MU-NLPC/Calc-aqua_rat huggingface dataset:
Two numbers are in respectively 10% and 40% more than a third number. The ratio of the two numbers is? Choices.
A) 11:14 B) 7:9 C) 17:25 D) 15:26 E) 2:3

Solution: Let the 3rd number be x   Then, first number = 110% of x = 110x/100 = 11x/10   second number = 140% of x = 140x/100 = 7x/5   Ratio of first two numbers = 11x/10 : 7x/5 = 11:14   11:14nswer is 11:14
Answer: A
A box contains 2 black, 3 orange and 4 pink ribbons. If two ribbons are drawn at random. What is the probability that both are orange?
Choose the correct choice from the following choices
A) 5/12 B) 1/13 C) 1/14 D) 1/12 E) 1/24

Solution: Total number of ribbons = 2 + 3 + 4= 
2 + 3 + 4 = 9
9   Let S be the sample space.   n(S)= Total number of ways of drawing 2 ribbons out of 9 = 9C2   Let E = Event of drawing 2 orange ribbons.   n(E) = Number of ways of drawing 2 orange ribbons= 3C2   P(E)=n(E)/n(S)=3C2/9C2 =(3*2/2) / (9*8/2) =3/36 =1/12   ANSWER:1/12
Answer: D
Integers 3n+2 and 8n+9 are divisible by an integer p. If p is not equal to 1, then p equals to?
Pick one
A) 2  B) 3  C) 5  D) 7  E) 11

Solution: If p divides 3n+2, then p divides 24n+16.   If p divides 8n+9, then p divides 24n+27.   Then p must equal 11.   The answer is 11.
Answer: E
Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 52 years. The age of E is?  Choose the correct choice from the following choices
A) 45 B) 60 C) 48 D) 49 E) 46

Solution: Solution   5 years ago average age of A,B,C,D = 45 years   => 5 years ago total age of A, B, C, D = 45 x 4 = 180 years   => Total present age of A, B, C, D = 180 + 5x4 = 200 years   If E's present age is x years = 200+x/5= 52   x=60 years. Answer 60
Answer: B
In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 120?
Choose the most appropriate option
A) 15	B) 77	C) 45	D) 18	E) 12

Solution: A scores 60 while B score 40 and C scores 30.   The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3= 
25 * 3 = 75
75.   In a game of 100 points, B gives (120 - 75)= 
(120 - 75) = 45
45 points to C.   Answer:45
Answer: C
A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 4 DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:  Pick.
A) 1/2 DAYS	B) 3/4 DAYS	C) 1/4 DAYS	D) 4/3 DAYS	E) NONE OF THESE

Solution: RATIO OF RATES OF WORKING OF A AND B = 2:1. SO, RATIO OF TIME TAKEN = 1:2   A'S 1 DAY'S WORK = 1/2, B'S 1 DAY'S WORK = 1/4   (A+B)'S 1 DAY'S WORK = (1/2+1/4)=3/4=4/3   SO, A AND B TOGETHER CAN FINISH THE WORK IN 4/3 DAYS.   CORRECT OPTION: 4/3 DAYS
Answer: D
You hold some gold in a vault as an investment. Over the past year the price of gold increases by 50%. In order to keep your gold in the vault, you must pay 8% of the total value of the gold per year. What percentage has the value of your holdings changed by over the past year. Choose the correct answer.
A) 35%  B) 36%  C) 37%  D) 38%  E) 40%

Solution: (100%+50%)*(100%-8%) = 150*0.92= 
150*0.92 = 138
138% an increase of 38%   Your gold holdings have increased in value by 38%.   The Answer is 38%
Answer: D
A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?  Choices:  A) Rs.18000  B) Rs.15000  C) Rs.17000  D) Rs.14000  E) Rs.16000

Solution: Explanation:   25*12: 30*12: 35*8   15:18:14   14/47 * 47000= 
14/47 * 47000 = 14_000
14000   ANSWER IS Rs.14000
Answer: D
If a choir consists of 2 boys and 7 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls. Choose one.
A) 120 B) 30 C) 24 D) 8 E) 17

Solution: There are 8 possibilities:   bbggggggg   gbbgggggg   ggbbggggg   gggbbgggg   ggggbbggg   gggggbbgg   ggggggbbg   gggggggbb   Think of all 2 boys as a single unit. Together with 7 girls it makes a total of 8 units. The difference between the arrangements is the position of the boys (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the boys who can occupy 1 of 8 available positions. If the number of available unique positions is 8, then the number of unique patterns equals 8 as well.   Answer: 8.
Answer: D
What is the cost of leveling the field in the form of parallelogram at the rate of Rs.60/10 sq.metre, whose base & perpendicular distance from the other side being 34m & 34m respectively?	Pick:  A) s.1156  B) s. 1300  C) s. 1400  D) s. 2480  E) s. 3600

Solution: Area of the parallelogram = Length of the base * Perpendicular height   = 34 * 34= 
34 * 34 = 1_156
1156   Total cost of levelling= Rs. 1156   s.1156
Answer: A
The product of all the prime number less than or equal to 11 is
Answers.
A) 10^1
B) 10^2
C) 10^3
D) 10^4
E) 10^5

Solution: 10^4)
Answer: D
In store A there are 10 pairs of pants for every 100 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned? Options
A) 3:16.  B) 2:3.  C) 1:3.  D) 3:4.  E) 2:15.

Solution: 1st statement : ratio of pants   Store A : Store B   10x : 100x   X:10X   Price :   4y:3y   Total revenue   4xy : 30xy   2:15   Answer is 2:15.
Answer: E
In how many ways can 10 Frenchmen, 10 Spanish be seated along a circle so that they are alternate?  Choose one
A) 8!*7!	B) 10!*9!	C) 5!*9!	D) 10!*5!	E) 11!9!

Solution: Required number is = 10!*9!   Answer is 10!*9!
Answer: B
Find the H.C.F. of 2^3 X 3^2 X 5 X 7^4, 2^2 X 3^5 X 5^2 X 7^3,2^3 X 5^3 X 7^2
Choose one.
A) 980	B) 990	C) 970	D) 950	E) 960

Solution: The prime numbers common to given numbers are 2,5 and 7.   H.C.F. = 2^2 x 5 x7^2 = 980.   980nswer is 980.
Answer: A
0.003 x 0.2 = ?
Choose the correct option:
A) 0.0006
B) 0.006
C) 0.06
D) 0.6
E) 6.0

Solution: 3 x 2 = 6.   Sum of decimal places = 4   0.003 x 0.2 = 0.0006   0.0006nswer: Option 0.0006
Answer: A
If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+1 ?
Choose the correct choice from the following answers
A) -2
B) 2
C) -5
D) -3
E) -4

Solution: let we put values. a=1, b=3, c=5   5-3-1= 
5-3-1 = 1
1   1+1= 
1+1 = 2
2   Answer :2
Answer: B
A bus takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Choose the correct choice from the following answers.
A) 50 Kmph  B) 60 Kmph  C) 63 Kmph  D) 65 Kmph  E) 70 Kmph

Solution: Time = 6   Distance = 540   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 540/9= 
540/9 = 60
60 Kmph   60 Kmph
Answer: B
The cost of 14 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?	Answers:  A) Rs 52.50  B) Rs 56  C) Rs 58.50  D) Rs 60  E) None of these

Solution: Explanation :   Let the required cost be Rs. x. Then,   More packets, More cost (Rs 60irect Proportion)   More weight, More cost (Rs 60irect Proportion)   Packets 14 : 27   Weight 900 : 1000 :: 28 : x   (14 x 900 x x) = (27 x 1000 x 28)   x = (27 x 1000 x 28) /14 x 900   =60   Answer Rs 60
Answer: D
Let C be defined as the sum of all prime numbers between 0 and 32. What is C/3
Choose the correct choice from the following:
A) 155 B) 129 C) 61 D) 47 E) 53.3

Solution: Prime numbers between 0 and 30 - 2 , 3 , 5 , 7, 11 , 13 , 17 , 19 , 23 , 29, 31   Sum,C = 160   C/3 = 53,3   Answer 53.3
Answer: E
Twelve contestants at the county fair have entered their cakes to be judged in the cake decorating competition. A purple ribbon, blue ribbon, red ribbon, and white ribbon will be given to the first, second, third, and fourth place competitors, respectively. How many different ways are there to award the four ribbons to the contestants?	Answers
A) 8!(4!*4!)
B) 12!(8!*4!)
C) 8!/4!
D) 12!/8!
E) 12!/4!

Solution: The mistake you are doing is that you are neglecting the 4! ways in you can arrange 4 contestants for the 4 prizes.   Number of ways you can select 4 people out of 12 = 12C4   Once you select the 4 people, you have the following arrangement, PBRW (PBRW being the 4 prizes) but the same group of people can also be chosen against BRWP etc. Thus you get 4! ways of arranging 4 prizes.   Thus total possible ways = 12C4*4! = 12!/8!. 12!/8! is the correct answer.
Answer: D
A man can hit the target once in four shots. If he fires three shots in succession, what is the probability that he will hit the target? Choose the correct choice from the following choices:
A) 1
B) 1/64
C) 81/64
D) 37/64
E) 185/256

Solution: In three shots he can hit once,twice,thrice,all hit   the probability of hitting the target is p(1hit out of 4)+P(2hit out of 4)++p(All hit)   it is total probability-probability of not hitting the target   =>1-(3/4*3/4*3/4)   =>37/64   ANSWER:37/64
Answer: D
A rectangular lawn of dimensions 80 m * 40 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m? Choose the correct choice from the following options:
A) 2288  B) 2779  C) 3300  D) 3900  E) 2781

Solution: Area = (l + b â€“ d) d   (80 + 40 â€“ 10)10 => 1100 m2   1100 * 3 = Rs.3300   Answer:3300
Answer: C
The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second? Choose the correct choice
A) 54%  B) 74%  C) 53%  D) 64%  E) 24%

Solution: r = 3 πr2 = 9   r = 5 πr2 = 25   25 π – 16 π   100 ---- ? => 64%   Answer:64%
Answer: D
A survey of a village showed that 1 / 10 of the total population speak neither Hindi nor English. 1 / 5 of them cannot speak English and 3 / 7 of them cannot speak Hindi. What percentages of people know only one language?	Choose the correct choice from the following answers.
A) 100/7	B) 200/7	C) 300/7	D) 400/7	E) 500/7

Solution: persons who can speak English = 1 - (1/5) = 4/5   persons who can speak Hindi = 1 - (3/7) = 4/7   persons who can speak any or both = 1 - 1/10 = 9/10   so total persons speak both = 4/5 + 4/7 - 9/10 = 33/70   persons speak any = 1 - 33/70 - 1/10 = 3/7   % = 300/7   ANSWER:200/7
Answer: B
An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 32-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce?	Choices:
A) 4 B) 6 C) 7 D) 8 E) 9

Solution: Going down = 32 m   Going Up = 16 --> Total = 48   Going down = 16 --> Total = 64   Going Up = 8 --> Total = 72   Going down = 8 --> Total = 80   Going up = 4 --> Total = 84   Going down = 4 --> Total = 86   Going up = 2 --> Total = 88 (Caught)   No of bounces = 4   4nswer : 4
Answer: A
Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.63000 after completion of one year. What will be Jose's share of profit? Choose the correct choice from the following answers
A) 20000	B) 10000	C) 25000	D) 35000	E) 30000

Solution: SoL = ~s- So Anju’s share = [5/9] x 63000 = 35000   35000
Answer: D
If py + z = p(y + z), which of the following must be true?
Choose the correct choice from the following options:	A) x = 0 and z = 0	B) p = 1 and y = 1	C) p = 1 and z = 0	D) p = 1 or y = 0	E) p = 1 or z = 0

Solution: py + z = py + pz   z = pz   case 1: z not= 0, p = z/z = 1   case 2: z = 0, 0 = p0 = 0   Combining 2 cases: p = 1 or z =0   E. is the answer.
Answer: E
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
Choose the correct option
A) 160
B) 170
C) 175
D) 195
E) 180

Solution: Suppose the man works overtime for x hours.   Now, working hours in 4 weeks = (5 x 8 x 4) = 160.   160 x 2.40 + x x 3.20 = 432   3.20x = 432 - 384= 
432 - 384 = 48
48   x= 15.   Hence, total hours of work = (160 + 15)= 
(160 + 15) = 175
175.   ANSWER :175
Answer: C
During school lunch, 60% of the children packed fruit in their lunches. Of those children, 25% have an apple. The remaining children eat from the cafeteria where they are given an apple. What percentage of children have an apple with their lunch?  Pick.
A) 15% of the children have an apple. B) 45% of the children have an apple. C) 55% of the children have an apple. D) 85% of the children have an apple. E) None of these.

Solution: Explanation:Let total number of children be 100,Then, number of children who packed fruit = 60.Number of those children with apples = 25% of 60 = 15.Number of children eating at the cafeteria = 40.Total number with an apple = 40 + 15= 
40 + 15 = 55
55.Thus, 55% of the children have an apple.Answer: Option 55% of the children have an apple.
Answer: C
A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent E of the cost would the gross profit on the item have been if it had been sold without the discount?  Choose the correct option.
A) 20%  B) 40%  C) 50%  D) 60%  E) 75%

Solution: Let the Market Price of the product is MP.   Let the Original Cost Price of the product is CP.   Selling Price (Discounted Price) = 100%of MP - 20%MP   = 80% of MP. ---------------- (1)   Profit made by selling at discounted price = 20% of 50%P -------------- (2)   Apply the formula:   Profit E= Selling Price - Original 50%ost Price   => 20% of 50%P = 80% of MP - 100% 50%P   => MP = 12050%P/80 = 3/2 (50%P)   Now if Product is sold without any discount, then,   Profit = Selling Price (without discount) - Original 50%ost Price   = Market Price - Original 50%ost Price   = MP - 50%P   = 3/2 50%P - 50%P   = 1/2 50%P   =50%of 50%P   Thus, Answer should be50%.
Answer: C
How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed. Choose one.
A) 2450
B) 1230
C) 5040
D) 1042
E) 2116

Solution: 'LOGARITHMS' contains 10 different letters   Required number of words   = Number of arrangements of 100 letters taking   4 at a time   = 10P4   = 10 * 9 * 8 * 7= 
10 * 9 * 8 * 7 = 5_040
5040   Ans: 5040
Answer: C
What is the 16th digit to the right of the decimal point in the decimal expansion of 1/37?  Choose the correct choice from the following answers.
A) 0 B) 2 C) 4 D) 7 E) 9

Solution: 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (2nd, 4th, 6th, ...) to the right of the decimal point is alternating by 2, 0, 7 thus 16th digit is 0.   0nswer: 0.
Answer: A
If a clock takes seven seconds to strike seven, how long will it take to strike ten ? Choose the correct choice from the following.
A) 7 seconds  B) 9 seconds  C) 10 seconds  D) 15 seconds  E) None of these

Solution: Explanation:   Clearly, seven strikes of a clock have 6 intervals while 10 strikes have 9 intervals.   Therefore, Required time=[7/6*9]seconds = 10 1/2 seconds.   Answer: None of these
Answer: E
A restaurant meal cost $34.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between Choose the correct choice from the following answers:
A) $40 and $42
B) $39 and $41
C) $38 and $40
D) $37 and $39
E) $36 and $37

Solution: The total amount for the meal was between 34.5*1.1= 
34.5*1.1 = 37.95
37.95 and 34.5*1.15=39.675. Only option which covers all possible values of the meal is C.   Answer: $38 and $40.
Answer: C
If {y} denote the remainder when 3y is divided by 2 then which of the following is equal to 1 for all positive integers y?
I. {2y+1}
II. {2y}+1
III. 2{y+1} Pick one:  A) I only  B) II only  C) I and II  D) III only  E) II and III

Solution: I and II - I and II   3y/2 = 0 or 1   I just substituted 1 in the equations and solved.
Answer: C
30 men can do a work in 40 days. When should 10 men leave the work so that the entire work is completed in 40 days after they leave the work?  Select:
A) 87 days B) 10 days C) 55 days D) 44 days E) 20 days

Solution: Total work to be done = 30 * 40= 
30 * 40 = 1_200
1200   Let 10 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.   40P + (10 * 40)= 1200   40P = 800 => P = 20 days   Answer:20 days
Answer: E
Joshua and Jose work at an auto repair center with 1 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen? Choose the correct choice from the following answers:
A) 1/15 B) 1/12 C) 1/9 D) 1/6 E) 1/3

Solution: Two Methods   1) Probability of chosing Josh first = 1/3   Probability of chosing Jose second = 1/2   total = 1/6   Probability of chosing Jose first = 1/3   Probability of chosing Josh second = 1/2   Total = 1/6   Final = 1/6 + 1/6 = 1/3   1/3
Answer: E
Jimmy Bullard and his friend went for fishing.
They got six fishes without heads, nine fishes without the tail and eight fishes cut in two halves.
How many fishes did they caught ?	Choose the correct choice from the following options
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Solution:   zero   6 without head => 0   9 without tail => 0   8 in two halves => 0 & 0   0nswer 0
Answer: A
Two unbiased coin are tossed. What is the probability of getting almost
one head?  Pick.
A) 1/2  B) 1/4  C) 3/4  D) 3/5  E) 1/6

Solution: Here S={HH,HT,TH,TT}   Let Ee=event of getting one head   E={TT,HT,TH}   P(E)=n(E)/n(S)=3/4   Answer option 3/4) 3/4
Answer: C
Mohit sold an article for Rs. 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?  Select the correct option:
A) 15000
B) 27767
C) 16688
D) 26678
E) 19987

Solution: Let the CP be Rs. x.   Had he offered 10% discount, profit = 8%   Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 10/100(18000) = 18000 - 1800 = Rs. 16200   => 1.08x = 16200   => x = 15000   \15000nswer: 15000
Answer: A
The sum of two numbers is 44. Five times one number is equal to 6 times the other. The smaller of the two numbers is  Pick.
A) 10
B) 12
C) 16
D) 22
E) 20

Solution: Sol.   Let the numbers be x and (44 - x).   Then, 5x = 6(44 - x)   ⇔ 11x = 264⇔ x = 24.   So, the numbers are 24 and 20.   Answer 20
Answer: E
Which of the following equations represents a line that is perpendicular to y=1/5*x+2?  Choose the correct choice from the following:
A) y−2x=8 B) 2x+4y=10 C) 3y+6x=12 D) 4y−8x=16 E) 5x−10y=20

Solution: For two lines to be perpendicular, the product of slopes should be equal to -1.   Slope of line 1 = 1/2   Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2   Answer: 2x+4y=10
Answer: B
If x and y are integers such that x^2+2x+2y+3=2x^2+3x+y+1, we can deduce that y is
Choose one:
A) not an even B) an even C) a perfect square D) an odd E) a prime

Solution: x^2 + 2x + 2y + 3 = 2x^2 + 3x + y + 1   y = x^2 + x - 2   y = (x+2)(x-1) (Note that one factor is even and one factor is odd.)   Then y must be even.   The answer is an even.
Answer: B
A meal cost $ 34.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:
Pick.
A) 40-42 B) 39-41 C) 38-40 D) 37-39 E) 36-37

Solution: 10%(34.5) = 3.45   15%(34.5) = 5.175   total amount could have been 34.5+3.45 and 34.5+5.175   => could have been between 37.95 and 39.675   => approximately between 38 and 40   Answer is 38-40.
Answer: C
What is the angle between the minute hand and the hour hand when the time is 1540 hours?
Choose the correct choice from the following answers:  A) 150  B) 160  C) 140  D) 130  E) None

Solution: Solution:   The total angle made by the minute hand during an hour is 360o. If it takes 360o for an hour, it will take   (40/60) * 360= 
  (40/60) * 360 = 240
240o. The angle between the hour hand the minute hand will therefore, be somewhere between  240 - 90= 
 240 - 90 = 150
150o, as the hour hand is between 3 and 4.   The angle made by the hour hand when it moves from say 3 to 4 will be 30o. That is the hour hand makes 30o during the course of an hour.   The hour hand will therefore, move (40/60) * 30= 
(40/60) * 30 = 20
20o.   Therefore, the net angle between the hour hand and the minute hand will be   150 - 20= 
  150 - 20 = 130
130o.   Answer 130
Answer: D
During a Pizza buffet where A eats more times 1.8 than B, and B eats 8 times less than C.find the leat number of times all the three has to eat
Choose the correct option.
A) 350
B) 260
C) 360
D) 380
E) 285

Solution: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 1.8:1 or 9:5 and as B eat 8 times less the C the the ratio of B : C is 5:40 the the least number of times all three has eat is the LCM of A,B,C that is 360 ..   ANSWER:360
Answer: C
504 can be expressed as a product of primes as
.
Select
A) 2 × 2 × 3 × 3 × 7 × 7
B) 2 × 3 × 3 × 3 × 7 × 7
C) 2 × 3 × 3 × 3 × 3 × 7
D) 2 × 2 × 2 × 3 × 3 × 7
E) NONE OF THE ABOVE

Solution: It is clear that 504 = 2 × 2 × 2 × 3 × 3 × 7   Answer: Option 2 × 2 × 2 × 3 × 3 × 7
Answer: D
Nancy works 3 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 2 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period? Choose the correct choice from the following answers.
A) a) 3y(7x+2xy)	B) b) 3x+12y	C) c) 2x(2y+9)	D) d) 3x(2y+7)	E) e) 4x(y+8)

Solution: Payment of a week for 3 days a week = $3x   Payment of 4 weeks for 3 days a week = $3x*4 = $12x   Payment of a week for y days overtime a week 3 *4= 
3 *4 = 12
$12x   Payment of a week for y days overtime a week= $3x+$2xy   Payment of 2 weeks for y days overtime a week = ($3x+$2xy)*2   Total Earnings = $12x + ($3x+$2xy)*2 = 18x+4xy =2x(2y+9)   Answer: option c) 2x(2y+9)
Answer: C
If f is a positive integer, and if the units' digit of f^2 is 4 and the units' digit of (f + 1)^2 is 1, what is the units' digit of (f + 2)^2 ?
Select:
A) 0
B) 2
C) 4
D) 6
E) 8

Solution: A for me.   _1² = _1   _2² = _4   _3² = _9   _4² = _6   _5² = _5   _6² = _6   _7² = _9   _8² = _4   _9² = _1   _0² = _0   On the list, the only number that squared has the units digit = 4 preceding a number that squared has the units digit = 1 is the _8.   So, f = _8, that has square 4. The next square is 1 andnext nextsquare is 0.
Answer: A
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 60 kmph, find the speed of the stream? Choose the correct choice from the following
A) 18 kmph  B) 19 kmph  C) 21 kmph  D) 22 kmph  E) 20 kmph

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= 60/3= 
60/3 = 20
20 kmph.   Answer: 20 kmph
Answer: E
A can do a piece of work in 24 days. B in 15 days and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?	Choose the correct answer
A) 8 2/5days
B) 10 2/5days
C) 6 2/5days
D) 18 2/5days
E) 17 2/5days

Solution: 8 2/5days + B = 1/24 + 1/15 = 13/120   8 2/5days + C = 1/24 + 1/12 = 1/8   13/120 + 1/8 = 28/120   4 1/5 days * 2 = 8 2/5days   8 2/5daysNSWER:8 2/5days
Answer: A
In how many ways letters of the word OCCUPAY be arranged?  Choose the correct answer
A) 6178	B) 9456	C) 387	D) 2520	E) 9812

Solution: OCCUPAY has 7 letters, out of which C repeated 2 times. Hence total ways = 7! / (2!) = 2520 ways   2520
Answer: D