equal to product of 5 and odd number   hence odd multiples of 5 which are less than 60 are 5,15,25,35,45,55( total=6);   ANSWER:6
Answer: B
The president of a country and 8 other dignitaries are scheduled to sit in a row on the 9 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 9 people?  Choose the correct option:  A) 4  B) 58720  C) 40320  D) 24080  E) 120

Solution: IMO C   Given that one chair is taken, i think the remaining 8 dignitaries can be arranged 8!. That is 8*7*6*5*4*3*2*1= 
8*7*6*5*4*3*2*1 = 40_320
40320.
Answer: C
A rectangular lawn of dimensions 90 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?  Options: A) s.3988 B) s.3900 C) s.3228 D) s.4200 E) s.3928

Solution: Area = (l + b – d) d   (90 + 60 – 10)10 => 1400 m2   1400 * 3   = Rs.4200   Answer:s.4200
Answer: D
Johny traveled the entire 60 miles trip. If he did the first 6 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour?
Pick: A) 20mph B) 24mph C) 30mph D) 32mph E) 48mph

Solution: Average speed=sum of distance/sum of time. If he travelled the first 6 miles at 24 miles/hr, it would take 0.25 hr. For the remaining trip, if he went at 48 miles/1hr, it would take 1 hour. Then, the average speed is 60miles/(0.25+1)hrs=48miles/1hr.   Therefore, the answer is 48mph.
Answer: E
Shreehari has 125 pencils. There are 25 students are studying in his class. He would like to give each student the same amount of pencils, how much should he give to each student?	Choose the correct choice from the following answers
A) 12
B) 7
C) 5
D) 15
E) 6

Solution: 125/25= 
125/25 = 5
5   The answer is 5.
Answer: C
A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? Pick one.
A) 3	B) 7.5	C) 2.25	D) 1.5	E) 4

Solution: M = 4.5   S = x   1.5S = 4.5 + x   US = 4.5 + x   4.5 + x = (4.5 - x)2   4.5 + x = 9 -2x   3x = 4.5   x = 1.5   ANSWER:1.5
Answer: D
In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 10 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
Choose the correct choice from the following:  A) 400  B) 625  C) 250  D) 2,500  E) 10,000

Solution: total fish = x   percentage of second catch = (10/50)*100= 
(10/50)*100 = 20
20%   so, x * 20%= 50   x = 250 ans.250
Answer: C
If 0 < a < b and k = (2a + 8b)/b , which of the following must be true?  Choose the correct choice from the following answers:  A) k < 2  B) k < 7  C) k < 10  D) k > 15  E) k > 11

Solution: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.   As for your question, it is very simple and straightforward with number plug in.   Assume a=1 and b=2 as a < b, you get k = (2+16)/2= 
(2+16)/2 = 9
9. This eliminates all but option k < 10 , making it the correct answer.
Answer: C
An aeroplane covers a certain distance of 420 Kmph in 6 hours. to cover the same distance in 4 2/3 hours, it Must travel at a speed of ?	Pick:  A) 450 Km  B) 480 Km  C) 500 Km  D) 540 Km  E) 590 Km

Solution: Speed of aeroplane = 420 Kmph   540 Kmistance travelled in 6 hours   = 420 * 6= 
420 * 6 = 2_520
2520 Km   Speed of aeroplane to acver 2520 Km in 14/3= 2520*3/14= 
2520*3/14 = 540
540 Km   Answer: Option '540 Km'
Answer: D
If x ≠ 0 and x^4 - (2- x^4)/x^4 = y/x^3, then y = Choose the correct answer:  A) -x  B) -x/2  C) -2/x  D) -2  E) -2x

Solution: x^4 - (2- x^4)/x^4 = y/x^3   -2/x^4 = y/x^3   y = -2/x   Answer : -2/x
Answer: C
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream?  Choose the correct answer: A) 5 kmph B) 67 kmph C) 22 kmph D) 88 kmph E) 12 kmph

Solution: Speed of the boat in still water   = (60+70)/2= 
(60+70)/2 = 65
65 kmph. Speed of the stream= (70-60)/2= 
(70-60)/2 = 5
5 kmph.   5 kmphnswer:5 kmph
Answer: A
If the simple interest on a sum of money at ten percent per annum for five years is Rs.6000, compound interest on the same sum for the same period at the same rate of interest is Choose the correct choice from the following answers.
A) 6480.0  B) 6840.0  C) 4800.0  D) 6000.0  E) 6040.0

Solution: S I for 5 years = 6000 ie for one year =1200   The compound interest for Rs.1200 for the next four years = 1200(4)= 4800*10/100= 
4800*10/100 = 480
480   The CI for two years 6000 + 480= 
6000 + 480 = 6_480
6480.00   6480.0NSWER:6480.0
Answer: A
Worker W produces n units in 5 hours. Workers V and W work independently but at the same time, produce n units in 2 hours. How long would it take V alone to produce n units? Choose the correct choice from the following answers.
A) 10/8
B) 10/3
C) 10/6
D) 10/2
E) 10/1

Solution: Explanation:   w's 1 hours production = n/5   (w + v)'s 1 hours production = n/2   v's 1 hour production = n/5 + V = n/2   v's 1 hour production = n/2 – n/5 = 3n/10= n/(10/3)   Ans = 10/3 hours   \Answer: 10/3
Answer: B
A van takes 6 hours to cover a distance of 270 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?	Choose the correct answer:
A) 50 Kmph
B) 30 Kmph
C) 70 Kmph
D) 80 Kmph
E) 90 Kmph

Solution: Time = 6   Distence = 270   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 270/9= 
270/9 = 30
30 Kmph   30 Kmph
Answer: B
5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?	Choose the correct choice from the following choices
A) 4400	B) 3500	C) 8700	D) 9000	E) 8000

Solution: X * (95/100) * (85/100) = 3553   X = 4400   4400NSWER 4400
Answer: A
Jackson invested $400,000, dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P? Choose one:
A) $115,384
B) $120,000
C) $121,072
D) $124,129
E) $130,000

Solution: x be the amount invested in account P   0.12*x +(300000-x)*0.25=60,000   15000/.13=x   x=1500000/13=11...=$120,000   hence answer is $120,000
Answer: B
Which of the following trains is the fastest?
Pick one.
A) 25 m/sec B) 1500 m/min C) 90 km/hr D) None of these E) Cannot be determined

Solution: 25 m/sec = (25*18/5)km/hr=90km/hr.   And, 25 m/sec=(25*60)m/min=1500 m/min.   So, all the three speeds are equal.   Correct Option: None of these
Answer: D
O(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x.
Likewise, E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x.
According to these definitions, the value of O(3.2) + E(–1.7) + o(–1.3) + e(2.7) is:
Choose the correct option
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: O(x) represents the least odd integer greater than x - O(3.2) = 5,   o(x) represents the greatest odd integer less than x - o(–1.3) = -3,   E(x) represents the least even integer greater than x - E(–1.7) = 0 ,   e(x) represents the greatest even integer less than x - e(2.7) = 2.   The value of O(3.2) + E(–1.7) + o(–1.3) + e(2.7) = 4   ANSWER:4
Answer: C
If the area of a circle decreases by 36%, then the radius of a circle decreases by
Choose the correct option: A) 20% B) 18% C) 36% D) 64% E) None of these

Solution: If area of a circle decreased by x % then the radius of a circle decreases by   (100−10√100−x)%=(100−10√100−36)%   = (100−10√64)%   = 100 - 80= 
100 - 80 = 20
20%   20%nswer 20%
Answer: A
The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:18:14, then find the ratio of their periods of investments.  Choices:
A) 1:3:2
B) 3:5:6
C) 3:2:4
D) 2:4:3
E) 2:5:3

Solution: The ratio of investments of A, B and C is 5:6:7.   The ratio of shares of A, B and C is 5:18:14.   Therefore, Ratio of their periods of investments is   (5/5) : (18/6) : (14/7) = 1:3:2   1:3:2NSWER:1:3:2
Answer: A
The length of rectangle is thrice its breadth and its perimeter is 48 m, find the area of the rectangle?	Choose the correct choice from the following answers:  A) 432  B) 108  C) 252  D) 992  E) 212

Solution: 2(3x + x) = 48   l = 18 b = 6   lb = 18 * 6= 
18 * 6 = 108
108   Answer:108
Answer: B
How many different three-digit integers can be composed of digits 1, 2, and 3 ?
Choose the correct choice from the following choices
A) 27  B) 54  C) 64  D) 72  E) 81

Solution: The possible number of variant =3*3*3= 
3*3*3 = 27
27   Option 27
Answer: A
Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
Choose the most appropriate option:
A) 476 B) 450 C) 500 D) 550 E) 300

Solution: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x = 476   476NSWER 476
Answer: A
Two trains of length 120 m and 320 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?  Options: A) 22 sec B) 77 sec C) 11 sec D) 20 sec E) 66 sec

Solution: Relative speed = (42 + 30) * 5/18 = 4 * 5= 
4 * 5 = 20
20 mps.   Distance covered in passing each other= 120 + 320= 
120 + 320 = 440
440 m.   The time required= d/s = 440/20 = 11 sec.   Answer:11 sec
Answer: C
What is 2 4/3 - 3 1/4 divided by 2/3 - 1/6 ?
Options: A) 5/4 B) 2/3 C) 1/6 D) 5/2 E) 1/8

Solution: 2 4/3 - 3 1/4 = 10/3 - 13/4 = (40 - 39 )/12 = 1/12   2/3 - 1/6 = (4-1)/6 = 3/6 = 1/2   So 1/12/1/2 = 2/12 = 1/6   Answer - 1/6
Answer: C
The area of a rectangular plot is 18 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth?
Choose the most appropriate option: A) 10 metres B) 8 metres C) 7.5 metres D) Data inadequate E) None of these

Solution: L × 8 metres = 18 × 8 metres   ∴ L = 18 m   and L – 8 metres = 10   ∴ 8 metres = 18 – 10 = 8 m   Answer 8 metres
Answer: B
Sudhir started a business with Rs.30,000 and after 8 months Ravi joined him with Rs.60,000. If they get a profit of Rs.28000 then ratio of their shares will be  Choose the most appropriate option.
A) 3:2 B) 2:3 C) 4:3 D) 3:4 E) 3:5

Solution: 30000*12:60000*(12-8)   =360000 :240000   =3:2   3:2NSWER:3:2
Answer: A
If l=4p where p is a prime number greater than 2, how many different positive even divisors does l have, including l?  Choose the correct option
A) two B) three C) four D) six E) eight

Solution: l=2, 2, p (p is in the prime factorization since were told it is a prime number in the question)   2   4 (because of 2*2)   2p (because of 2 * p)   4p (because of 2 * 2 * p)=four
Answer: C
If -4-X < (2-5X)/3, which of the following is correct?	Pick:
A) X < 7. B) X > -5. C) X > 5. D) -5 < X < 0. E) 0 < X < 5.

Solution: -4-X < (2-5X)/3   -12-3X < 2- 5X   -14 < -2X   7>X   X < 7. is the answer
Answer: A
The edge of a cube is 2a cm. Find its surface?
Choose the most appropriate option.
A) 23a2 cm2 B) 84a2 cm2 C) 64a2 cm2 D) 24a2 cm2 E) 14a2 cm2

Solution: 6a2 = 6 * 2a * 2a = 24a2   Answer:24a2 cm26 * 2  * 2= 
6 * 2  * 2 = 24
24a2   Answer:24a2 cm2
Answer: D
In what time a sum of money double itself at 3% per annum simple interest?	Pick.
A) 33 1/4% B) 33 1/3% C) 33 7/3% D) 33 5/3% E) 33 1/7%

Solution: P = (P*3*R)/100   R = 33 1/3%   Answer: 33 1/3%
Answer: B
Which is better investment: 11% stock at 143 or 9% stock at 117?  Select the correct option
A) 9 3/4% stock at 119
B) 9 3/4% stock at 117
C) 9 3/4% stock at 112
D) 9 3/4% stock at 118
E) 9 3/4% stock at 111

Solution: Let investment in each case be Rs. (143 x 117).   Income in 1st case = Rs. 11	x 143 x 117 = Rs. 1287.   143   Income in 2nd case = Rs. 39	x 143 x 117 = Rs. 1394.25   4 x 117   Clearly, 9	3	% stock at 117 is better.   4   Answer:9 3/4% stock at 117
Answer: B
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 45 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?	Choose the correct answer
A) 35
B) 36
C) 37
D) 43
E) 39

Solution: James worked for 41 hours hence he earned 40*x+5*2x=50x dollars;   We know that Harry also earned the same 50x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 20x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 20x/1.5x=13 additional hours, so Harry worked for total of 30+13= 
30+13 = 43
43 hours.   Answer: 43.
Answer: D
64 + 5 * 12 / (180/3) = ?	Choose the correct option.
A) 22	B) 77	C) 29	D) 65	E) 21

Solution: 64 + 5 * 12 / (180/3) = 64 + 5 * 12 / (60)   = 64 + (5 * 12)/60 = 64 + 1= 
64 + 1 = 65
65.Answer:65
Answer: D
Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?  Choose the correct choice from the following answers
A) 15 days B) 13 days C) 12 days D) 11 days E) 18 days

Solution: 11 days   (5 + x)/20 + 5/25 = 1 => x = 11 days
Answer: D
Of 70 players on a football team, 43 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Choose the correct choice from the following answers:
A) 54	B) 59	C) 63	D) 61	E) 92

Solution: Total = 70   Thrower = 43   Rest = 70 - 43= 
70 - 43 = 27
27   Left Handed= 27/3= 
27/3 = 9
9   Right handed= 18   If all Thrower are right handed then total right handed is   43 + 18= 
  43 + 18 = 61
61   so D. 61 is the right answer
Answer: D
If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?  Pick.
A) 132 km  B) 167 km  C) 143 km  D) 162 km  E) 245 km

Solution: 162 km   12 m/s = 12 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   162 kmistance = speed * time = 12 * 18/5 * 15/4= 
12 * 18/5 * 15/4 = 162
162 km.
Answer: D
The ratio of 2 numbers is 10:20 and their H.C.F. is 100. Their L.C.M. is ?	Choose the correct choice from the following answers
A) 1100  B) 3000  C) 2100  D) 1000  E) 2000

Solution: Let the numbers be 10x and 20x   Their H.C.F. = 100   so the numbers are 10*100 , 20*100 = 1000, 2000 L.C.M =2000   Answer is 2000
Answer: E
X is able to do a piece of work in 8 days and Y can do the same work in 12 days. If they can work together for 3 days, what is the fraction of work left?
Choose the correct choice from the following answers
A) 8/5
B) 6/5
C) 7/5
D) 3/5
E) 4/5

Solution: Explanation :   Amount of work X can do in 1 day = 1/8   Amount of work Y can do in 1 day = 1/12   Amount of work X and Y can do in 1 day = 1/8+ 1/12= 5/24   Amount of work X and Y can together do in 3 days = 3 × (5/24) = 5/8   Fraction of work left = 1 – 5/8= 3/5   Answer : Option 3/5
Answer: D
If 0 < P < Y, P is an odd number and Y is a prime number, which of the following can be the value of P + Y ?  Pick
A) 11. B) 13. C) 17. D) 10. E) 7.

Solution: If P is odd ,implies p(odd)+y(odd/even prime)=(Even/Odd)   If Y is even, the 2 is the even prime , therefore y=2p=1 since 0<P<Y therefore P+Y =3. But 3 is not an option   which implies y is odd,   Now P(odd)+Y(odd)=Even   10 is the only option that is even=10.
Answer: D