MU-NLPC/Calc-aqua_rat huggingface dataset:
A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?  Choices.
A) Â²Â²Câ‚â‚€ B) Â²Â²Câ‚â‚€+1 C) Â²Â²Câ‚‰ + Â¹â°Câ‚ D) Â²Â²Câ‚â‚€ - 1 E) None of these

Solution: Explanation:   The total number of ways of forming the group of ten representatives is Â²Â²Câ‚â‚€.   The total number of ways of forming the group that consists of no seniors is Â¹â°Câ‚â‚€ = 1 way   The required number of ways = Â²Â²Câ‚â‚€ - 1   ANSWER IS Â²Â²Câ‚â‚€ - 1
Answer: D
If x is an odd integer and y = 3x + 2, which of the following CANNOT be a divisor of y?	Choices.
A) 23	B) 5	C) 14	D) 17	E) 11

Solution: x takes odd values as 1,3,5,7.,   y=3x+2   x is an odd term so 3x must be an odd term when it adds with 2 so it must be a odd integer   14 didn't follows this condition ans is 14
Answer: C
If the length of an edge of cube P is thrice the length of an edge of cube Q, what is the ratio of the volume of cube Q to the volume of cube P?  Choose the correct answer
A) 1/4
B) 1/5
C) 1/6
D) 1/27
E) 1/9

Solution: The length of cube Q = 1;   The length of cube P = 3;   The ratio of the volume of cube Q to the volume of cube P = 1^3/3^3 = 1/27   Answer : 1/27
Answer: D
The parameter of a square is equal to the perimeter of a rectangle of length 36 cm and breadth 20 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?	Choices
A) 23.56
B) 23.59
C) 44.0
D) 23.53
E) 23.57

Solution: Let the side of the square be a cm.   Parameter of the rectangle = 2(36 + 20) = 112 cm Parameter of the square = 112 cm   i.e. 4a = 112   A = 28   Diameter of the semicircle = 28 cm   44.0ircimference of the semicircle   = 1/2(âˆ)(28)   = 1/2(22/7)(28) = 44cm to two decimal places   Answer:44.0
Answer: C
If an item that originally sold for c dollars was marked up by a percent and then discounted by b percent, which of the following expressions represents the final price of the item?  Choose the most appropriate option
A) (10,000c + 100c(a – b) – abc)/10,000
B) (10,000c + 100c(b – a) – abc)/10,000
C) (100c(a – b) – abc)/10000
D) (100c(b – a) – abc)/10000
E) 10000 /(a – b)

Solution: Assume c=100, a=10, b=10. So final price is 99. Now put these value each option. Only option (10,000c + 100c(a – b) – abc)/10,000 will give right answer.
Answer: A
A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 30%. Their gross income from sales for one month increases by what percent?	Select the correct option:
A) 9%  B) 11%  C) 13%  D) 15%  E) 17%

Solution: Let P be the original price and let x be the number of items sold originally.   The original income is P*x.   After the changes, the income is 0.9P*1.3x = 1.17*(P*x), an increase of 17%.   The answer is 17%.0.9 *1.3= 
0.9 *1.3 = 1.17
1.17*(P*x), an increase of 17%.   The answer is 17%.
Answer: E
Can you find the missing number in the sequence given below?
11 17 23 12 18 ? 13 19 25 14 20 26
Options.
A) 20 B) 21 C) 22 D) 23 E) 24

Solution: Solution:   24   Explanation :   The sequence is given in the puzzle is :   11 17 23 12 18 ? 13 19 25 14 20 26   Let's break the given series as below:   11 17 23   12 18 ?   13 19 25   14 20 26   Now read the number from left hand side from top to bottom as :   So the number that will replace '?' is 24.   Answer 24
Answer: E
A train 110 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.
Answers:
A) 45 kmph B) 50 kmph C) 55 kmph D) 61 kmph E) 70 kmph

Solution: Explanation:   Let the speed of the train be x kmph.   Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.   Therefore 110/((x+5)×5/18)=6 <=> 30 (x + 5) = 1980 <=> x = 61   Speed of the train is 61 kmph.   Answer: Option 61 kmph
Answer: D
A bag contains 6 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green.  Choose the correct option.
A) 19/20	B) 17/20	C) 7/15	D) 8/10	E) 9/40

Solution: Let A be the event that ball selected from the first bag is red and ball selected from second bag is green.   Let B be the event that ball selected from the first bag is green and ball selected from second bag is red.   P(A) = (2/3) x (3/5) = 2/5.   P(B) = (1/3) x (2/5) = 2/15.   Hence, the required probability is P(A) + P(B) which is nothing but 7/15.   ANSWER:7/15
Answer: C
If the average of 1, 2, 4, 5, 6, 9, 9, 10, 12 and x is 7, what is the value of x?	Choose the correct choice from the following.
A) 7	B) 9	C) 11	D) 12	E) 13

Solution: Sum of the deviations of the numbers in the set from the mean is always zero   1, 2, 4, 5, 6, 9, 9, 10, 12   mean is 7   so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero   but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero   hence the answer is  7 + 5= 
 7 + 5 = 12
12   12
Answer: D
A boat takes 38 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?	Choose the most appropriate option:
A) 240 km
B) 120 km
C) 360 km
D) 180 km
E) None of these

Solution: Explanation :   velocity of the stream = 4 kmph   Speed of the boat in still water is 14 kmph   Speed downstream = (14+4)= 
(14+4) = 18
18 kmph   Speed upstream= (14-4)= 
(14-4) = 10
10 kmph   Let the distance between A and B be x km   Time taken to travel downstream from A to B + Time taken to travel upstream from B to C(mid of A and B)= 38 hours   ⇒x/18+(x/2)10=38   ⇒x/18+x/20=38   ⇒19x/180=38   ⇒x/180=2   ⇒ x = 360   i.e., the distance between A and B = 360 km. Answer : Option 360 km
Answer: C
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero? Choose the most appropriate option:  A) 7  B) 4  C) 12  D) 19  E) 28

Solution: Average of 20 numbers = 0   Sum of 20 numbers = (0 * 20)= 
(0 * 20) = 0
0   It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).   Answer: 19
Answer: D
a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the maximum and minimum possible values of 'a - b'? Answers:
A) 28
B) 29
C) 34
D) 38
E) 36

Solution: possible values of a and b can be 5,4; 4,5 and 1,20; 20,1   maximum possible value for a-b is   20-1= 
  20-1 = 19
19   minimum possible value for a-b is 1-20=-19   19-(-19)= 
19-(-19) = 38
38 ans is 38
Answer: D
Three candidates contested in an election and received 1136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
Choose the correct choice from the following answers.
A) 45%
B) 49%
C) 57%
D) 51%
E) 62%

Solution: Total number of votes polled = 1136+7636+11628= 
1136+7636+11628 = 20_400
20400   Required percentage= 11628*100/20400= 
11628*100/20400 = 57
57%   Answer is 57%
Answer: C
If 50% of (x-y) = 20% of (x+y), then what percent of x is y?  Choose the correct answer.
A) 50.5%
B) 42.8%
C) 22.2%
D) 33.3%
E) 25%

Solution: 50% of (x-y) = 20% of (x+y)   50/100 (x-y) = 20/100 (x+y)   3x = 7y   Required percentage = y/x *100 = 3y/7y * 100 = 42.85%   Answer is 42.8%
Answer: B
A departmental store charges the commission of 15 percent on the first sale of items worth $50,000 and then an additional 12 percent on any sale price that exceeds the initial $50,000. If the department store earned $24,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set? Choose the correct choice from the following options
A) $215,000  B) $365,000  C) $115,000  D) $240,000  E) $187,500

Solution: 24,000 = 0.15 *(50000) + 0.12 (x - 50000)   24000 - 7500 = 0.12 (x-50000)   137500 = x - 50000   x = 1,87,500   Answer : $187,500
Answer: E
What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number R?
Choose the correct choice from the following answers.
A) 126  B) 1386  C) 3108  D) 308  E) 13986

Solution: As we are using digits 1,5, 8 and digits are allowed to repeat. Each of the unit, tenth and hundredth digit can be used by each of three digits.   So,Total possible numbers with these digits=3 X 3 X 3 =27.   First, As we have 27 three digit number, Sum will be for sure more than 2700..Eliminate options A,B,D   Second, If you imagine numbers R with the given digits 1,5,8. We have numbers like 888,885,855,858,851. Sum is for sure more than 4000.Eliminate option C.   You are left withanswer 13986.
Answer: E
In how many years, Rs. 300 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ?	Pick
A) 4 years	B) 6 years	C) 8 years	D) 9 years	E) 12 years

Solution: Explanation :   Let Simple Interest for Rs.300 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years   300×6×n/100=800×9/2×2/100   300×6×n=800×9/2×2   300×6×n=800×9   n=4 years   4 yearsnswer : Option 4 years
Answer: A
What is the units digit of 32! + 50! + 2! + 4!?
Select the correct option
A) 0
B) 2
C) 4
D) 6
E) 8

Solution: For all N greater than 4, the units digit of N! is 0.   The sum of the four units digits is 0 + 0 + 2 + 4= 
0 + 0 + 2 + 4 = 6
6   The units digit is 6.   The answer is 6.
Answer: D
Sharmila works 10 hours per day on Monday, Wednesday and Friday, and 8 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $460 per week. How much does she earn in dollars per hour? Choose the correct choice from the following answers
A) 8	B) 9	C) 9.5	D) 10	E) 11

Solution: So, she works 30 hours in 3 days   So, she works 16 hours in 2 days   So in a week she works 46 hours ( 30 + 16 ) and earns $460   So, Hourly wage is  460/46= 
 460/46 = 10
> 10   Hence answer will be (10) 10
Answer: D
A whale goes on a feeding frenzy that lasts for 12 hours. For the first hour he catches and eats 30 kilos of plankton. In every hour after the first, it consumes 2 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 600 kilos of plankton, how many kilos did he consume on the 10th hour?
Pick:
A) 36	B) 45	C) 28	D) 48	E) 52

Solution: Therefor in 10th hour he consume x+2*9=30+18= 
30+18 = 48
48   correct option is 48
Answer: D
From a class consisting of 12 computer science majors, 10 mathematics majors, and 9 statistics majors, a committee of 4 computer science majors, 4 mathematics majors, and 3 statistics majors is to be formed. How many distinct committees are there?	Choose one.
A) 15200	B) 16200	C) 17200	D) 18000	E) 19500

Solution: From a class consisting of 12 computer science majors, 10 mathematics majors, and 9 statistics majors, a committee of 4 computer science majors, 4 mathematics majors, and 3 statistics majors is to be formed. How many distinct committees are there?   Alright, I just started learning combinations tonight, but I have hit a wall. I ran across this problem but cannot get the answer right. Apparently, the answer is 8-some-thousand, but I keep coming up with 16,200. This is how I am working it.   12!/4!(12-4)! * 10!/4!(10-4)! * 9!/3!(9-3!)   (12*...*1/4*...*1*8*...1) * (10*...*1/4*...1*6...*1) * (9*...1/3*2*1*6*...1)   (12*10*9/4*3*2*1) * (10*9*8*7/4*3*2*1) * (9*8*7/3*2*1)   (3*5*3/1*1*1) * (5*3*7/1*1*1) * (3*4*7/1*1*1)   45 * 30 * 12   Answer: 16,200 16200
Answer: B
A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002?	Select the correct option.
A) $18,400 B) $19,700 C) $20,200 D) $20,400 E) $21,100

Solution: Price in 96 = 22000   Price decrease each year = 2.5/100*22000= 
2.5/100*22000 = 550
550   Price in 97= 22000 - 550   Price in 98 = 22000 - 2*550   Price in 99 = 22000 - 3*550   Price in 00 = 22000 - 4*550   Price in 01 = 22000 - 5*550   Price in 02 = 22000 - 6*550= 
22000 - 6*550 = 18_700
18700   Investment in the car= 1000   Net price of the car in 02 = 18700 + 1000= 
18700 + 1000 = 19_700
$19700   Correct Option: $19,700
Answer: B
Four hundred multiples of seven are chosen at random, and 100 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd?  Choose the correct answer:
A) 30%
B) 50%
C) 60%
D) 55%
E) 40%

Solution: --> Multiples of 7 are 7, 14, 21, 28, 35, 42....   Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.   So approx. 50 % of the 400 multiples are odd i.e 200 multiples.   --> Similalrly, for 8 multiples are:8,16,24...   All are even so 0 % are odd.   Total odd= (200+0)/(400+100)= 200/500=(2/5) = 40%   Answer 40%
Answer: E
What is the area M of the square with the following coordinates: (x, y), (20, 20), (20, 5), (x, 5)? Choose one.
A) 60.	B) 85.	C) 125.	D) 225.	E) It cannot be determined from the information given

Solution: Length of one side= 15 (20-5)   Since, its a square, the area will be M= 15^2= 225   225. is the answer
Answer: D
The speed of a car is 120 km in the first hour and 70 km in the second hour. What is the average speed of the car?	Options
A) 72 kmph	B) 75 kmph	C) 95 kmph	D) 80 kmph	E) 82 kmph

Solution: S = (120 + 70)/2= 
(120 + 70)/2 = 95
95 kmph   ANSWER:95 kmph
Answer: C
An air conditioner can coo the hall in 12 minutes while another takes 15 minutes to cool under similar conditions. if both air conditioners are switched on at same instance then how long will it take to cool the room?
Choose the correct choice from the following options:
A) about 7 minutes
B) about 8 minutes
C) about 9 minutes
D) about 10 minutes
E) about 5 minutes

Solution: Take LCM of 12 and 15 = 60   12*5= 
12*5 = 60
60/ 15*4=60.   So if both are switched on together , room cooled in 60/(5+4)=60/9=6.66 minutes   6.66 can be round to 7 minutes , so about 7 minutes   about 7 minutesNSWER: about 7 minutes
Answer: A
The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? Choose one
A) 18 2/71% B) 18 2/11% C) 18 2/15% D) 18 2/19% E) 18 2/21%

Solution: 13 CP = 11 SP   11 --- 2 CP   100 --- ? =>18 2/11%   Answer: 18 2/11%
Answer: B
4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?	Choose the correct choice from the following answers.
A) 2800
B) 2500
C) 3000
D) 3500
E) 4000

Solution: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144   3x/100 + 200 â€“ 5x/100 = 144   2x/100 = 56 Ã¨ x = 2800   2800NSWER 2800
Answer: A
John deposited $10,000 to open a new savings account that earned 6 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened?
Choices: A) $10,100.30 B) $10,101.50 C) $10,200.75 D) $10,302.25 E) $10,400.25

Solution: 6 percent annual interest compounded quarterly --> 1.5% in 3 moths.   For the first 3 moths interest was 1.5% of $10,000, so $150;   For the next 3 moths interest was 1.5% of $10,000,plus2.25 earned on previous interest of $150, so $150+$2.25=$152.25;   Total interest for 6 months was $150+$152.25  150+ 2.25= 
  150+ 2.25 = 152.25
$152.25;   Total interest for 6 months was $150+$152.25=$302.25, hence balance after 6 months was $10,000+ $302.25 150+ 152.25= 
 150+ 152.25 = 302.25
$302.25, hence balance after 6 months was $10,000+ $302.25=$10,302.25.   Answer: $10,302.25.
Answer: D
90kg of an alloy A is mixed with 140 kg of alloy B. If alloy A has lead and tin in the ratio 3:4 and alloy B has tin and copper in the ratio 2:5, then the amount of tin in the new alloy is? Options.
A) 100.6kg B) 95.4kg C) 117.5kg D) 91.4kg E) 92kg

Solution: Quantity of tin in 90kg of A = 90*4/7 = 51.4kg   Quantity of tin in 140kg of B = 140*2/7= 
140*2/7 = 40
40kg   Quantity of tin in the new alloy= 51.4+40= 
51.4+40 = 91.4
91.4kg   Answer is 91.4kg
Answer: D
The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least three ingredients? (Also assume that each bin can hold one and only one blend.)	Choose the correct choice from the following options
A) 1
B) 4
C) 5
D) 11
E) 10

Solution: We're told that there are 4 ingredients (we'll call them A, B, C and D); we're told that each 'mix' must include AT LEAST 3 ingredients...   3 ingredient blends:   AB5   ABD   A5D   B5D   4 ingredient blends:   AB5D   Total blends =4+1= 
4+1 = 5
5   5
Answer: C
If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of four consecutive even integers starting with 10, respectively, what is the probability that b/a will not be an integer? Select the correct option:
A) 3/16	B) 1/4	C) 5/16	D) 3/8	E) 1/2

Solution: a is from the following set {1,2,3,4}   b is from the following set {10,12,14,16}   The total number of ways of choosing 2 integers, one from each set is  4*4= 
 4*4 = 16
16 ways.   The possibilities where b/a is not an integer is for the following outcomes:   {b,a}= {10,3},{10,4},{14,3},{14,4},{16,3} = 5 ways   Thus the probability is 5/16   The answer is 5/16.
Answer: C
Lastly, jenny compared Canada’s CN Tower and Seattle’s Space
Needle. How tall is the Space Needle if the CN Tower stands at 553m
high and it is taller than the Space Needle by 369m?	Choose the correct choice from the following choices:	A) 127	B) 184	C) 170	D) 113	E) 099

Solution: 553-369= 
553-369 = 184
184.Answer is 184.
Answer: B
A student chose a number, multiplied it by 6, then subtracted 250 from the result and got 122. What was the number he chose?
Choose the correct choice:
A) 59
B) 60
C) 61
D) 62
E) 63

Solution: Let x be the number he chose, then   6⋅x−250=122   6x=372   x=62   correct answer 62
Answer: D
Min (a, b, c)=min of a, b, c Max (a, b, c,)=max of a, b, c then what is the value of MAX {min (2,5,7), max (-7, -2, -3), 3} Pick.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: MAX {min (2,5,7), max (-7, -2, -3), 3}   = MAX {2,-2,3}   =3   ANSWER:3
Answer: C
A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
Options
A) 12 B) 15 C) 10 D) 48 E) 17

Solution: Two students can be selected from 6 in 6C2 =15 ways.   Therefore, the teacher goes to the zoo 15 times.   Ans: 15
Answer: B
If x and y are positive integers such that x/y = 2.60, which of the following numbers could be y?	Answers:	A) 3	B) 4	C) 6	D) 5	E) 10

Solution: With the given information, we are trying to find the value of y.   To achieve this we must convert the given decimal to a fraction and reduce it to it's lowest integer form.   Take the decimal x/y = 2.60 and because it's in the hundreds decimal place, put the given value (x/y = 2.60/1) and multiply it by 100.   Take the resulting fraction (x/y = 260/100) and reduce it to it's lowest form.   Both of the numbers are divisible by 20.   The result is x/y = 13/5.   Thus y = 5.   The correct answer is 5.
Answer: D
Initially two cups of same volume are present with milk filled upto 3/5th and 4/5th of their volumes.Water is then filled. Then two mixtures are mixed. Find the ratio of water to milk in the mixture	Pick.
A) 1/7 B) 2/7 C) 3/7 D) 4/7 E) 5/7

Solution: water content can b in 1st and second is 2/5 and1/5 total:3/5.the total milk content is 7/5.the ratio is ((3/5)/(7/5))=3/7.   ANSWER:3/7
Answer: C
What smallest number should be added to 8444 such that the sum is completely divisible by 7 ?  Choose the correct answer:
A) 6
B) 5
C) 4
D) 3
E) 2

Solution: Explanation:   8444 ÷ 7 = 1206, remainder = 2   7 - 2= 
7 - 2 = 5
5   Hence, 5 should be added to 8444 such that the sum is completely divisible by 7.   Answer: 5
Answer: B
The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?
Choose the correct choice from the following answers:  A) 13.5  B) 14  C) 15  D) 12.5  E) None

Solution: Solution:   At present the total age of the family = 5*20= 
5*20 = 100
100.   The total age of the family at the time of the birth of the youngest member,=[100−10−(10*4)]=50.   Therefore, average age of the family at the time of birth of the youngest member,   = 50/4 = 12.5.   Answer: Option 12.5
Answer: D
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 27 seconds. What is the length of each train (in meters)?  Options
A) 50.5 B) 88.5 C) 37.5 D) 55.5 E) 23.5

Solution: The relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr= 10 * 5/18 = 25/9 m/s   In 27 seconds, the relative difference in distance traveled is  27 * 25/9= 
 27 * 25/9 = 75
75 meters   This distance is twice the length of each train.   The length of each train is  75/2= 
 75/2 = 75/2 = around 37.5
37.5 meters   The answer is 37.5.
Answer: C
180 metres long yard, 11 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees  Choose the correct choice from the following options.
A) 18
B) 12
C) 14
D) 16
E) 17

Solution: 11 trees have 10 gaps between them,   Required distance (180/10)= 
(180/10) = 18
18   18
Answer: A
If x and y are integers such that x^2+4x+2y+6=2x^2+5x+y-6, we can deduce that y is
Select the correct option.
A) not an even	B) an even	C) a perfect square	D) an odd	E) a prime

Solution: x^2 + 4x + 2y + 6 = 2x^2 + 5x + y - 6   y = x^2 + x - 12   y = (x+4)(x-3) (Note that one factor is even and one factor is odd.)   Then y must be even.   The answer is an even.
Answer: B
A, B and C can do a work in 7 , 14 and 21 days respectively. They completed the work and got Rs.242. What is the share of C?  Choose one.
A) 33  B) 44  C) 55  D) 77  E) 99

Solution: The ratio of their working rates = 1/7 : 1/14 : 1/21 = 6 : 3 : 2.   Since, they work together, the share of C   = 2/11 * 242 = Rs.44   \Answer: 44
Answer: B
Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is q, what is the difference between the probability that q is even and the probability that q is odd?
Options
A) 1/9	B) 1/6	C) 2/9	D) 1/4	E) 1/2

Solution: 1/9ge of Boys q:4, 6, 7   Sum of ages taken 2 at a time: 10,13,11   1/9ges of Girls:5, 8, 9   Sum of ages taken 2 at a time: 13,17,14   9 Combinations of sum between sets(10,12,11)(13,17,14)   =23,27,24- 16,30,17- 24,28,25   Prob(Even)= 5/9   Prob(Odd) =4/9   1/9nswer=5/9 - 4/9 = 1/9
Answer: A
On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 180,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?  Choose the correct option:
A) 77,500 B) 1,860,000 C) 2,880,000 D) 3,720,000 E) 4,960,000

Solution: 180,000 × 2 × 2×2×2 = 180,000 × 16 = 2,880,000
Answer: C
Having received his weekly allowance, a student spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.60 at the candy store. What is this student’s weekly allowance?  Choose the correct choice from the following answers
A) $2.25
B) $2.75
C) $3.00
D) $3.50
E) $3.75

Solution: Let x be the value of the weekly allowance.   (2/3)(2/5)x = 60 cents   (4/15)x = 60   x = $2.25   The answer is $2.25.
Answer: A