MU-NLPC/Calc-aqua_rat huggingface dataset:
By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 300 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?
Choose the correct choice:
A) 1.5% B) 1.9% C) 10% D) 15% E) 19%

Solution: I think there is a typo in question.   It should have been "By weight Liquid 'X ' makes up..... "   Weight of Liquid X = 0.8 % of Weight of 1.5% + 1.8% of Weight of B   When 300gms of 1.5% and 700gms of B is mixed :   Weight of Liquid X = (0.8 * 300)/100 + (1.8* 700)/100= 
(0.8 * 300)/100 + (1.8* 700)/100 = 15
15gms   % of Liquid X in resultant mixture= (15/1000) *100= 
(15/1000) *100 = 3/2 = around 1.5
1.5%   1.5%nswer : 1.5% 1.5%NSWER:1.5%
Answer: A
In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate?
Choose the correct choice from the following answers
A) 355600  B) 355800  C) 356500  D) 356800  E) 357000

Solution: Total number of invalid votes = 15 % of 560000   = 15/100 × 560000   = 8400000/100= 
8400000/100 = 84_000
84000   Total number of valid votes 560000 – 84000= 476000   Percentage of votes polled in favour of candidate A = 75 %   Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000   = 75/100 × 476000   = 35700000/100= 
35700000/100 = 357_000
357000   357000)
Answer: E
Tom is chasing Jerry. In the same interval of time Tom jumps 8 times while Jerry jumps 6 times. But the distance covered by Tom in 7 Jumps is equal to the distance covered by Jerry in 5 Jumps. The ratio of speed of Tom and Jerry is:
Choose the correct choice.
A) 48 :35	B) 28 :15	C) 24 :20	D) 20 :21	E) None

Solution: Solution:   Given;   7 jumps of Tom = 5 jumps of Jerry.   Or, Tom / Jerry = 5/7;   Let Jerry's 1 leap = 7 meter and Tom's 1 leap = 5 meter.   Then, ratio of speed of Tom and Jerry = 8*5/6*7 = 40/42 = 20 :21.   Answer: Option 20 :21
Answer: D
A man saves Rs. 200 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?  Choose the correct option:
A) 662.07 B) 662.0 C) 662.02 D) 362.02 E) 662.05

Solution: Amount = [200(1 + 5/100)3 + 200(1 + 5/100)2 + 200(1 + 5/100)]   = [200 * 21/20(21/20 * 21/20 + 21/20 + 1)] = Rs. 662.02   Answer:662.02
Answer: C
A large box contains 19 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?  Choose the correct option.
A) 475  B) 350  C) 450  D) 550  E) 650

Solution: The number of chocolate bars is equal to   19 * 25= 
19 * 25 = 475
475   correct answer 475
Answer: A
Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them? Select the correct option:  A) 5/9  B) 5/4  C) 5/1  D) 5/6  E) 5/2

Solution: P(at least one graduate) = 1 - P(no graduates)   (6 * 5 * 4)/(10 * 9 * 8) = 5/6   Answer: 5/6
Answer: D
A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 50 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?  Pick:
A) 2.4
B) 3.2
C) 4.0
D) 4.8
E) 5.6

Solution: In 2 hours, A travels 60 km.   B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts.   So A and B both travel a distance of 240 km.   C needs 4.8 hours to travel 240 km, so C leaves 3.2 hours after A.   The answer is 3.2.
Answer: B
Mr.Govind invested an amount of Rs.13900 divided in two different schemes S1 and S2 at the simple interst rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in two years was Rs.3508, what was the amount invested in Scheme S2? Choose the correct answer:
A) Rs.6400	B) Rs.6500	C) Rs.7200	D) Rs.7500	E) Rs.7800

Solution: Let the sum invested in Scheme S1 be Rs.x and that in Scheme S2 be Rs.(13900-x).   Then, (x*14*2)/100 + ((13900-x)*11*2)/100 = 3508;   28x-22x= 3350800-(13900*22);   6x = 45000; x= 7500   So sum invested in Scheme S2 = Rs. (13900-7500) = Rs.6400   Rs.6400NSWER:Rs.6400
Answer: A
Let S be the set of permutations of the sequence 2, 3, 4, 5, 6 for which the first term is not 2. A permutation is chosen randomly from S. The probability that the second term is 5 is given by a/b (in lowest terms). What is a+b?	Choose the correct choice from the following options:
A) 5
B) 6
C) 11
D) 16
E) 19

Solution: The number of possible permutation without 2 in the first digit is   4X4X3X2X1=96 ways.   The number of possible permutations with 5 in the second term is= 3X3X2X1=18 ways.   18c1/96c1 = 18/96= 3/16= > a+b=19.   ANSW19R:19
Answer: E
The sum of three from the four numbers A, B , C , D are 3957 , 4012 , 4370 and 4374 What is the largest of the numbers A , B , C and D?
Choose the correct choice
A) 1614
B) 1200
C) 1560
D) 1198
E) 1298

Solution: 3*(1614+B+C+D)=3957+4012+4370+4374   1614+B+C+D=5571   5571-(Least sum of 3 numbers)=Largest number   5571-3957= 
5571-3957 = 1_614
1614   so Largest number is 1614   1614NSWER:1614
Answer: A
John has to secure 60% marks to clear his exam of class 5th.
He got 10 marks and failed by 50 marks.
What is the maximum marks ?	Choose the correct choice from the following options
A) 110 B) 105 C) 100 D) 95 E) 90

Solution: C   100   To pass the exam ravish needs 10 + 50= 
10 + 50 = 60
60 marks.=> (60/60) *100= 
(60/60) *100 = 100
100
Answer: C
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 48 kmph, find the speed of the stream?	Choose the most appropriate option:
A) 77
B) 88
C) 14
D) 16
E) 17

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 48/3= 
48/3 = 16
16 kmph.   Answer:16
Answer: D
There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total?  Choices
A) 1101	B) 1141	C) 1120	D) 1130	E) None

Solution: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.   Answer 1141
Answer: B
Find the odd man out
36, 315, 612, 810, 966, 1362
Choose the correct answer:	A) 966	B) 612	C) 315	D) 36	E) 1362

Solution: 315is divisible by 3 which is odd number where as all others are even numbers divisible by 3.   ANSWER:315
Answer: C
The price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be reduction in the usage of raw materials so as to keep the cost same?	Choose the most appropriate option:
A) 28% B) 17% C) 27% D) 24% E) Cannot determined

Solution: Solution: Let the initial cost of raw material be 100. So, initial labour cost was 25 and net cost was 125.   Now,   15% increment in raw materials cost and labour cost has gone up to 30% from 25 %.   Raw material cost = 115. And   Labour cost = (115 *30) = 34.5   So, New net cost,   = 115 + 34.5= 
115 + 34.5 = 149.5
149.5   %reduction= 24.5/149.5 = 17%(approx.)   Answer: Option 17%
Answer: B
If 40% of 3/5 of a number is 36, then the number is? Options:
A) 80	B) 150	C) 75	D) 90	E) None of these

Solution: Let the number be x. Then 40% of 3/5 of x=36   40/100*3/5*x=36   x=(36*50/12)= 
(36*50/12) = 150
150   Required number=150.   Correct Option: 150
Answer: B
A train 90 m long running at 56 kmph crosses a platform in 18 sec. What is the length of the platform? Choose the correct choice from the following:
A) 190	B) 200	C) 180	D) 881	E) 271

Solution: D = 56 * 5/18 = 25 = 280 – 90 = 190   190nswer: 190
Answer: A
In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
Pick
A) 52%	B) 58%	C) 82%	D) 32%	E) 12%

Solution: Total = 100   T= 40 NT= 60   40*(60/100)= 
40*(60/100) = 24
24 60*(40/100)=24   24 + 24= 
24 + 24 = 48
48=> 100 - 48= 
100 - 48 = 52
52%   52%nswer: 52%
Answer: A
The ratio of the amount of the oil bill for the month of February to the amount of the oil bill for the month of January was 5:4. If the oil bill for February had been $30 more, the corresponding ratio would have been 3:2. How much was the oil bill for January?
Choose the correct choice from the following:
A) $60
B) $80
C) $100
D) $120
E) $140

Solution: 5:4 = 15:12 and 3:2 = 18:12.   An increase in $30 increases the ratio by 3:12.   Therefore an increase in $10 increases the ratio by 1:12.   Therefore, January's bill was 12($10) = $120.   The answer is $120.
Answer: D
An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.3200, what will be the difference between Q and R's share?	Choose the correct choice from the following answers:
A) 2788	B) 4000	C) 7282	D) 2782	E) 2729

Solution: 4 --- 3200   5 --- ? => 4000   Answer:4000
Answer: B
Data sufficiency question.
Pick one
A) 37
B) 277
C) 299
D) 26
E) 192

Solution: Statement 1 has three solutions,(8, 0), (5, 1), (2, 2) but we cannot say precisely about the relationship   Statement 2 has three solutions, (8, 0), (5, 1), (2, 2) but we cannot say about the relationship.   So data insufficient.   Answer:277
Answer: B
Today Joelle opened an interest-bearing savings account and deposited $5,000. If the annual interest rate is 4 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account? Pick:  A) $5200  B) $5408  C) $5208  D) $5608  E) $5808

Solution: Interest for 1st year = 5000*4/100= 
5000*4/100 = 200
200   Interest for 2nd year= 5200 *4/100= 
5200 *4/100 = 208
208   Total=5000+200+208= 
5000+200+208 = 5_408
5408   Answer : $5408
Answer: B
A boat can row 18 kmph in still water.It takes twice as long to row up as to row down the river.Find the rate of stream.
Choose one:  A) 6 km/hr  B) 7 km/hr  C) 8km/hr  D) 5 km/hr  E) 9 km/hr

Solution: still water-18kmph   It takes twice as long to row up as to row down the river.   then let upstream=2x and downstream=x   now buy the formulae   18=0.5(x+2X)----->x=12   so stream=0.5*(24-12)= 
0.5*(24-12) = 6
6kmph   6 km/hrNSWER:6 km/hr
Answer: A
If e is an integer, what is the greatest possible value for e that would still make the following statement true: 11*10^e < 1/10 ? Choose the correct choice from the following answers:	A) –4	B) –3	C) –2	D) –1	E) 0

Solution: Just putting values, the LHS becomes   e=0 --> 11   e=-1 --> 11/10   e=-2 --> 11/100   e=-3 --> 11/1000   Anything lower will be smaller than 11/1000. e=-2, equality does not hold but it does for e=-3.   Answer is –3.
Answer: B
Evaluate 50% of 450 + 45% of 500	Choose one:
A) 232	B) 450	C) 252	D) 262	E) 272

Solution: Explanation:   = (50/100) * 450 + (45/100) * 500= 
(50/100) * 450 + (45/100) * 500 = 450
450   Option 450
Answer: B
Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 94% water by weight. What is the new weight of the cucumbers, in pounds?	Select:
A) 2
B) 16
C) 92
D) 96
E) 98

Solution: Out of 100 pounds 99% or 99 pounds is water and 1 pound is non-water. After somewaterevaporates the cucumbers become 94% water and 6% of non-water, so now 1 pound of non-water composes 6% of cucucmbers, which means that the new weight of cucumbers is 1/0.06=16 pounds.   Answer: 16.
Answer: B
If the radius of a circle is increased by 50% then the area is increased by:  Choose one:
A) 44%
B) 125%
C) 144%
D) 40%
E) None of the above

Solution: initially A=pi*r2   now R2=150/100r   then area=Pi*(150R/100)2   area=225R/100   that is area increases from 100 to 225=increase in area=125%   ANSWER:125%
Answer: B
The market value of a certain machine decreased by 30 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later?	Choose the correct choice from the following choices
A) $8,000
B) $5,600
C) $3,200
D) $2,400
E) $800

Solution: Market value in 1982= $ 8000   Market value in 1983 = $ 8000- ($ 8000 x 30/100) = 8000-2400= 
8000-2400 = 5_600
$ 5600   Market value in 1984= Market value in 1983 - (30 % of $8000)= 5600-2400= 
5600-2400 = 3_200
$3200   ANSWER:$3,200
Answer: C
If an integer n is to be selected at random from 1 to 100, inclusive, what is probability n(n+1) will be divisible by 32?
Select
A) 2/7 B) 3/7 C) 1/16 D) 1/14 E) 1/12

Solution: because n(n+1) is always an even product of even*odd or odd*even factors,   there is a probability of 1 that that it will be divisible by 2,   and, thus, a probability of 1/2 that it will be divisible by 4   and, thus, a probability of 1/4 that it will be divisible by 8   and, thus, a probability of 1/8 that it will be divisible by 16   and, thus, a probability of 1/16 that it will be divisible by 32   1*1/16=1/16   Answer : 1/16
Answer: C
Find the value of 72517 x 9999 = m?	Choices.
A) 345434667	B) 246465757	C) 465767867	D) 725097483	E) 645354643

Solution: 72518 x 9999 = 72517 x (10000 - 1)   = 72517 x 10000 - 72517 x 1   = 725170000 - 72517= 
725170000 - 72517 = 725_097_483
725097483   725097483
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? Choices
A) 11 B) 87 C) 66 D) 88 E) 62

Solution: (5 + x)/20 + 5/25 = 1 => x = 11 days   Answer: 88
Answer: D
A number n is chosen from {2, 4, 6 … 48}. The probability that ‘n’ satisfies the equation (2x – 6) (3x + 12) (x – 6) (x – 10) = 0 is	Choose the correct choice from the following options:
A) 1/24
B) 1/12
C) 1/8
D) 1/6
E) 1/5

Solution: Given, set is {2, 4, 6 … 48}   n(s) = 24   The roots of given equations are 3,4,4,10. The number of chosen from the set are 4, 10, which are the roots of given equation.   n(E) = 2   Therefore, required probability = 2/24 = 1/12.   ANSWER:1/12
Answer: B
In a company, 56 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?
Options:
A) 45% B) 50% C) 55% D) 60% E) 65%

Solution: The percent of employees who are unionized and men is 0.7*0.6 = 42%   The percent of employees who are unionized and women is 60 - 42= 
60 - 42 = 18
18%   44% of all employees are women, so non-union women are 44%-18% = 26%   40% of all employees are non-union.   The percent of non-union employees who are women is 26%/40%  44 -18= 
 44 -18 = 26
26%   40% of all employees are non-union.   The percent of non-union employees who are women is 26%/40%= 65%   The answer is 65%.
Answer: E
In Township K, 1/5 of the housing units are equipped with cable television . If 1/10 of the housing units , including 1/3 of those that are equipped with cable television , are equipped with videocassette recorders ,what fraction of the housing units have neither cable television nor videocassette recorders ?  Choose the correct choice from the following choices:
A) 23/30	B) 11/15	C) 7/10	D) 1/6	E) 2/15

Solution: Let total Housing Units = 5x.   As per question, Equipped with Cable TV = x   Equipped with VCR = x/2, which includes x/3 CTV. So, only VCR = x/2 - x/3 = x/6.   So, Cable TV + VCR = x + x/6 = 7x/6   No Cable TV and VCR = 5x - 7x/6 = 23x/6.   Fraction = 23x/(6 * 5x) = 23/30. Hence, 23/30
Answer: A
Name the quadrant , if any , in which each point is locted.
(a) (1,6)
(b) (-4, -2) Choose one
A) I, III	B) I, IV	C) III, IV	D) V, III	E) II, I

Solution: (a) (1,6) ---I Quadrant   (b) (-4, -2) ---III Quadrant   Correct answer : (I, III)
Answer: A
In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is
Options:	A) 16 years	B) 88 years	C) 39 years	D) 66 years	E) 77 years

Solution: Let B's age = x years.   Then, As age = (x+ 9) years.   (x+9+10)=2(x—10)   hence x=39.   Present age of B = 39 years   Answer: 39 years
Answer: C
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 1/2 of its present?
Choose one
A) 61.5  B) 60.5  C) 63.5  D) 62.5  E) 50

Solution: Let capacity of 1 bucket = x   Capacity of the tank = 25x   New capacity of the bucket = 1x/2   Hence, number of buckets needed = 25x/(1x/2)=(25×2)/1=50   Answer is 50.
Answer: E
A fair silver coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?	Choose the correct choice from the following.
A) A)37/256  B) B)56/256  C) C)65/256  D) D)70/256  E) E)81/256

Solution: Landing on tails more than 5 times means tails has to hit 6, 7 or 8 times.   8!/6!2! = 7*4= 
7*4 = 28
28   8!/7!1!= 8   8!/8! = 1   28 + 8 + 1 8 /8= 
8 /8 = 1
1   28 + 8 + 1= 
28 + 8 + 1 = 37
37/256   ans:37/256
Answer: A
Anand starts from a point P towards point Q, where PQ = 60 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.  Choose the correct choice from the following answers.
A) (45/7) kmph	B) (60/7) kmph	C) (40/7) kmph	D) (30/7) kmph	E) (65/7) kmph

Solution: Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (60-x) km   Anand traveled this x kms in 3 hours, making his speed x/3 kmph   Ram traveled the same x kms in 2 hours, making his speed x/2 kmph   So, in 6 hours:   Anand will cover=6x/3=2x km   Ram will cover6 /3= 
6 /3 = 2
2x km   Ram will cover=6x/2=3x km   And between their first meeting point and second, they both together covered a distance of 2(90-x) km.   2x+3x6 /2= 
6 /2 = 3
3x km   And between their first meeting point and second, they both together covered a distance of 2(90-x) km.   2x+3x=2(60-x)   5x=120-2x   7x=120   x=120/7 km   Anand's speed=x/3=120/(3*7)=40/7 kmph   Ans:(40/7) kmph
Answer: C
A wheel has a diameter of y inches and a second wheel has a diameter of x inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?
Choose the correct choice from the following
A) 100xy
B) 100y - x
C) 100x - y
D) 100y/x
E) 100x/y

Solution: First Wheel with diameter y inches ----> So the circumference = y*pi --------- (1)   Second Wheel with diameter x inches ----> So the circumference = x*pi --------- (2)   Revolutions = distance/circumference   So, from equation (1)   100 = d/(y*pi)   d = 100 * y * pi ---------- (3)   From equation (2)   Revolutions = d/(x*pi) = (100 * y * pi) / (x*pi) = 100y/x   Answer (100y/x)
Answer: D
Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next?	Choose the correct choice from the following:
A) 7	B) 10	C) 14	D) 15	E) 16

Solution: Explanation: This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on.   Answer: Option 15
Answer: D
A wolf eats 4.5 Kg of meat in 2 days. A baby tiger eats 3 Kg of meat in 4 days. How much meat can the two combined eat in three days?	Pick:  A) 10.  B) 9.  C) 8.  D) 7  E) 6.

Solution: We will have to get them to common ratio may be per 4 days and then convert to 3 days...   So wolf will it  5.5*2= 
 5.5*2 = 11
11 kgs in 4 days...   Total in 4 days= 11+3=14...   So in 3 days= 14*3/4=10.5...   For answer to be B, wolf could be eating 4.5....   So 4.5*2=9..   Combined 9+3= 
9+3 = 12
12 in 4 days..   In three days   12*3/4= 
  12*3/4 = 9
9   ANSWER:9.
Answer: B
137+276=435 how much is 731+672?	Choose the correct answer:	A) 534	B) 1403	C) 1623	D) 1513	E) 1613

Solution: 137-731 and 276-672 similarly 435-534   534NSWER:534
Answer: A
A man tosses three coins in the air. When they land, he finds that two of the coins have heads up and one has tails up.
What is the probability that when the coins are tossed again, they will land again with two heads up and one tails up.
Please note that the coins are unbiased.  Choose the correct choice from the following options: A) 50% B) 40% C) 70% D) 60% E) 55%

Solution: A   50%   Explanation:   When the coins are tossed there can be eight possible outcomes (2*2*2)   HHH   HTT   HTH   HHT   TTT   THH   THT   TTH   If you find out, we have only four favorable outcomes. Also, the events here are independent and thus we can calculate the probability by using these only.   Thus the probability is 50 percent.
Answer: A
Which one of the following numbers is exactly divisible by 11?	Choose the correct choice from the following.
A) 9
B) 10
C) 11
D) 13
E) 15

Solution: (4 + 5 + 2) - (1 + 6 + 3)= 
(4 + 5 + 2) - (1 + 6 + 3) = 1
1, not divisible by 11.   (2 + 6 + 4) - (4 + 5 + 2)= 
(2 + 6 + 4) - (4 + 5 + 2) = 1
1, not divisible by 11.   (4 + 6 + 1) - (2 + 5 + 3)= 
(4 + 6 + 1) - (2 + 5 + 3) = 1
1, not divisible by 11.   (4 + 6 + 1) - (2 + 5 + 4)= 
(4 + 6 + 1) - (2 + 5 + 4) = 0
0, So, 415624 is divisible by 11.   11
Answer: C
The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people C who purchased only book A?  Choose the correct choice from the following choices:
A) 250 B) 500 C) 750 D) 1000 E) 1500

Solution: This is best solved using overlapping sets or a Venn Diagram. We know that A = 2B, and that 500 people purchased both A and B. Further, those purchasing both was double those purchasing B only. This gives us 250 people purchasing B only. With the 500 that pruchased both, we have a total of 750 that purchased B and this is 1/2 of those that purchased A. So, 1500 purchased A. Less the 500 that purchased both, C=1000 purchased A only. (This is much simpler to solve using the Venn diagram).   Correct answer is D. 1000
Answer: D
Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 6:00 am and Pipe B at 7:00 am, at what time will the pool be full?  Select the correct option: A) 14:00 B) 15:00 C) 13:00 D) 16:00 E) 17:00

Solution: Pipe A fills the pool in 4 hrs.   1 hour's work : 1/4   Pipe B empties the pool in 6 hrs.   1 hour's work : 1/6   Together if they work, 1 hour's work = 1/4 -1/6 = 1/12   Given : Pipe A started at 6:00 a.m and Pipe B at 7:00 a.m   Pool filled after 1 hour by Pipe A : 1/4 or 3/12   After 7:00 a.m   Pool filled after 1 hour with both the pipes on : 1/12   Pool filled after 9 hours with both pipes on : 9/12   Pool filled in 1 hour + Pool filled in 9 hours = 3/12 +9/12= 
3/12 +9/12 = 1
1   Therefore, it takes 10 hrs to fill the pool   As Pipe A started at 6:00 a.m, pool is full at 16:00 hrs   Answer : 16:00
Answer: D
If $792 are divided between worker A and worker B in the ratio 5:6,what is the share that worker B will get? Pick.
A) 54.54%
B) 55.55%
C) 56.56%
D) 57.57%
E) 58.58%

Solution: Worker B will get 6/11 = 54.54%   The answer is 54.54%.
Answer: A