MU-NLPC/Calc-aqua_rat huggingface dataset:
An article sold at a profit of 20% if both the cost price and selling price would be Rs.20/- the profit
would be 10% more. What is the cost price of that article?
Choices.
A) 40 B) 50 C) 60 D) 70 E) 80

Solution: if both cost price and selling price would be Rs.20 less.   let c.p-x and s.p-1.2x   1.2x-20 = 1.3(x-20)   x = 60   ANSWER:60
Answer: C
The sum of three consecutive multiples of 3 is 117. What is the largest number? Select:
A) 45 B) 48 C) 51 D) 42 E) 54

Solution: Let the numbers be 3x, 3x + 3 and 3x + 6.   Then,   3x + (3x + 3) + (3x + 6) = 117   9x = 108   x = 12   Largest number = 3x + 6 = 42   Answer : 42
Answer: D
A train running at the speed of 30 km/hr crosses a pole in 12 seconds. What is the length of the train? Pick.
A) 70	B) 80	C) 90	D) 100	E) 110

Solution: Speed=(30 x(5/18)m/sec	=(25/3)m/sec.   Length of the train = (Speed x Time).   Length of the train =	((25/3)x 12)m = 100 m   100
Answer: D
A man sells two articles for Rs.3600 each and he gains 25% on the first and loses 25% on the next. Find his total gain or loss? Choices.
A) 9% loss	B) 6.25% Loss	C) 4000	D) 324	E) 8% LOSS

Solution: (25*25)/100= 
(25*25)/100 = 25/4 = around 6.25
6.25%loss   ANSWER:6.25% Loss
Answer: B
The probability of shooting a target increases after a certain skill is enhanced and is equal to the new probability of NOT shooting the target. Given this fact, which of the following must be false?
Choose the correct choice from the following choices
A) The new probability of shooting the target is greater than 0.5
B) The original probability of shooting the target is less than 0.5
C) The original probability of NOT shooting the target and the new probability of shooting the target are the same
D) The original probability of shooting the target and that of NOT shooting the target are the same.
E) The sum of the original and the new probabilities of shooting the target is ALWAYS equal to 1

Solution: 1. Let p(i), q(i), be the initial probability of shooting and missing the target respectively and let p(n) and q(n) be the new probability of shooting and missing the target respectively.   Given:   1. p(i) + q(i) =1   2. P(n) + q(n) =1   3. p(n) > p(i)   4. p(i) = q(n)   Deductions:   5. q(n) + q(i) =1 ( from (1) and (4) )   6. p(n) + p(i) =1 ( from (2) and (4) ) - ( Choice E always true)   7. From ( 3) and (6), p(i) < 0.5 and p(n) > 0.5 - ( Choice A and Choice B always true)   8. From (1) and (6), q(i) = p(n) - ( Choice C always true)   9. From (3) and (8), q(i) > p(i) - ( choice The original probability of shooting the target and that of NOT shooting the target are the same. always false)   Therefore the answer is Choice The original probability of shooting the target and that of NOT shooting the target are the same.
Answer: D
A man can row downstream at the rate of 32 Kmph and upstream at 17 Kmph. Find the man’s rate in still water and rate of current?
Options.
A) 7.5  B) 8.0  C) 9.5  D) 9.0  E) 8.25

Solution: Rate of still water = 1/2 (down stream + upstream)   = 1/2 (32 + 17) = 24.5 Kmph   rate of current = 1/2 (down stream - upstream)   = 1/2 (32 - 17)   = 1/2 (15)   = 7.5 kmph   7.5nswer is 7.5.
Answer: A
Edward earns $7.00 per hour for the first 40 hours he works per week, and twice this rate for overtime. If Michael earned $210 last week, how many hours did he work?
Options:  A) 43  B) 44  C) 45  D) 46  E) 47

Solution: $7*40 + $12*x = $210 --> x = 5 hours.   Total working hours = 40 + 5= 
40 + 5 = 45
45   Answer: 45.
Answer: C
The price of lunch for 10 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? Select:
A) 11.73	B) 12	C) 13.8	D) 14	E) 18

Solution: Clearly 18 is the answer   I used PO18 here   Lets consider option (18) 10*18= 180 now 180(115/100)=207 => possible ANSW18R IMO 18
Answer: E
Which of the following inequalities is always true for any real number 'a' and 'b'?
Choose the correct answer.
A) |a+b| >= |(|a|-|b|)| B) |a-b| <= |(|a|-|b|)| C) |a-b| = |(|a|-|b|)| D) |a-b| >= |(|a|-|b|)| E) |a-b| <= |a|-|b|

Solution: The answer here is D. One of the fundamental properties of absolute value is subadditivity, and this is a reverse triangle inequality, which is equivalent to subadditivity. So this means that difference of two any elements is something (some number) which is greater than or equal to the difference of the each element taken on itself separately, i.e. |a-b| >= |(|a|-|b|)|
Answer: D
S = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set S and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?
Choose the correct choice from the following choices
A) 0.15  B) 0.20  C) 0.25  D) 0.30  E) 0.33

Solution: The total number of pairs S,B possible is   4*5= 
  4*5 = 20
20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.   Answer: 0.20.
Answer: B
What will come in place of the x in the following Number series? 5,28,57,88,125
Choose one:	A) 123	B) 143	C) 166	D) 190	E) 210

Solution: 28=23+5   57=29+28   88=31+57   125=37+88   166=41+125= 
41+125 = 166
166   166
Answer: C
One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is? Choose one
A) 5:4  B) 5:6  C) 5:0  D) 5:4  E) 4:5

Solution: 36 * 5/18 = 12.5   20:25 => 4:5   Answer: 4:5
Answer: E
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:  Choices
A) 40%
B) 44%
C) 50%
D) 54%
E) 60%

Solution: Let original length = x metres and original breadth = y metres.   Original area = (xy) m2.   New length = 120 x m = 6 x m.   100 5   New breadth = 120 y m = 6 y m.   100 5   New Area = 6 x x 6 y m2 = 36 xy m2.   5 5 25   The difference between the original area = xy and new-area 36/25 xy is   = (36/25)xy - xy   = xy(36/25 - 1)   = xy(11/25) or (11/25)xy   Increase % = 11 xy x 1 x 100 % = 44%.   25 xy   44%
Answer: B
Find the unit's digit in 264^102 +264^103 Choices: A) zero 0 B) 1 C) 2 D) 4 E) 5

Solution: Required unit's digit = unit's digit in 4102+4103.4102+4103.   Now, 4242 gives unit digit 6.   ⇒ 41024102 gives unit digit 6.   ⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.   Hence, unit's digit in 264102+264103264102+264103   = unit's digit in (6+4)=0   zero 0
Answer: A
If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is: Answers:
A) 1:1
B) 1:9
C) 1:2
D) 1:5
E) 1:6

Solution: Explanation:   1:1 square and a rhombus on the same base are equal in area   1:1nswer: 1:1) 1:1
Answer: A
You had a math quiz at class. The quiz had 5 questions; three of them have 3 marks each, and the other two have 4 marks each. You managed to correctly solve 2 questions with the 3 marks and one question with the 4 marks. What is the percentage of the marks that you got in this quiz?
Choose the correct choice
A) 48.8% B) 58.8% C) 38.8% D) 28.8% E) None

Solution: Solution:   The total marks = 3x3 + 2x4 = 17 marks   Marks obtained = 2x3 + 4 = 10 marks   Percent of marks obtained = 10/17 x 100 = 58.8%   Answer 58.8%
Answer: B
A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 92.16, the number of the member is the group is:	Choose the correct choice from the following answers:
A) 57
B) 67
C) 77
D) 87
E) 96

Solution: Explanation:   Money collected = (92.16 x 100) paise = 9216 paise.   ∴ Number of members = √(9216) = 96.   Answer: 96
Answer: E
There are 660 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?  Choose the correct choice from the following options:
A) 75	B) 110	C) 125	D) 175	E) 225

Solution: female = x   Male = 660-x   x/2 + 660-x/4 = 1/3* (660)= 
1/3* (660) = 220
220   x= 220   x/2 = 110 is supposed to be the answer   M is missing something   Correct Option 110
Answer: B
For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.988] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?  Choose the correct choice from the following options:
A) 0  B) 1  C) 27  D) 54  E) Cannot be determined

Solution: It cannot be determined.As we do not know the actual value of K.   however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer   K=[lCM of 80 and 45] * (any integer)   for value of k(60) * any integer unit value will be always zero .   0
Answer: A
Isabelle decided to go on an 8 mile run in which she ran from home to the school four miles away and then back the same route. The first four miles took her 40 minutes to complete, and the returning four miles took her 24 mins to complete. What was the wind speed in mph?	Pick one.
A) 1 mph
B) 2 mph
C) 3 mph
D) 4 mph
E) 5 mph

Solution: Explanation:   Speed from home to school: (4/40) X 60 = 6 mph   Speed from school to home: (4/24) X 60 = 10 mph   Wind speed: 1/2 (10 - 6) = 4/2= 
4/2 = 2
2 mph   Answer: Option 2 mph
Answer: B
Four of the following five numbered parts (a), (b), (c), (d) and (e) are equal. The number of the part which is not equal to the other four parts is the answer.
Choose the correct choice from the following answers
A) 115 × 8 ÷ 10 + 8	B) 425 ÷ 17 × 4	C) 36 × 5 ÷ 6 + 17 × 4	D) 2(6) + √256 + 20	E) 35 × 12 ÷ 14 + 14 × 5

Solution: All others are equal to 100. But option (c) gives a value equal to 98.   Answer 36 × 5 ÷ 6 + 17 × 4
Answer: C
If m and n are positive integers of W such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
Select the correct option
A) 2m/n + 1
B) 2n/m + 1
C) 2n/(m+1)
D) 2m/n
E) 2n/m

Solution: Lets say N=10, M=5   2N = 20. so the answer should be 4 (20/5)   lets try to plug in the answers:   A-not an integer   B-not an integer   C-not an integer   D-1 (not the answer)   E-4 - the answer. (the only one).   I would choose E.   Method 2   N=M*A (A is an integer)   So - A=N/M   therefore in 2N A will be 2N/M   Again - Answer is 2n/m.
Answer: E
A rectangular Box 60 m long and 40 m wide has two concrete crossroads running in the middle of the box and rest of the box has been used as a lawn. The area of the lawn is 2109 sq. m. what is the width of the road? Choose the most appropriate option.
A) 3 m
B) 4 m
C) 5 m
D) 6 m
E) 2 m

Solution: Total area of cross roads=60x+40x−x2   But total area of the cross roads =291 m2   Hence,   60x+40x−x2=291   ⇒100x−x2=291   ⇒x2−100x+291=0   ⇒(x−97)(x−3)=0   ⇒x=3   3 mNSWER:3 m
Answer: A
Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute).	Select
A) 3 hours 5 minutes
B) 4 hours 5 minutes
C) 5 hours 5 minutes
D) 6 hours 5 minutes
E) 7 hours 5 minutes

Solution: In 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill   1/5 + 1/8 = 13 / 40 of a tank   Since the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving   (13/40) t = 1   t = 40 / 13 = 39/13 + 1/13 hours   = 3 hours and (1/13)*60 minutes   = 3 hours 5 minutes (rounded to the nearest minute)   correct answer 3 hours 5 minutes
Answer: A
A clock store sold a certain clock to a collector for 35 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 15 percent of what the collector had paid. The shop then sold the clock again at a profit of 65 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $105, for how much did the shop sell the clock the second time?  Choose the correct choice from the following:
A) $75.44
B) $88.23
C) $64.77
D) $54.32
E) $43.99

Solution: Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 35% profit.   This means the clocks' selling price was C (1.35) and this becomes cost price for the collector.   Now, when the collector tries to sell the same clock to the store, the store buys it for 15% the price at which the collector bought it.   Thus, you get = 1.35*0.15*C = 0.2025 C   Furthermore, the store sells the clock for the second time for 65% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.65 = 1.65 * 0.2025 C   Finally given that C - 0.2025 C = 105 ----> C = 131.66$   Thus, the cost of the clock the second time around = 1.65*0.2025 C = 1.65 * 0.2025 * 131.66 = 43.99$. Hence $43.99 is the correct answer.
Answer: E
The area of an isosceles trapezoid with sides of length 5 and bases of length 6 and 12 is?	Choose the correct choice from the following choices.
A) 44  B) 42  C) 40  D) 38  E) 36

Solution: Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 12 will be divided into 3 parts= 6, 3 and 3 (Making one square and two right triangles)   For the right triangle, height will be= (5^2-3^2)^1/2= 4   And the area of trapezoid = 1/2 (B1+B2)H= 1/2*18*4= 
1/2*18*4 = 36
36   36
Answer: E
Two tains of equal lengths take 10 seconds and 20 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?  Select:
A) 12
B) 14
C) 16
D) 20
E) 13.3

Solution: Sol.   Speed of the first train = [120 / 10] m/sec = 12 m/sec.   Speed of the second train = [120 / 20] m/sec = 6 m/sec.   Relative speed = (12 + 6) = m/sec = 18 m/sec.   ∴ Required time = (120 + 120) / 18 secc = 13.3 sec.   Answer 13.3
Answer: E
The probability that a computer company will get a computer hardware contract is 3/4 and the probability that it will not get a software contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that it will get both the contracts?
Choose the most appropriate option:
A) 11/30  B) 31/60  C) 41/80  D) 51/120  E) 71/180

Solution: Let, A ≡ event of getting hardware contract   B ≡ event of getting software contract   AB ≡ event of getting both hardware and software contract.   P(A) = 3/4, P(~B) =5/9   => P(B) = 1- (5/9) = 4/9.   A and B are not mutually exclusive events but independent events. So,   P(at least one of A and B ) = P(A) + P(B) - P(AB).   => 4/5 = (3/4) + (4/9) - P(AB).   => P(AB) = 71/180.   Hence, the required probability is 71/180.   The answer is 71/180.
Answer: E
Tough and Tricky questions: Word Problems.
AK Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit? Choose the correct choice from the following answers:
A) $4,035
B) $4,036
C) $9,035
D) $16,140
E) $36,140

Solution: The AK company plans to make a profit of $30,500,000 and it needs to earn the fixed costs of $50,200,000, so it needs to earn $80,700,000 on top of the costs for the production of the 20,000 cars.   Therefore, price of each car needs to be the unit costs plus $80,700,000/20,000. After removing the 0's, we end with the unit costs plus $8,070/2, which is $5,000 plus $4,035. Therefore, Answer $9,035 is correct.
Answer: C
How many consonants are present between the first and third vowel in the sequence of English alphabet ?	Choose the correct choice from the following options
A) 12 B) 13 C) 6 D) 10 E) None of these

Solution: Explanation:   Ref : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z   The first and third vowels are A and I respectively. There are 7 letters between A and I; out of which 'E' is a vowel. Thus, there are 6 consonants between A and I.   ANSWER 6
Answer: C
In how many ways the word "PACK" can be arranged?	Choose the correct choice from the following choices
A) 14  B) 24  C) 28  D) None  E) Cannot be determined

Solution: Explanation :   The required number of ways = 4!   = 24   Answer : 24
Answer: B
Andrew travelling to 7 cities. Gasoline prices varied from city to city. $1.75, $1.61, $1.79, $2.11, $1.96, $2.09, $1.82. What is the median gasoline price?  Select the correct option:
A) $1  B) $1.82  C) $1.92  D) $2.13  E) $2.15

Solution: Ordering the data from least to greatest, we get:   $1.61, $1.75, $1.79, $1.82, $1.96, $2.09, $2.11   The median gasoline price is $1.82. (There were 3 states with higher gasoline prices and 3 with lower prices.)   $1.82
Answer: B
A cat leaps 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?
Select:
A) 11:15
B) 15:11
C) 16:15
D) 15:16
E) 11:16

Solution: Solution: Given;   3dog = 4 cat;   Or, dog/cat = 4/3;   Let cat's 1 leap = 3 meter and dogs 1 leap = 4 meter.   Then, ratio of speed of cat and dog = 3*5/4*4= 
3*5/4*4 = 15
15:16.''Answer: Option 15:16
Answer: D
A train crosses a platform in 15 sec, same train crosses another platform of length 250 m in 20 sec. If the speed of the train is 15 m/sec then find the length of the platform?	Pick one:
A) 277m
B) 180m
C) 165m
D) 278m
E) 175m

Solution: Length of the train be ‘X’   (X + 250)/20 = 15   X = 50m   Let the length of the platform be y   (y + 50)/15 = (50 + 250)/20   4y + 200 = 900   X = 1750m   Answer: 175m
Answer: E
Define A = The sum of digits of the number 7^100 and B = The sum of the digits of A. What is the sum of the digits of B?
Choose the most appropriate option.
A) 7 B) 16 C) 10 D) 11 E) Cannot be Determined

Solution: Following approach will take you only couple of sec.   \(7^{100} = (7^{50})^2\)   The sum of digits (digital root) of a PERFECT SQUARE can only be 1, 4, 7 or 9.   For example \(7^2=49\) => DR=4+9= 
4+9 = 13
13=> 1+3= 
1+3 = 4
4 and etc.   Checking available options.   7nswer 7.
Answer: A
A 260 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train ?	Pick one:
A) 240 mts
B) 270 mts
C) 260 mts
D) 250 mts
E) 280 mts

Solution: Explanation:   Relative speed = 120 + 80= 
120 + 80 = 200
200 km/hr.= 200 x 5/18 = 500/9 m/sec.   Let the length of the other train be L mts.   Then, (L + 260)/9 = 500/9 => L = 240 mts.   240 mtsNSWER IS 240 mts
Answer: A
A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/4 chance that engine one will fail. There is a 75% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?  Choose the correct choice from the following answers.
A) 7/12
B) 1/4
C) 1/2
D) 7/24
E) 17/24

Solution: In probability questions the trap answer is just the multiple of the numbers in the question.   i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer   The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer   So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.   7/12
Answer: A
A store raised the price of an item by exactly 20 percent. Which of the following could NOT be the resulting price of the item?  Choose the correct choice from the following answers.
A) 6
B) 12
C) 18
D) 24
E) 58

Solution: If it raised the value by 20% then the resulting price is 1.2 times the original price. So the final answer has to be a multiple of 1.2. Check the answers.   6 - Yes   12 - Yes   18 - Yes   24 - Yes   58 - No   Answer : 58
Answer: E
A departmental store charges the commission of 25 percent on the first sale of items worth $50,000 and then an additional 10 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? Choices
A) $215,000	B) $165,000	C) $115,000	D) $240,000	E) $160,000

Solution: 24,000 = 0.25 *(50000) + 0.10 (x - 50000)   24000 - 12500 = 0.10 (x-50000)   115000 = x - 50000   x = 1,65,000   Answer : $165,000
Answer: B
The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 30 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
Choose the correct choice from the following
A) 63%  B) 40%  C) 64.8%  D) 70%  E) 72%

Solution: original price = 100   day 1 discount = 10%,price = 100-10= 
100-10 = 90
90   day 2 discount= 10%,price = 90-9= 
90-9 = 81
81   day 3 discount= 30%,price = 81-24.3= 
81-24.3 = 56.7
56.7   which is 56.7/90 *100 of the sale price on day 1= ~63%   63%nswer 63%
Answer: A
A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 112 km downstream  Choose the correct answer:
A) 3 hours B) 4 hours C) 5 hours D) 6 hours E) 7 hours

Solution: Explanation:   Speed of the boat in still water = 24 km/hr   speed of the stream = 4 km/hr   Speed downstream = (22+5) = 28 km/hr   Distance travelled downstream = 112 km   Time taken = distance/speed = 112/28= 
112/28 = 4
4 hours   Answer: Option 4 hours
Answer: B
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?	Choose the correct answer:
A) 14
B) 15
C) 16
D) 17
E) 18

Solution: Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.   Then,	((6x + 6) + 4)/ ((5x + 6) + 4)	=	11/10   10(6x + 10) = 11(5x + 10)   5x = 10   x = 2.   Sagar's present age = (5x + 6) = 16 years.   ANSWERS : 16
Answer: C
The sum of five consecutive even numbers is 500. Find the middle number of the five?  Pick one
A) 140
B) 66
C) 100
D) 99
E) 120

Solution: Middle number =500/5= 
500/5 = 100
100   Ans 100
Answer: C
One vessel contains a mixture of 4 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 9 parts pure wine and 5 parts soda. Compare the strength of the wine.  Select the correct option:
A) 35;36 B) 10 : 9 C) 7 : 4 D) 14 : 5 E) None of these

Solution: 4/7 : 9/14   LCM of 7,14 = 14   (5/7)*14: (9/14)*14   10:9   Answer is 10 : 9.
Answer: B
A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent W should the number of hours worked be increased?
Choose the correct choice.
A) 12.5%  B) 20%  C) 25%  D) 50%  E) 100%

Solution: Correct Answer: C   Solution: C. We can set up equations for income before and after the wage reduction. Initially, the employee earns W wage and works H hours per week. After the reduction, the employee earns .8W wage and works X hours. By setting these equations equal to each other, we can determine the increase in hours worked: WH = .8WX (divide both sides by .8W) 1.25H = X We know that the new number of hours worked W will be 25% greater than the original number. The answer is 25%.
Answer: C
A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?
Pick:
A) 3 B) 4 C) 5 D) 6 E) 78

Solution: Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/4 + 1/12 = 1/3.   Total time required to complete the work = 2 * 3= 
2 * 3 = 6
6 days.Answer:6
Answer: D