MU-NLPC/Calc-aqua_rat huggingface dataset:
From among the 31 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?	Choose the correct option
A) 1360	B) 1260	C) 1060	D) 1160	E) 930

Solution: There are 31 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 31 ways. When one person is appointed as leader, we are left with 35 students. Out of these 30 teachers, we can select one class representative. So, a class representative can be selected in 30 ways. Hence, the number of ways in which a leader and class representative can be selected = 31 x 30 = 930   ANSW930R:930
Answer: E
A person is traveling at 20 km/hr and reached his destiny in 8 hr then find the distance?
Pick one
A) 180 km
B) 200 km
C) 160 km
D) 220 km
E) 240 km

Solution: T = 8 hrs   D= T*S = 20*8= 
20*8 = 160
160 km   Answer is 160 km
Answer: C
In how many ways can 6 apples (identical) be distributed among 5 children? (Some children may get no apples.)	Answers
A) 124  B) 210  C) 128  D) 130  E) 132

Solution: Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.   n=6 r= 5   10C4 =210   Answer : 210
Answer: B
If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 52.5 miles ahead of Joe? Choose the correct choice:
A) 15
B) 240
C) 75
D) 90
E) 105

Solution: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.   Teena covers 55 miles in 60 mins.   Joe covers 40 miles in 60 mins   So teena gains 15 miles every 60 mins   Teena need to cover 7.5 +52.5 miles.   Teena can cover 7.5 miles in 30 mins   Teena will cover 52.5 miles in 210 mins   So answer 30+210= 
30+210 = 240
240 mins. (ANSWER 240)
Answer: B
What is the rational number for recurring decimal 0.890890890.... ? Choose the correct answer.
A) 890890/1000
B) 67/421
C) 890/999
D) None of these
E) Cannot be determined

Solution: Explanation :   0.890890890.... = 0.890¯=890/999. Answer : Option 890/999
Answer: C
If each side of a rectangle is increased by 100%, by what % the area increases? Answers:
A) 100%
B) 200%
C) 250%
D) 300%
E) 400%

Solution: if length is l and width is b then area=l*b   now new l and b is 2l and 2b respectively.   so new area is=4*l*b   % increase= 300%   ANSWER:300%
Answer: D
A man saves Rs 250 at the end of each year and lends the money at 5% compound interest. How
much will it become at the end of 3 years.  Answers.
A) Rs 662 B) Rs 862.01 C) Rs 827.53 D) Rs 686.53 E) None of these

Solution: Explanation:   =[250(21/20×21/20×21/20)+250(21/20×21/20)+250(21/20)]=827.53   Answer: Rs 827.53
Answer: C
If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $86, how much does one shirt cost? Choose the most appropriate option.
A) $10 B) $12 C) $13.20 D) $15 E) $24

Solution: 3J + 2S = 69   2J + 3S = 86   ----------------   5J + 5S = 155 ----(divide by 5)---> J + S = 31   3J + 2S = J + 2(J + S) = J + 62 = 69 ---> J = 7   3*7 + 2S = 69   21 + 2S = 69   2S = 48   S = 24   Answer: $24
Answer: E
If x/y = 2/z, then 5x^2 =	Choose the correct choice:
A) y/z
B) 20y²/z²
C) y²z²
D) 5y²/z²
E) yz

Solution: This question is most easily solved by isolating y in the equation and substituting into the expression 5x²:   x/y = 2/z   x = 2y/z   If we substitute 2y/z into the expression for x, we get:   5(2y/z)² = 5(4y²/z²) = 20y²/z².   The correct answer is choice (20y²/z²)
Answer: B
P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?	Choose one
A) 10 days
B) 14 days
C) 15 days
D) 9 days
E) 19 days

Solution: Explanation :   Amount of work P can do in 1 day = 1/20   Amount of work Q can do in 1 day = 1/30   Amount of work R can do in 1 day = 1/60   P is working alone and every third day Q and R is helping him   Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5   So work completed in 15 days = 5 × 1/5 = 1   Ie, the work will be done in 15 days   Answer : Option 15 days
Answer: C
If the LCM of two integers P, Q (where Q> P and P>1) is P*Q, then which of the following can not be true? Answers:
A) Both P and Q can be consecutive integers.  B) Both P and Q can be Prime Numbers.  C) P and Q do not have a common factor.  D) P and Q do not share any Prime factors.  E) All Prime factors of P must be Prime factors of Q.

Solution: If LCM of two numbers P and Q is the product PQ then both numbers are Co- prime.   (Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1).   Numbers that can be Co-Prime are :   1) Two consecutive natural numbers.   2) Two consecutive odd numbers.   3) Two prime numbers.   4) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.   With above four statements it can be concluded that Options A, B, C and D are all true.   Only Option E cannot be true.   Hence answer is All Prime factors of P must be Prime factors of Q.
Answer: E
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?  Choose the correct choice from the following answers.
A) 10/21
B) 11/21
C) 2/7
D) 5/7
E) 3/7

Solution: Total number of balls = (2 + 3 + 2)= 
(2 + 3 + 2) = 7
7.   Let S be the sample space.   Then, n(S)= Number of ways of drawing 2 balls out of 7   = 7C2 `   =(7 x 6)/(2 x 1)   = 21.   Let E = Event of drawing 2 balls, none of which is blue.   n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.   = 5C2   =(5 x 4)/(2 x 1)   = 10.   P(E) =n(E)/n(S)=10/21   10/21nswer :10/21
Answer: A
In the biology lab of "Jefferson" High School there are 6.48*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish? Choose the correct choice:	A) 100	B) 200	C) 500	D) 600	E) 5000

Solution: 6.48*10^6/ 10800==> 64.8*10^3/108==> 64800/108= 
64800/108 = 600
600   ANSWER:600
Answer: D
Of the science books in a certain supply room, 41 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 100 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? Choose the correct choice from the following choices.
A) 81 B) 159 C) 166 D) 315 E) 324

Solution: First, you can take all 41 Botany books, all 65 zoology books and all 50 geology books because you're sure to never pick 80 of them.   There are still 90 on physics and 100 on chemistry   The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry.   Minimum number of books picked to reach 80 in the same science should be : 41 + 65 + 50 + 79 +79 + 1= 
41 + 65 + 50 + 79 +79 + 1 = 315
315   315
Answer: D
Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 2 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book?  Choose the correct choice from the following options.
A) 12	B) 15	C) 10	D) 20	E) 14

Solution: 12ctually u can set up 2 equation   P--stands for the pages   D--stands for the days   1) P*D=480 (we want to find the Days, soP=480/D)   2) (P+16)(D-2)=480 => PD-2P+16D-32=480   as the 1) stated u can put 1) into 2)   => 480-2P+16D-32=480 => 16D-2P=32   put the bold one into it => 16D-2(480/D)=80   the we get the final equation 16D^2-960=80D (divide 16)   => D^2-5D-60=0   (D-12)(D+5)=0 so D=12 days 12ns: 12
Answer: A
If 625(5^x) = 1 then x= Choose the most appropriate option
A) –2
B) -4
C) 0
D) -1
E) 2

Solution: 5^x = 1/625   5^x = 1/5^4   5^x= 5^-4   x = -4   -4
Answer: B
Ten years ago, P was half of Q's age. If the ratio of their present ages is 3:4, what will be the total of their present ages?  Select the correct option.
A) 35	B) 38	C) 37	D) 36	E) 30

Solution: Let present age of P and Q be 3x and 4x respectively.   Ten years ago, P was half of Q's age   ⇒(3x−10)=12(4x−10)⇒6x−20=4x−10⇒2x=10⇒x=5   Total of their present ages   =3x+4x=7x3 +4= 
3 +4 = 7
7x=7×5=35   35nswer is 35.
Answer: A
(2^2+4^2+6^2+.....+40^2)=?
Answers:
A) 11480	B) 76868	C) 57898	D) 68886	E) 75865

Solution: =(1x2)^2+(2x2)^2,+(2x3)^3+......(2x20)^2   =2^2 x (1^2+2^2+3^2+.......+20^2)   formula is =1/6 n(n+1)(2n+1)   =(4x1/6x20x21x41)   =(4x2870)=11480   11480nswer is 11480
Answer: A
Using all the letters of the word "THURSDAY", how many different words can be formed? Select the correct option:  A) 8  B) 8!  C) 7!  D) 7  E) 6!

Solution: Explanation:   Total number of letters = 8   Using these letters the number of 8 letters words formed is â¸Pâ‚ˆ = 8!.   ANSWER IS 8!
Answer: B
A box contains 3 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
Choose the most appropriate option:
A) 1/2 B) 3/5 C) 7/12 D) 2/3 E) 7/10

Solution: Total selection ways: 5C2=5!/2!3!=10   Selecting one blue chip out of two: 2C1=2!/1!1!=2   Selecting one red chip out of four: 3C1=3!/2!1!=3   Thus, (2C1*3C1)/5C2=(2*3)/10=6/10=3/5=3/5
Answer: B
Two integers are in the ratio of 1 to 4. If 6 is added to the smaller number, the ratio becomes 1 to 2. Find the larger integer. Pick:
A) 4
B) 6
C) 12
D) 24
E) 30

Solution: Assume the integers to be x and y, where x < y   Given x/y = 1/4 - (i) or y = 4x   and x+6 / y = 1/2 - (ii) or y = 2x + 12   Substituting the value of y from (i), 4x = 2x + 12   x = 6   Hence y = 4*6= 
4*6 = 24
24   ANSWER 24
Answer: D
In the x-y plane, point (x, y) is a lattice point if both x and y are integers. Circle C has a center at (-2, -2) and a diameter of 8. Some points, such as the center (-2, -2), are inside the circle, but a point such as (-2, 2) is on the circle but not in the circle. How many lattice points are in circle C? Choose the correct choice from the following answers
A) 40 B) 10 C) 73 D) 60 E) 63

Solution: The lattice points that are in the circle that lie on the perspective axes is as follows: since the diameter is 8, 9 points lie on the horizontal axis (8 + center), but the end points are not in the circle, so 9 - 2 (the same for the vertical axis, but don't count center again), 7 - 1. The lattice points in the circle and not on the horizontal and vertical axes is as follows: lattice points can be found at 45, 45/2 and 30 degrees of axes (30 and 45/2 degrees from horizontal and vertical axes), so same numbers as before, but don't count center again. So, 13 + 5 * 12 = 73   There are a total of 73 lattice points in the circle.   Answer: 73
Answer: C
A and B enter into partnership with capitals in the ratio 3 : 4. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 5 : 6. Find how long B remained in the business?  Choose the correct choice from the following answers.
A) 9 months  B) 8 months  C) 6 months  D) 7 months  E) None of these

Solution: Initially A’s investment = 3x and B’s investment = 4x   Let B remain in the business for ‘n’ months.   ⇒ 3x × 10 : 4x × n = 5 : 6   ∴ 3x × 10 × 6 = 4x × n × 5   ⇒ n = 9   9 monthsnswer 9 months
Answer: A
8103/x is a non-terminating decimal. Which of the following could be a value of x?
Choose one
A) 2 B) 5 C) 9 D) 12 E) 1

Solution: Then:   c. 9=3*3   d. 12=3*2*2   e. 15=3*5   The sum of digits in 8103 is 12, it means that 8103 is divisible by 3 (i.e. 3 is one of the factors of 8103), which will eliminate one "3" from x, leaving us with only 2's or 5's in options d. and e. Only c is left.   ANSWER:9
Answer: C
Bill downloads the movieRevenge of the Avengersto his computer in 2.5 hours, using a download manager that downloads from 3 sources marked A, B and C. Each source provides download at a constant rate, but the rates of different sources are not necessarily identical. If the movie was downloaded from sources A and C alone, it would take 4 hours to complete the download. The next day, source B is available, but the other sources are inactive. How long will it take to download the trailer of the movie, a file that is 50 times smaller, from source B alone?
Choose the correct choice from the following:
A) 6 hours and 40 minutes
B) 8 minutes
C) 12 minutes
D) 10 minutes
E) 3 minutes

Solution: Let the movie size be 400 u.   Given,A+C=4 hrs.   A+C=100 u/hr   And A+B+C=2.5 hrs or   400/2.5= 
  400/2.5 = 160
160 u/hr   B alone=160-100= 
160-100 = 60
60 u/hr   Trailer=40 times smaller or  400/50= 
  400/50 = 8
8 u   B will take 8/60 hrs or 8 minutes.   Ans 8 minutes
Answer: B
A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 6600. What is the share of B ?
Choices: A) 1100 B) 800 C) 1400 D) 1200 E) None of them

Solution: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x   A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.   Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.   Hence, B's share = Rs. ( 6600 x (2/11))= Rs. 1200.   Answer is 1200.
Answer: D
The average salary of all the employees in a small organization is Rs 8,000. The average salary of 7 technicians is Rs 12,000 and the average salary of the rest is Rs 6,000. The total number of employees in the organisation is? Choose the correct choice from the following options.
A) 21	B) 20	C) 26	D) 22	E) 25

Solution: Let total number of employees be X.   Then, 8000 x X = 7 x 12000 + (X - 7) x 6000   X = 26.   Thus, the total number of employees in the organization is 26.   ANSWER:26
Answer: C
In a stack of boards at a lumber yard, the 24th board counting from the top of the stack is immediately below the 14th board counting from the bottom of the stack. how many boards are in the stack? Choose the correct choice from the following options:	A) 36	B) 46	C) 55	D) 54	E) 42

Solution: 1 2 3 ... 14 15 16 ...................   ..............24 23 ................. 1   So the number of boards = 24+12= 
24+12 = 36
36   Option: 36
Answer: A
If $100 invested at a certain rate of simple interest amounts to $140 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years?
Answers:
A) $190
B) $180
C) $200
D) $240
E) $270

Solution: 100 amounts to 140 in 3 years.   i.e (principal + interest ) on 120 in 3 years = 140   100 + 100*(r/100)*(3) = 140 => r = 40/3   150 in 6 years = principal + interest   = 150 + 150*(r/100)*(6)   = 270   Answer is $270.
Answer: E
A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 245, then how much amount should C pay as his share of rent? Choose the correct choice from the following answers.
A) 35 B) 45 C) 25 D) 63 E) 55

Solution: A : B : C   =10×7:12×5:15×3   =2×7:12×1:3×3   =14:12:9   Amount that C should pay   =245×9/35=7×9=63   Answer is 63
Answer: D
The average age of A and B is 30 years. If C were to replace A, the average would be 25 and if C were to replace B, the average would be 40. What are the age of A, B and C?  Select the correct option:
A) 45,15,35	B) 35,15,45	C) 30,25,53	D) 40,30,25	E) None of the above

Solution: Given 45,15,35 + B = 60â€¦(i)   C + B = 50 â€¦ (ii)   45,15,35 + C = 80â€¦(iii)   (i) + (ii) + (iii) â‡’ 45,15,35 + B + C = 95â€¦(iv)   from (i) and (iv), we get   C = 35years   âˆ´ B = 15 years and 45,15,35 = 45 years   45,15,35nswer 45,15,35
Answer: A
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 Q 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 answers:
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 Q is the inverse of work, the the answer is 7 to 10   CORRECT ANSWER 7 to 10
Answer: D
What is the sum of all the composite numbers up to 22? Select the correct option:  A) 228  B) 277  C) 153  D) 132  E) 281

Solution: Explanation:   4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 +21= 153   Answer: 153
Answer: C
36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ? Choose the correct choice from the following choices:  A) 24  B) 77  C) 88  D) 29  E) 21

Solution: Explanation:   Less Men, means more Days {Indirect Proportion}   Let the number of days be x   then,   27 : 36 :: 18 : x   [Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]   {\color{Blue} x=\frac{36\times 18}{27}}   x = 24   So 24 days will be required to get work done by 27 men.   24nswer: 24) 24 days
Answer: A
Vijay lent out an amount Rs. 10000 into two parts, one at 8% p.a. and the remaining at 10% p.a. both on simple interest. At the end of the year he received Rs. 890 as total interest. What was the amount he lent out at 8% pa.a?  Choose the correct choice from the following answers.
A) 5529	B) 5500	C) 5529	D) 5502	E) 5029

Solution: Let the amount lent out at 8% p.a. be Rs. A   => (A * 8)/100 + [(10000 - A) * 10]/100 = 890   => A = Rs. 5500.Answer:5500
Answer: B
When 999^500 is divided by 5, the remainder is  Choose the correct choice from the following:  A) 0  B) remainder is 1  C) 2  D) 3  E) 4

Solution: 999^500 is to be divided by 5   We can reduce the number to 4^500 (as the remainder of 999/5 is 4 and we can get the same remainder for 4^500 and 999^500 regardless of which is divided 5 )   Now, let's notice the pattern of remainders of powers of 4 when divided by 5   R{(4^1)/5} = 4   R{(4^2)/5} = 1   R{(4^3)/5} = 4   R{(4^4)/5} = 1   and so on   So, even powers of 4 give a remainder of 1   Hence, R{(4^500)/5} will be 1   R{(999^500)/5} will also be 1   Correct Option : remainder is 1
Answer: B
A factory has 500 workers, 10 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent? Pick one.
A) 3
B) 10
C) 25
D) 30
E) 60

Solution: Currently the factory has 0.10*500= 
0.10*500 = 50
50 women.   After 50 additional workers are hired, there will be total of 550 workers and we need 0.2*550= 
0.2*550 = 110
110 of them to be women, so we need 110-50= 
110-50 = 60
60 more women.   Answer: 60.
Answer: E
If x, y, and z are positive integers, and 2x = 5y = 8z, then the least possible value of x + y + z is Choose the most appropriate option: A) 15 B) 28 C) 33 D) 42 E) 60

Solution: Take LCM of 2,5 and 8 = 40   Now 2x = 40 => x =20   5y = 40 => y = 8   8z = 40 => z =5   20+8+5= 
20+8+5 = 33
33.   Option 33.
Answer: C
A secret can be told only 2 persons in 5 minutes .the same person tells to 2 more persons and so on . How long will take to tell it to 768 persons ?
Choose the correct choice from the following options:	A) 25 min	B) 32 min	C) 33 min	D) 34 min	E) 35 min

Solution: at start one person will tell to 2 persons, it will take 5 min, now that  1+2= 
 1+2 = 3
3 persons will tell this to next 6 persons, then 1+2+6= 
1+2+6 = 9
9 persons will tell to next 18 persons, then 1+2+6+18= 
1+2+6+18 = 27
27 persons to 54 similarly   1+2+6+18+54= 
  1+2+6+18+54 = 81
81 persons will tell this to 162 persons similarly  1+2+6+18+54+162= 
 1+2+6+18+54+162 = 243
243 persons will tell this to 486 persons, upto this step total persons who have listened this secret= 2+6+18+54+162+486= 
2+6+18+54+162+486 = 728
728, and total time taken upto this step= 5*6= 
5*6 = 30
30 min, now next 5 min will be sufficient to tell this message to next 40 persons so total time taken= 35 min   ANSW35 minR:35 min
Answer: E
In a game of 70 points, A can give B 5 points and C 25 points. then how many points can B give C in a game of 50?  Choose the correct choice from the following:
A) 9.38	B) 8.38	C) 15.38	D) 13.38	E) 16.38

Solution: In a game of 70 points,A give B 5 points and c 25 points means B=65,15.38=45   In 65 points B give 20 since  65-45= 
 65-45 = 20
20   In 50 points B gives=50*20/65=15.38   ANSWER:15.38
Answer: C
A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?	Select
A) 26% B) 20% C) 21% D) 29% E) 22%

Solution: 900 ---- 180   100 ---- ? => 20%   Answer: 20%
Answer: B
A fruit seller sells mangoes at the rate of Rs.11 per kg and thereby loses 10%. At what price per kg, he should have sold them to make a profit of 10%?  Choose the most appropriate option:
A) Rs.13.44
B) Rs.12
C) Rs.12.25
D) Rs.12.31
E) None

Solution: Solution   90 : 11 = 110 : x   x= (11Ã—110/90)   = Rs.13.44   Hence, S.p per Kg	= Rs.13.44   Rs.13.44nswer Rs.13.44
Answer: A
If 4 spiders make 4 webs in 4 days, then 1 spider will make 1 web in how many days?  Choose the correct choice from the following: A) 4 B) 6 C) 5 D) 4 E) 3

Solution: Let the required number days be x.   Less spiders, More days (Indirect Proportion)   Less webs, Less days (Direct Proportion)   spiders 1:4   Webs 4:1   1 x 4 x x = 4 x 1 x 4   => x= 4   4nswer is 4
Answer: A
The three sides of an acute angled triangle (all in cms) are 12, 19 and k. How many integer values can k take?  Choose the correct choice from the following answers
A) 23  B) 22  C) 15  D) 8  E) 7

Solution: In acute angle triangles all angles in the triangle should be less than 90.   The maximum length of k can be when it is the hypotenuse of the triangle.   So, k= sqrt(12^2 + 19^2) = 22.5 (approx)   The maximum length of k can be when side of length 12 is the hypotenuse of the triangle.   So, k = sqrt (19^2 - 12^2) = 14.7 (approx)   So, k>14.7 and k<22.5.   Hence, possible values for k can be 15,16,17,18,19,20,21 and 22. Total 8 values.   Answer 8.
Answer: D
A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 100, the runs scored by B are?
A. 15 B. 18  Choose one:
A) 22	B) 24	C) 99	D) 77	E) 24

Solution: A:24 = 2:3   24:C = 2:5   A:24:C = 4:6:15   6/25 * 100= 
6/25 * 100 = 24
24   Answer: 24
Answer: B
The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 112 ounces, what is the volume, in cubic inches, of 60 ounces of this substance?	Choose the correct choice from the following.
A) 27
B) 36
C) 25
D) 64
E) 147

Solution: 112 ounces of a substance has a volume of 48 cubic inches   60 ounces of a substance has a volume of (48/112)*60 = 25 cubic inches   Answer A   Alternatively , we can use estimation   112 ounces of a substance has a volume of 48 cubic inches   56 ounces of a substance has a volume of 24 cubic inches   Therefore , 60 will have a volume a little more than 24 ,that is 25   25
Answer: C
There are 3 red shoes, 2 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
Choose the correct choice from the following
A) 3/5 B) 2/9 C) 5/9 D) 4/9 E) 2/3

Solution: total 5 from take one.   5c1=5   red 3 from one   3c1=3   3/5   3/5NSWER:3/5
Answer: A
X does a work in 20 days. Y does the same work in 40 days. In how many days they together will do the same work?  Choose the most appropriate option
A) 10	B) 12	C) 20	D) 30	E) 13.33

Solution: X's 1day's work= 1/20   Y's 1 day's work=1/40   (X+Y)'s 1day's work= (1/20+1/40)=1/13.33   both together will finish the work in 13.33 days.   correct option is 13.33
Answer: E