MU-NLPC/Calc-aqua_rat huggingface dataset:
Look at this series: -2, 0, 2, 4,... What number should come next? Choose the correct choice from the following.
A) 6	B) 12	C) 8	D) 9	E) 10

Solution: Explanation: This is a simple addition series; each number is added by 2 to the previous number. In other terms to say, the number is added by 2 successively to get the next result.   -4+2 = -2   -2+2= 
-2+2 = 0
0   0+2= 
0+2 = 2
2   2+2= 
2+2 = 4
4   4+2= 
4+2 = 6
6 and so on.   6nswer: Option 6
Answer: A
Dhoni decides to attend a tennis game with four friends. If the party of five sits together in five consecutive seats, and Dhoni must NOT sit in between two of his friends, how many ways can the five friends be arranged?	Choose the correct choice from the following answers
A) 6  B) 48  C) 36  D) 24  E) 12

Solution: Dhoni have to sit at either of the ends.   If Dhoni sits on the left most corner, then other 5 friends can be arranged in 4! = 24   David can also sit on the other end, then another 4! ways we can arrange.   So total number of ways = 24+24= 
24+24 = 48
48   Answer : 48
Answer: B
Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 20% Vermouth by volume. How many ounces of Gin must he add? Choose one.
A) n/6  B) n/3  C) 3n/5  D) 5n/6  E) 8n/5

Solution: 4 ounces is vermouth   6 ounces of gin...   Total volume 10.   To make vermouth account for 20% of total volume the new volume must be....   x*0.2=4   x=20 ounces....   So now you see that he must add 10 ounces of gin...   Plug in 12 for n in the answer choices and look for answer 10   5n/6
Answer: D
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.90 less, he could have gained 25%. What is the cost price?  Choose the correct choice from the following answers:
A) 372  B) 375  C) 278  D) 267  E) 450

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   90 ----- ?=> 450   Answer:450
Answer: E
Surekha started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajesh joined him with an amount of Rs. 35,000. In 2001, Surekha invested another additional amount of Rs.10,000 and Jay joined them with an amount of Rs.35,000. What will be Rajesh's share in the profit of Rs.1,50,000 earned at the end of 3 years from the start of the business in 1999?  Choose the correct choice from the following answers
A) Rs 45000	B) Rs 50000	C) Rs 70000	D) Rs 75000	E) None

Solution: Surekha:Rajesh:Jay= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajesh's share =Rs.(150000×2/6) = Rs.50000.   Answer Rs 50000
Answer: B
A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 5 games? Choose the correct option: A) x + 3y/(n + 3) B) x + y/(n + 3) C) (x + 3y)/(n + 3) D) (nx + 3y)/(n + 5) E) (3x + ny)/(n + 3)

Solution: Total points in first n games = nx   Total marks in next 3 games is 3y   So, Average marks in n + 5 games = (nx+3y)/(n+5)   Hence, correct answer will be ((nx + 3y)/(n + 5))
Answer: D
How many 4-digit no's that are divisible by 10 can be formed from the no.'s 3, 5, 7, 8, 9, 0 such that no no. repeats?
Choose the most appropriate option.
A) 20
B) 30
C) 60
D) 70
E) 90

Solution: If a number is divisible by 10, its units place should contain a 0.   _ _ _ 0   After 0 is placed in the units place, the tens place can be filled with any of the other 5 digits.   Selecting one digit out of 5 digits can be done in 5C1 = 5 ways.   After filling the tens place, we are left with 4 digits. Selecting 1 digit out of 4 digits can be done in 4C1 = 4 ways.   After filling the hundreds place, the thousands place can be filled in 3C1 = 3 ways.   Therefore, the total combinations possible = 5*4*3= 
5*4*3 = 60
60.   60
Answer: C
The "Racing magic" takes 120 seconds to circle the racing track once. The "Charging bull" makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?
Choose the correct choice from the following answers:
A) 3  B) 6  C) 9  D) 12  E) 15

Solution: Time taken by Racing magic to make one circle = 120 seconds = 2 mins   Time taken by "Charging bull" to make one circle = 60 mins / 40 = 1.5 mins = 90 seconds   LCM of 90 and 120 seconds = 360 seconds = 6 mins   Time taken for them to meet at the starting point for the second time = 6 mins *2 = 12 mins   Answer 12
Answer: D
Find value of x
(11^2 + 12^2 + 13^2 + ... + 20^2) = x  Choose the most appropriate option:	A) 1200	B) 1340	C) 1234	D) 1203	E) 2485

Solution: (11^2 + 12^2 + 13^2 + ... + 20^2) = (1^2 + 2^2 + 3^2 + ... + 20^2) - (1^2 + 2^2 + 3^2 + ... + 10^2)   6   = 20 x 21 x 41	-	10 x 11 x 21   6	6   = (2870 - 385)= 
(2870 - 385) = 2_485
2485   2485
Answer: E
A certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts, by weight. What is the number of pounds of almonds in 350 pounds of the mixture ? Answers.
A) 250	B) 84	C) 40	D) 28	E) 20

Solution: 250lmonds : Walnuts = 5 : 2   Total mixture has 7 parts   In a 350 pound mixture, 250lmonds are 5/7 (total mixture)   = 5/7 * 350= 
5/7 * 350 = 250
250 pounds   250nswer (250)
Answer: A
A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $90 to incur a loss 20%?  Pick one
A) 45
B) 36
C) 40
D) 50
E) 48

Solution: Production cost per article: $60*(100%-20%) / 20 = $2.40   Required production costs for a loss of 20%: $90*(100% + 20%) = $108   Number of articles to be sold for $108 to incur a 20% loss: $108 / $2.40 = 45   Thus, solution 45 is correct.108 /  2.40= 
108 /  2.40 = 45
45   Thus, solution 45 is correct.
Answer: A
Two vessels contains equal number of mixtures milk and water in the ratio 5:2 and 6:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained? Pick one
A) 1:3 B) 9:13 C) 5:11 D) 11:3 E) 15:4

Solution: The ratio of milk and water in the new vessel is = (5/7 + 6/7) : (2/7 + 1/7)   = 11/7 : 3/7 = 11:3   Answer is 11:3
Answer: D
A man can row upstream at 7 kmph and downstream at 10 kmph.Find man's rate in still water and the rate of current?  Choose the correct choice from the following choices:
A) 1.2 km/hr
B) 1.5 km/hr
C) 1.6 km/hr
D) 1.8 km/hr
E) None

Solution: Solution   Rate in still water	= 1 / 2 (10 + 7) km/hr   = 8.5 km/hr.   Rate of current	= 1 / 2(10 - 7) km/hr   = 1.5 km/hr.   Answer 1.5 km/hr
Answer: B
The sum of two number is 25 and their difference is 13. Find their product.	Choose the most appropriate option:
A) 104
B) 114
C) 315
D) 325
E) None

Solution: EXPLANATION   Let the numbers be x and y.   Then, x + y = 25 and x – y = 13.   4xy = (x + y)2 – (x– y)2   = (25)2 – (13)2   = (625 – 169)   = 456   xy = 114.   Answer 114
Answer: B
Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? Choose the correct choice from the following answers.
A) 10	B) 88	C) 267	D) 28	E) 21

Solution: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.   x + y = 7 --- (1) ; 2x = 4 --- (2)   solving both the equations, we get y = 5   So, time taken to cover both ways by cycle = 2y hours = 10 hours.   10nswer: 10
Answer: A
The present worth of a sum due sometimes hence is Rs.5760 and the banker's gain is Rs.10. What is the true discount?  Select:
A) Rs. 480
B) Rs. 420
C) Rs. 120
D) Rs. 240
E) Rs. 260

Solution: Explanation:   TD = √PW × BG=√5760×10=√57600 = Rs. 240   Answer: Option Rs. 240
Answer: D
In an Examination there are three subject of 100 marks each. A student scores 60% in the 1st subject and 80% in the second subject. He scored 70% in aggregate. His percentage of marks in the third subject is: Choose the correct answer.
A) 70	B) 80	C) 60	D) 65	E) 66

Solution: Explanation :   Let be the score of third subject = X   70 student of score in first subject = 60% = 60 x 100/100 = 60   70 student of score in second subject = 80% = 80 x 100/100 = 80   70% of 300 = 300 x 70/100 = 210   score of third subject = 210 – ( 60 + 80)   = 210 – 140 = 70   Percentage of score in third subject = 70 x 100/100 = 70%   Hence, the answer is 70%   70nswer : 70
Answer: A
The arithmetic mean of the scores of a group of students in a test was 62. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?
Select:
A) A)61.4.
B) B)51.7
C) C)69.54
D) D)51.1
E) E)51.2

Solution: Let the required mean score be x. Then,   20 * 80 + 25 * 31 + 55 * x = 62 * 100   = 1600 + 775 + 55x = 6200   = 55x = 3825   = x = 69.54   Answer:69.54
Answer: C
Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill? Choose the correct choice from the following answers:	A) 1/0	B) 1/3	C) 1/1	D) 1/7	E) 1/5

Solution: 1/10 + 1/15 = 1/6 * 4 = 2/3   1 - 2/3 = 1/3   1/10 + 1/15 - 1/x = 1/3   x = 8   Answer: 1/3
Answer: B
The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1240. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?  Select.
A) 2480
B) 3490
C) 6785
D) 8215
E) 9255

Solution: sum of square of n numbers is found using the formula [n (n+1) (2n+1)]/6   we have sum of 1st 15 numbers = 1240   we need to find sum of squares from 16 to 30 which is = sum of squares of 1st 30 +ve integers - sum of squares of 1st 15 +ve integers.   we will get 8215 - 8215;ANSWER:8215
Answer: D
Eight men, ten women and six boys together can complete a piece of work in eight days. In how many days can 20 women complete the same work if 20 men can complete it in 12 days?	Choose the correct choice from the following answers:  A) 33  B) 77  C) 66  D) 22  E) 99

Solution: Let the number of units which can be completed by each man, each women and each boy be m/day, w/day and b/day respectively.   Work = 8(8m + 10w +6b)units = 12(20m)   10w +6b = 22m   b is unknown.   We cannot find the relation between m and w.   We cannot answer the question.   Answer:22
Answer: D
Which of the following is divisible by the first five positive integer multiples of 23?
(i) 11110
(ii) 102120
(iii) 307740  Choose the correct choice from the following choices:
A) None  B) iii only  C) i and iii only  D) ii and iii only  E) i, ii and iii

Solution: A positive integer x is divisible by the first five integer multiples of 23 if and only if it is divisible by their least common multiple, 3*4*5*23=60*23= 
60*23 = 1_380
1380.   The sum of the integers of 11110 is 4 so 11110 is not divisible by 3, hence not divisible by 1380.   102=17*6 and 120=20*6, so 102120=60*(1700+2)=60*1702=60*2*851. Now, 851-30*23=851-690= 
851-690 = 161
161=7*23, so 102120 is divisibly by   60*23= 
  60*23 = 1_380
1380.   Finally, 102120*3=306360, and   306360+1380= 
  306360+1380 = 307_740
307740, so (iii) is also divisible by 1380.   Answer ii and iii only.
Answer: D
A local bank that has 20 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 20 codes?  Options.
A) 3 B) 4 C) 7 D) 6 E) 5

Solution: Pick any two integer.   Integers: 12   Code: 11, 12, 21, 22 = 4 Codes   Add one more integer: 3   13, 31, 33, 23, 32 = 5 Codes   Add one more integer: 4   44, 14, 41, 24, 42, 34, 43 = 7 Codes   Add one more integer: 5   55, 15, 51, 25, 52, 35, 53,54,45 = 9 Codes   Total = 25 Codes. Enough.   Answer: 5
Answer: E
The cost of the paint is rs.50 per kg. if 1kg of paint covers 20 sq.ft, how much will it cost to paint outside of a cube having 20 feet each side
Choose the correct choice from the following answers:	A) Rs.962	B) Rs.6000	C) Rs.546	D) Rs.876	E) None of these

Solution: Explanation:   surface area of a cube= 6 x 20^2 = 2400 sq.ft   quantity of paint required=(2400/20)= 
(2400/20) = 120
120 kg   cost of painting= 50x 120= Rs.6000   Answer: Rs.6000
Answer: B
If the city centers of Tokyo and Rome are 6124 miles apart, which of the following is closest to the distance between the city centers in inches? (There are 5,280 feet in a mile.)  Choose the correct answer
A) 1.7 × 10^7
B) 4.8 × 10^7
C) 3.9 × 10^8
D) 2.7 × 10^9
E) 1.5 × 10^10

Solution: 6124 miles = 6124 x 5280 feet/mile x 12 inches/foot which is about 3.9 x 10^8 inches.   The answer is 3.9 × 10^8.
Answer: C
Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business? Select the correct option
A) 12:15:18	B) 12:15:16	C) 12:15:10	D) 12:15:12	E) 12:15:11

Solution: Explanation:   Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)   = 12:15:16   Answer: 12:15:16
Answer: B
The mean of 50 observations was 36. it was found later an observation 48 was wrongly taken as 23 . the corrected new means is :  Choose the correct choice from the following answers
A) 35.2 B) 36.1 C) 36.5 D) 39.1 E) None of these

Solution: Solution   Correct sum = (36 × 50 + 48 - 23) = 1525.   ∴ correct mean = 1825/50= 
1825/50 = 73/2 = around 36.5
36.5 Answer 36.5
Answer: C
Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 7%. What is the approximate interest he pays annually?
Choose the correct choice from the following choices.
A) 1000 B) 1500 C) 3000 D) 2500 E) 2400

Solution: An easy way too attempt this is by approximation:   For the first quarter, he pays 7% of 10,000 which is $700.   So for the four quarters in the year, he will approximately play  700*4= 
 700*4 = 2_800
2800 over the entire year.   Because of compound interest it will be more than 2800. Approx. option C is correct.   Answer : 3000
Answer: C
Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?	Choose the correct option:
A) 2:9
B) 2:7
C) 1:6
D) 1:4
E) 1:3

Solution: (10/100)A+(3/100)B = (4/100)(A+B)   6A =B   => A/B = 1/6   Answer is 1:6.
Answer: C
If P (A) = 0.18, P (B) = 0.5 and P (B|A) = 0.2, find P(A n B)? Choices:
A) 0.36	B) 0.4	C) 0.42	D) 0.43	E) 0.64

Solution: P(B|0.36) = P(0.36 n B)/P(0.36)   P(0.36 n B) = P(B|0.36) × P(0.36)   P(0.36 n B) = 0.2 × 0.18   P(0.36 n B) = 0.36   0.36
Answer: A
Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 8200, then what will be the share of Sameer in the profit?	Choose one:  A) s.2323  B) s.2380  C) s.2800  D) s.2329  E) s.2312

Solution: Kamal : Sameer = (9000 * 12) : (8000 * 7)   = 108:56 = 27:14   Sameer's share = 8200 * 14/41   = Rs.2800.   Answer: s.2800
Answer: C
The difference between the local value and the face value of 7 in the numeral 32675149 is  Select.
A) 69950 B) 69993 C) 69997 D) 70000 E) 01000

Solution: (Local value of 7) - (Face value of 7) = (70000 - 7)= 
(70000 - 7) = 69_993
69993   69993
Answer: B
Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 4 fantasy books, there are 5 reference books. If the proportion of history to fantasy books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?	Choose the correct choice from the following choices:
A) 6
B) 21
C) 24
D) 32
E) 36

Solution: For every 2 history books, there are 7 fantasy books:   Originally H:F = 2:7. After the change, H:F = 4:7 = 16:28   For every 4 fantasy books, there are 5 reference books:   F:R = 4:5 = 28:35   H:F:R = 16:28:35   There are fewer than 60 fantasy books, so there are 28 or 56 fantasy books.   The number of history books could be 16 or 32.   The answer is 32.
Answer: D
One side of a triangle has length 9 and a second side has length 4. Which of the following could be the area of the triangle?
I. 30
II. 20
III. 10 Pick.
A) I only B) II only C) III only D) II and III only E) I, II, and III

Solution: The triangle will have a maximum area when it is a right angled triangle   The largest triangle will be formed when 9 and 4 are the base and height of triangle .   Area = 1/2 * 9 * 4= 
1/2 * 9 * 4 = 18
18   There is no lower limit on the area of any triangle whose only 2 sides are known.   Then 0 < Area <= 18   The answer is III only.
Answer: C
The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area? Choose the correct answer: A) 37.6 B) 37.5 C) 37.7 D) 37.2 E) 37.1

Solution: 100 * 100= 
100 * 100 = 10_000
10000   110 * 125= 
110 * 125 = 13_750
13750   -----------   3750   10000 ------ 3750   100 ------- ?=> 37.5%.Answer: 37.5
Answer: B
If the two-digit integers F and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of F and N?	Choose the correct choice from the following
A) 181
B) 165
C) 121
D) 99
E) 44

Solution: Since the question asks for the answer that CANNOT be the sum of F and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.   We're told that F and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of F and N.   Let's start with the 'easiest' answer first:   44. Can we get to 44 in the manner described?   Yes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E   Now let's work through the rest of the list....   Can we get to 99 in the manner described?   Yes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D   Can we get to 121 in the manner described?   Yes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C   Can we get to 165 in the manner described?   Yes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B   There's only one answer left....   181
Answer: A
There is a 10% chance that Tigers will not win at all during the whole season. There is a 30% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?	Choose the correct answer:
A) A)55% B) B)60% C) C)80% D) D)72% E) E)70%

Solution: There is a 10% chance that Tigers will not win at all during the whole season   We can infer that there is 90% chance Tigers will win .   Similarly There is a 30% chance that Federer will not play at all in the whole season   We can also infer that there is 70% chance that Federer will play.   Answer 70%
Answer: E
Solve below question 2x + 1 = -17  Choose the most appropriate option: A) 7 B) -9 C) 10 D) -1 E) 2

Solution: 1. Subtract 1 from both sides:   2x + 1 - 1 = -17 - 1   2. Simplify both sides:   2x = -18   3. Divide both sides by 2:   4. Simplify both sides:   x = -9   -9
Answer: B
To be elected president of a certain organization, a candidate needs the votes of at least 2/3 of its 1,331 members. What is the least number of votes the candidate needs to be elected? Choose the correct option.
A) 443	B) 444	C) 887	D) 888	E) 889

Solution: required votes>= 1331∗2/3   votes should be an integer, thus we can take   required votes = 1332∗2/3( because 1332/3 will be an integer )   = 888   ANSWER:888
Answer: D
What is the dividend. divisor 17, the quotient is 9 and the remainder is 5.	Choose the correct choice from the following:  A) 148  B) 150  C) 152  D) 158  E) 160

Solution: 158 = d * Q + R   158 = 17 * 9 + 5   158 = 153 + 5   158 = 158
Answer: D
An equity analyst needs to select 4 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 8, in how many ways can she choose and rank her top 4 picks?
Select the correct option.
A) 1200	B) 1680	C) 2102	D) 4020	E) 1840

Solution: Number of ways of choosing 4 stocks = 8C4   Number of ways of ranking the chosen stocks = 4!   Hence total ways of chosing and ranking = 8C4 * 4! = 1680   Correct Option: 1680
Answer: B
A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?  Options:  A) 118  B) 110  C) 112  D) 113  E) 115

Solution: Original price = 100   112P = 80   S = 80*(140/100)= 
80*(140/100) = 112
112   100 - 112= 12%   Answer: 112
Answer: C
Today John is 3 times older than Mark. If in 13 years, John will be one year younger than twice the age of Mark on that day, how old is Mark today?	Choose the correct choice from the following answers:
A) 12
B) 33
C) 36
D) 38
E) 39

Solution: today +13yrs   J =3M 3M+13   M M+13   Given after 13yrs john will be 1 year younger than twice mark's age   i.e 3M+13 = 2(M+13)-1   M=12   12nswer is 12.
Answer: A
A train moves fast a telegraph post and a bridge 245 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Choices:
A) 73.5
B) 39.5
C) 79.9
D) 79.2
E) 79.1

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 245)/20 = y   y = 20.42   Speed = 20.42 m/sec = 20.42 * 18/5 = 73.5 km/hr.   73.5nswer:73.5
Answer: A
The side of a square is increased by 25% then how much % does its area increases?  Select:
A) 52.65
B) 56.25
C) 50.75
D) 42.75
E) 52.75

Solution: a = 100 a2 = 10000   a = 125 a2 = 15625   ----------------   10000 --------- 5625   100 -------? => 56.25 %   ANSWER:56.25
Answer: B
Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?	Choose the correct choice from the following:
A) 1:7  B) 2:15  C) 9:31  D) 8:17  E) 9:19

Solution: 1/4 : 3/4 = (1:3)5 = 5:15   1/5 : 4/5 = (1:4)4 = 4:16   ------   9:31   9:31
Answer: C
How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 11 inches than that of a rectangular sheet of paper measuring 5.5 inches by 11 inches? Select the correct option:
A) 50%
B) 87%
C) 100%
D) 187%
E) 200%

Solution: Let's just look at the dimensions (no calculation needed).   With dimension 11 the same, the other dimension 11 is twice 5.5   Then the area will be double which means 100% greater.   The answer is 100%.
Answer: C
To mail a package, the rate is 20 cents for the first pound and 5 cents for each additional pound. Two packages weighing 5 pounds and 10 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?	Select
A) Combined, with a saving of 10 cents
B) Separately, with a saving of 10 cents
C) Combined, with a saving of 15 cents
D) Separately, with a saving of 15 cents
E) Combined, with a saving of 5 cents

Solution: 5 pounds = 1*20+4*5= 
1*20+4*5 = 40
40   10 pounds= 1*20+9*5= 
1*20+9*5 = 65
65   total= 105   15 pound = 1*20+14*5= 
1*20+14*5 = 90
90   dif. 15   Answer : Combined, with a saving of 15 cents
Answer: C