MU-NLPC/Calc-aqua_rat huggingface dataset:
A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 50 cents. How many cents does a solution of 1 liter of spirit and 3 liters of water cost? Choose the correct answer.
A) 13
B) 33
C) 56
D) 50
E) 52

Solution: C. 50 cents   Yes, ensure that you understand the relation thoroughly!   Cost per liter = K * Fraction of Spirit   50 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 25 cents. Fraction of spirit is 1/2.   25 = K * (1/2)   K = 50   Cost per liter = 50 * (1/4) (1 part spirit, 3 parts water)   Cost for 4 liters = 50 * (1/4) * 4= 
50 * (1/4) * 4 = 50
50 cents   D. 50 cents
Answer: D
The difference between the simple interest received from two different sources on Rs. 1000 for 3 years is Rs. 13.50. The difference between their rates of interest is?  Select:  A) A)2.4%  B) B)2.6%  C) C)0.3%  D) D)0.25%  E) E)1.3%

Solution: (1000 * R1 * 3)/100 - (1000 * R2 * 3)/100 = 13.50 4000(R1 - R2) = 1350   R1 - R2 = 0.25%   Answer:0.25%
Answer: D
Find the compound interest on $1200 for 6 years at 20% p.a. if CI is component yearly?
Choose the correct answer:
A) $120
B) $150
C) $2383
D) $250
E) $300

Solution: A = P(1 + R/100)^T   = 1200(1 + 20/100)^6   =$3583   $2383I = $2383   Answer is $2383
Answer: C
A bank offers 5% C.I. calculated on half-yearly basis . A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is?
Choose the correct choice from the following
A) Rs.181	B) Rs.121	C) Rs.126	D) Rs.128	E) Rs.129

Solution: Amount = [1600 * (1 + 5/(2 * 100)2 + 1600 * (1 + 5/(2 * 100)]   = [1600 * 41/40(41/40 + 1)   = [(1600 * 41 * 81)/(40 * 40)] = Rs. 3321.   C.I. = 3321 - 3200 = Rs. 121.   Answer: Rs.121
Answer: B
What is the value of the following expression?
(1/ (2^2 – 1)) + (1/ (4^2 – 1)) + (1/ (6^2 – 1)) + .... + (1/ (24^2 – 1))
Choose the correct choice:
A) a. 9/19
B) b. 10/19
C) c. 12/25
D) d. 11/21
E) e. 11/19

Solution: it can be written into   1/3+1/15+ 1/35.....1/575   i.e   1/3+1/2*(1/3-1/5)+1/2*(1/5-1/7).... til last term - 1/2*(1/25)   all terms from 1/5 .. to second last term get cancelled   left with   1/3+1/6-1/50=1/2-1/50=24/50=12/25 c. 12/25
Answer: C
If y ≠ 3 and 2m/y is a prime integer greater than 2, which of the following must be true?
I. m = y
II. y = 1
III. m and y are prime integers.
Choose the correct choice from the following
A) None	B) I only	C) II only	D) III only	E) I and II

Solution: Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.   So we should try to make the listed statements not true for some m and y (which satisfy y≠3 and 2m/y=prime>2).   I. m = y --> not necessarily true: m=3 and y=2 (2m/y=3=prime>2);   II. y=1 --> not necessarily true: m=3 and y=2 (2m/y=3=prime>2);   III. m and y are prime integers --> not necessarily true: m=10 and y=4 (2m/y=5=prime>2).   Nonenswer: None.
Answer: A
The sum of two numbers is 75 and their difference is 20. Find the difference of their squares.  Choose the correct answer
A) 3000
B) 2700
C) 1500
D) 1254
E) 3421

Solution: If the sum of two numbers is x and their difference is y, then the difference of their squares is xy.   Here x= 75 and y = 20   75 × 20 = 1500
Answer: C
The value for G=(0.889 × 55)/9.97 to the nearest tenth is Choose the most appropriate option: A) 0.5 B) 4.63 C) 4.9 D) 7.7 E) 49.1

Solution: if we read the Q, we can easily home on to the answer,,   the numerator is clearly between 40 and 50..   denomiator is close to 10..   so G=(0.889 × 55)/9.97 is between 4 and 5..   It may tempt us to solve it since ther are two values between 4 and 5..   but the catch is innearest tenth   4.63 can be called nearest to hundreth and no tenth, so can be eliminated..   4.9 is our answer...   4.9
Answer: C
Two quarts containing 6⁄7 water and 1/7 formula are mixed with three quarts containing 7⁄10 water and 2⁄10 formula. Approximately what percent of the combined five-quart mixture is water? Choose the most appropriate option:	A) 74%	B) 76%	C) 73%	D) 72%	E) 60%

Solution: 6/7 of 2 quarts = 12/7 quarts of water   7/10 of 3 quarts = 21/10 quarts of water   12/7 = 1.714   21/10= 
21/10 = 21/10 = around 2.1
2.100   Total water= 1.714 + 2.100= 
1.714 + 2.100 = 3.814
3.814   Total quarts= 5   3.814/5 = 76.28% approx. 76%   Answer : 76%
Answer: B
The price of a book is increased from $300 to $360. What is the % of increase in its price?  Choose the correct choice from the following choices.
A) 10%	B) 20%	C) 35%	D) 40%	E) 50%

Solution: Explanation: Change in the price = Rs 360 – Rs 300   = Rs 60   Percentage of increase = Change in the price Initial Price   * 100.   Percentage increase in price =( 60 300   ) *100 = 20%   20%
Answer: B
Linda and Angela contract to paint a neighbor's house. Even though Linda
spends 75% more time painting the house than Angela, each receives a payment
of m dollars when the work is completed. If Angela decides to pay Linda n
dollars so that they would have received the same compensation per hour
worked, what is n in terms of m?
Select the correct option.
A) A)(1/2)m
B) B)(1/3)m
C) C)(9/33)m
D) D)(1/5)m
E) E)(1/6)m

Solution: let angela work for 12 hrs and get 1650 rs. (m =1650)   According to question, linda works 75% more time and gets the same amount. so let linda work 21 hrs and get 1650 rs.   so they do a total of  21 +12= 
 21 +12 = 33
33 hrs of work and get 3300 rs together . The question basically asks to equalise their payment. so a total of 3300 rs is received by them and they do 10 hrs work together. average rate will be  3300/33= 
 3300/33 = 100
100 rs per hr. so linda should get 21*100= 
21*100 = 2_100
2100 rs. But she got only 1650. so angela should give 450 rs to linda. answer= 450/1650 =9/33   answer (9/33)m
Answer: C
The speed of a car is 65 km in the first hour and 45 km in the second hour. What is the average speed of the car?  Choose the correct option:
A) 72 kmph B) 55 kmph C) 50 kmph D) 80 kmph E) 82 kmph

Solution: S = (65 + 45)/2= 
(65 + 45)/2 = 55
55 kmph   ANSWER:55 kmph
Answer: B
4, 16, 36, 49, 64 ?, F ind the missing number(?).
Pick
A) 88 B) 74 C) 110 D) 99 E) 100

Solution: The series consists of squares of consecutive EVEN numbers.   Answer : 100.
Answer: E
A train is running at a uniform speed of 80 kmph. It passes a railway platform in 15 seconds. If the length of the platform is 130 m,then the length of the train is Choose the correct choice from the following answers: A) 160 m B) 203.33 m C) 140.5 m D) 150.5 m E) None of these

Solution: Let the length of train be X m.   We know that Speed = Distance / Time.   Thus, (X + 130)/15 = 80 x 5/18   or, (X + 130)/15 = 400/18   or, (X + 130) = 1000/3   or X= 1000/3 - 130   X = 203.33   ANSWER:203.33 m
Answer: B
Sophika can buy watches at a price of P dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of P and X and Y, what is the percent of the markup from her buy price to her sell price?
Choose one.
A) (YP)/100X	B) 100X/(YP)	C) (YP)+100X	D) (YP)-100X	E) (YP)*100X

Solution: Algebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/P *100 = 100X/(YP)   Answer : 100X/(YP)
Answer: B
Fence X is twice as long as fence Y, and fence Y is 2 feet shorter than fence Z. If 2 feet were added to each fence, which of the following must be true?
I) X is twice as long as Y.
II) Y is 2 feet shorter than Z.
III) X is longer than Z.  Choose the correct choice from the following options.
A) I only	B) II only	C) II and III	D) I and II	E) III only

Solution: If X= 6   Y= 3   Z= 5   Then, after adding 3 feet to each:   X= 8   Y=5   Z=7   And the answer would be II and III, which is wrong.
Answer: C
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:	Answers:
A) 14 Years
B) 18 Years
C) 20 Years
D) 22 Years
E) 17 Years

Solution: Let the son's present age be x years. Then, man's present age = (x + 24) years.   (x + 24) + 2 = 2(x + 2)   x + 26 = 2x + 4   x = 22.   ANSWER 22 Years
Answer: D
If a > 1, which of the following is equal to (2a + 6)/(a^2 + 4a + 3)?  Choose the correct answer:	A) a	B) a + 3	C) 2/(a - 1)	D) 2a/(a - 3)	E) 2/(a + 1)

Solution: Here's the algebraic approach:   (2A + 6)/(A^2 + 4A + 3) can be rewritten as...   2(A + 3)/(A+3)(A+1)   We can simplify the fraction, which leaves us with...   2/(A+1)   Ans : 2/(a + 1)
Answer: E
A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. His average speed for the whole journey in km/hr is ?  Options:
A) 37.9	B) 37.53	C) 37.5	D) 37.1	E) 37.4

Solution: Explanation:   Average speed = (2xy) /(x + y) km/hr   = (2 * 50 * 30) / (50 + 30) km/hr.   37.5 km/hr.   Answer: 37.5
Answer: C
A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years? Choose the correct option:
A) 3:4:9	B) 3:4:7	C) 3:4:2	D) 3:4:4	E) 3:4:3

Solution: A:3:4:7:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)   = 144:192:336 = 3:4:7   Answer: 3:4:7
Answer: B
Two different primes may be said to “rhyme” around an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?  Select the correct option.
A) 12
B) 15
C) 17
D) 18
E) 20

Solution: Let's test each option:   A. 12 --> 2*12=24 --> 24=5+19=7+17=11+13: 6 rhyming primes (start from the least prime and see whether we can get the sum of 24 by adding another prime more than 12 to it);   B. 15 --> 2*15=30 --> 30=7+23=11+19=13+17: 6 rhyming primes;   C. 17 --> 2*15=30 --> 34=7+23=11+19=13+17: 6 rhyming primes;   D. 18 --> 2*18=36 --> 36=5+31=7+29=13+23=17+19: 8 rhyming primes;   E. 20 --> 2*20=40 --> 40=3+37=11+29=17+23: 6 rhyming primes.   Answer: 18.
Answer: D
A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges? Choose the correct option.
A) 20%
B) 30%
C) 40%
D) 50%
E) 55%

Solution: Let the side of the square(ABCD) be x metres.   Then, AB + BC = 2x metres.   AC = 2x = (1.41x) m.   Saving on 2x metres = (0.59x) m.   Saving % = (0.59x)/2x	x 100	%	= 30% (approx.)   30%)
Answer: B
A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?  Select the correct option:	A) 10	B) 99	C) 77	D) 65	E) 55

Solution: 1/6 – 1/15 = 1/10 => 10   10nswer: 10
Answer: A
One night 25 percent of the female officers on a police force were on duty. If 500 officers were on duty that night and half of these were female officers, how many female officers were on the police force?  Choose one
A) 90
B) 180
C) 270
D) 500
E) 1,000

Solution: Let total number of female officers in the police force = F   Total number of officers on duty on that night = 500   Number of female officers on duty on that night = 500/2= 
500/2 = 250
250   (25/100)*F= 250   =>F = 1000   Answer 1,000
Answer: E
In a group of Peacocks and cows, the total number of legs are 36 more than twice the no. of heads. Find the total no.of buffaloes. Choose the most appropriate option.
A) 10 B) 19 C) 12 D) 16 E) 18

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 36   => 2x = 36 => x = 18   18
Answer: E
Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? Select the correct option.
A) 10  B) 8  C) 77  D) 26  E) 22

Solution: RS = 60 -40= 
60 -40 = 20
20 * 5/18= 100/18   T = 50   D = 50 * 100/18 = 2500/9   RS = 60 + 40= 
60 + 40 = 100
100 * 5/18   T= 2500/9 * 18/500= 
2500/9 * 18/500 = 10
10 sec.10nswer: 10
Answer: A
Which of these must the factor W of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80
Choose the correct choice
A) W=1,2 only	B) W=2,3 only	C) W=1,2,3 only	D) W=1,2,3,4 only	E) All of them

Solution: Let the four variables be a< b< c< d.   Assume a worst case scenario where the a equal to a prime number (hence odd).   therefore   a = divisible by 1   b = a + 1 (divisible by 2)   c = a + 3 (divisible by 3)   d = a + 4 (divisible by 4)   therefore   each answer choice must be divisible by 2 x 3 x 4 = 24   only 80 is not divisible. Therefore answer = W=1,2,3,4 only
Answer: D
There are 2 available positions and 50 candidates, one half of whom are democrats and another half are republicans. If it was decided that the positions would be filled at random, then what is the probability Q that the both positions will be taken by members of just one party?	Answers:
A) 1/25	B) 12/49	C) 1/4	D) 24/49	E) 1/2

Solution: Q probability of one party having both spots:   (1/2) * (24/49) = 12/49   (1/2) or (25/50) because it does not matter which party or which person gets the first spot. (24/49) because after one person from a particular party is chosen, there are 24 members of the same party left out of 49 total candidates.   Since this result can happen for both parties, (12/49) + (12/49) = (24/49)   Answer: 24/49
Answer: D
If there are 4 peanuts in a box and Mary puts 12 more peanuts inside, how many peanuts are in the box?	Choose the correct choice from the following options: A) 8 B) 16 C) 10 D) 11 E) 12

Solution: 12+4= 
12+4 = 16
16   correct answer is 16)16
Answer: B
A qualified worker digs a well in 4 hours. He invites 2 apprentices, both capable of working 3/4 as fast and 2 trainees both working 1/5 as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?  Choose the correct choice from the following options: A) 1:24 B) 1:34 C) 1:44 D) 1:36 E) 2:14

Solution: and answer is correct as you have calculated : 100/72 hrs that is 1.64 hrs - 1 hr and 36 minutes, so 1:36, hence, 1:36.
Answer: D
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream? Choose the correct choice from the following answers:	A) 10 kmph.	B) 15 kmph.	C) 18 kmph.	D) 11 kmph.	E) 12 kmph.

Solution: Speed of the boat in still water = (60+90)/2= 
(60+90)/2 = 75
75 kmph. Speed of the stream= (90-60)/2= 
(90-60)/2 = 15
15 kmph.   Answer:15 kmph.
Answer: B
A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped three times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 4? Choose the correct choice from the following choices
A) 3/8
B) 1/16
C) 1/8
D) 1/2
E) 1/4

Solution: Cases for sum to be greater than 4 are as mentioned below   Case 1: (1, 2, 2)   Case 2: (2, 1, 2)   Case 3: (2, 2, 1)   Case 4: (2, 2, 2)   Total Outcomes = 2 x 2 x 2 = 8   Probability = Favorable Outcomes / Total Outcomes   I.e. Probability = 4/8 = 1/2   Answer: Option 1/2
Answer: D
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. 850 as total interest. What was the amount he lent out at 8% pa.a? Choose the correct choice:
A) Rs. 15000
B) Rs. 6000
C) Rs. 25000
D) Rs. 10000
E) Rs. 18000

Solution: Let the amount lent out at 8% p.a. be Rs. A   => (A * 8)/100 + [(10000 - A) * 10]/100 = 850   => A = Rs. 15000.   Rs. 15000NSWER:Rs. 15000
Answer: A
What is the next number of the following sequence
3^2,27,3^4,243
Select the correct option:  A) 3^6  B) 3^5  C) 3^4  D) 3^2  E) 3^1

Solution: 3^2,27,3^4,243,x   3^2,3^3,3^4,3^5,3^6   x=3^6   3^6NSWER:3^6
Answer: A
Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? Choose the correct choice from the following options.
A) 1/8 B) 1/7 C) 1/9 D) 1/2 E) 1/1

Solution: A leap year has 52 weeks and two days   Total number of cases = 7   Number of favourable cases = 1   i.e., {Saturday, Sunday}   Required Probability = 1/7   Answer: 1/7
Answer: B
The number of sequences in which 10 players can throw a ball, so that the youngest player may not be the last is ?  Choose the correct choice from the following choices:	A) 4300028	B) 3265920	C) 4320201	D) 3786220	E) 3101242

Solution: x Not younger   The last ball can be thrown by any of the remaining 10 players. The first 6 players can throw the ball in 9P9 ways.   The required number of ways = 9(9!)   = 3265920   Answer:3265920
Answer: B
A and B are two partially filled buckets of water. If 5 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 3 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?  Choose the correct answer:	A) 11	B) 13	C) 17	D) 49/5	E) 23

Solution: Let A contains A, B contains B liters   so, (A-5)/(B+5)= 1/3.......(1)   again, (B-3)/(A+3)= 1/2..........(2)   from (1)(2) we find A= 49/5   ans: (49/5)
Answer: D
Two bullet trains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post. If the length of each bullet train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Choose the correct answer:
A) 11 sec.
B) 15 sec.
C) 12 sec.
D) 17 sec.
E) 19 sec.

Solution: Speed of the first bullet train = 120/10 m/sec = 12 m/sec.   Speed of the second bullet train = 120/12 m/sec = 10 m/sec.   Relative speed = (12 + 10)= 
(12 + 10) = 22
22 m/sec.   Required time= (120 + 120)/22 sec = 11 sec.   11 sec.
Answer: A
A batsman scored 120 runs which included 10 boundaries and 6 sixes. What % of his total score did he make by running between the wickets  Pick: A) 40% B) 50% C) 36.67% D) 70% E) 75%

Solution: Number of runs made by running = 120 - (10 x 4 + 6 x 6)   = 120 - (76)= 
120 - (76) = 44
44   Now, we need to calculate 60 is what percent of 120.=> 44/120 * 100 = 36.67 %   36.67%
Answer: C
In the interior of a forest, a certain number of apes equal to the square of one-sixth of the total number are playing and having great fun. The remaining five apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes?	Choose the correct choice from the following options.
A) 48  B) 16  C) 64  D) 6 or 30  E) 16 or 48

Solution: Let total number be x   No in the interior = (x/6)^2   No outside = 5   So : x - (x/6)^2=5   x^2-36x+180=0   x^2-30x-6x+180=0   (x-6)(x-30)=0   So either x=6 or x=30   6 or 30
Answer: D
Ajay and Vijay have some marbles with them. Ajay told Vijay "if you give me 'x' marbles, both of us will have equal number of marbles". Vijay then told Ajay "if you give me twice as many marbles, I will have 30 more marbles than you would". Find 'x'? Choose the most appropriate option
A) 6  B) 5  C) 8  D) 7  E) 9

Solution: Explanation:   If Vijay gives 'x' marbles to Ajay then Vijay and Ajay would have V - x and A + x marbles.   V - x = A + x --- (1)   If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A - 2x and V + 2x marbles.   V + 2x - (A - 2x) = 30 => V - A + 4x = 30 --- (2)   From (1) we have V - A = 2x   Substituting V - A = 2x in (2)   6x = 30 => x = 5.   Answer: 5
Answer: B
If x and y are integers and x^2*y is a negative odd integer, which of the following must be true?
I. xy^2 is odd.
II. xy is negative.
III. x + y is even. Choose the correct choice from the following answers
A) I only B) III only C) I and II only D) I and III only E) I, II, and III

Solution: x^2*y = negative odd integer   inference:   1. Odd * Odd = Odd   2. y is negative odd integer   3. x is odd (since its squared, the result is positive - so x could be either positive or negative).   Statement I - xy is odd, so is its sqaure - statement must be true   Statement II - xy may or may not be negative - statement may be true but NOT must   Statement III - x and y are odd, so Odd + Odd = Even - statement must be true   Answer is I and III only
Answer: D
Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 240 feet in circumference.After how many minutes are the three of them together again?
Choose the correct choice from the following answers.
A) 4 mins B) 10 mins C) 15 mins D) 3 mins E) 7 mins

Solution: 4 minsnswer will be 4 mins   The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of 4 mins.
Answer: A
A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed? Answers
A) 1 min	B) 9 min	C) 4 min	D) 3 min	E) 8 min

Solution: 4 min   4 min   S = 600/40= 
600/40 = 15
15 mps   S= 3600/15= 
3600/15 = 240
240 sec= 4 min
Answer: C
P is three times as fast as Q and working together, they can complete a work in 16 days. In how many days can Q alone complete the work?
Choose the correct choice from the following choices:
A) 11 days
B) 16 days
C) 13 days
D) 64 days
E) 19 days

Solution: P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 16 days,   which means Q can alone do the work in 4*16= 
4*16 = 64
64 days.   Answer : 64 days
Answer: D
Set A: {1, 3, 6, 9, 12, 15,18}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3? Choose the correct choice from the following options:
A) 3/14
B) 2/7
C) 9/14
D) 4/7
E) 11/14

Solution: probability : 6/7*5/6*4/5=4/7.   Ans 4/7
Answer: D
The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 5 and 8 slices per customer. How many slices cannot be bought?  Pick one.
A) 42.
B) 38.
C) 33.
D) 22.
E) 20

Solution: Let X pizzas of 5 slices and Y pizzas of 8 slices.   5X + 8Y.   Lets check options wise.   A. 42 => 5(2) + 8(4)   B. 38 => 5(6) + 8(1)   C. 33 => 5(5) + 8(1)   D. 22 = we can't write anything with 5 and 8 series..Lets try 5(1) + 8(2) = 21 , 5(3) + 8(1) = 23 , nothing works out.   E. 20 = 5(4) + 8(0)   Answer: correct option is 22.
Answer: D
A room contains 240 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?  Select the correct option:  A) 02  B) 04  C) 06  D) 08  E) 10

Solution: Say group of x people left the room.   # of women in the room was 0.15*240= 
0.15*240 = 36
36;   # of women in the group that left 0.3x;   # of women in the room after the group left it is 0.1(240-x);   So, 36-0.3x= 0.1(240-x) --> x=6.   Answer: 06.
Answer: C
If a and b are positive integers such that a/b = 9.32, which of the following must be a divisor of a
Choose the correct choice from the following
A) 4
B) 3
C) 11
D) 10
E) 5

Solution: a/b = 9.32   a/b = 932/100   a/b = 466/50   a = 466/50*b   We require to find from the available 5 options that must be a divisor of a"   This also means which of the following 5 options can divide 466 evenly   (Ignore b as its value unknown; Ignore 50 as in denominator)   Only option 4 = 4 best fits in   4nswer = 4   4NSWER:4
Answer: A