MU-NLPC/Calc-aqua_rat huggingface dataset:
If a, b, c and d are positive integers and a/b < c/d, which of the following must be true?
I. (a+c)/(b+d) < c/d
II. (a+c)/(b+d) < a/b
III. (a+c)/(b+d) = a/b +c/d Choose the correct answer:	A) None	B) I only	C) II only	D) I and II	E) I and III

Solution: If a, b, c and d are positive integers and a/b < c/d, which of the following must be true?   Since the numbers are positive we can safely cross-multiply. So, we are given that ad<bcad<bc.   I. a+cb+d<cda+cb+d<cd = ad+cd<bc+cd   ad+cd<bc+cd= cdcd cancels out: ad<bc. This is given to be true.   II. a+cb+d<aba+cb+d<ab = ab+bc<ab+adab+bc<ab+ad= ab   ab cancels out: bc<ad bc<ad. Opposite what is given, thus this option is not true.   III. a+cb+d=ab+cda+cb+d=ab+cd. From I we already know that a+cb+d<cda+cb+d<cd, thus when we add a positive value (abab) to (cdcd)we make the right hand side even bigger.Thus a+cb+d=ab+cda+cb+d=ab+cd cannot be true.   Answer: I only.
Answer: B
For a road work, a contractor was given a deadline to complete the work in 25 days. Hence, he employed a certain number of workers to accomplish the job. But from the very first day 9 workers were absent and the remaining workers could finish the work in 40 days. What number of workers did the contractor hired in the beginning?	Choose the correct choice from the following options:  A) 20  B) 30  C) 24  D) 16  E) 19

Solution: Explanation :   Let the number of workers initially hired be x.   Hence, x workers can complete the work in 25 days and (x-9) workers can complete the work in 40 days.   Now, the number of men and the amount of work are in direct proportion and number of men and number of days in indirect proportion.   x*25 = (x 9)*40   25x = 40x 360   15x = 360   x = 24   Answer : 24
Answer: C
A particular library has 150 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 108 books in the special collection at that time, how many books of the special collection were loaned out during that month?	Choices.
A) 40	B) 60	C) 80	D) 100	E) 120

Solution: The total number of books is 150.   Let x be the number of books which were loaned out.   65% of books that were loaned out are returned.   35% of books that were loaned out are NOT returned.   Now, there are 108 books, thus the number of un-returned books is 150-108= 
150-108 = 42
42 books.   0.35x= 42   x = 120   The answer is 120.
Answer: E
It rained on exactly 7 of the days during Jane's summer holiday trip. On
each day that it rained, it rained either in the morning or the afternoon
but not both. There were exactly 5 afternoons when it did not rain and
exactly 6 mornings when it did not rain. How many days did the trip
last?  Choices
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: Let M be the number of days it rained in the morning; A - the number of   days it rained in the afternoon; and let N be the number of days when it did not rain.   We have M + A = 7 (days when it rained); M + N = 5 (afternoons when it did not   rain); and A + N = 6 (mornings when it did not rain). Adding the equations we get   2(M + A + N) = 18, M + A + N = 9.   correct answer 9
Answer: C
The median annual household income in a certain community of 21 households is $50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median Q income in the community be in 2 years?
Choose the correct choice from the following answers:
A) $50,000	B) $60,000	C) $60,500	D) $65,000	E) Cannot be determined

Solution: Answer is E, because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean Q is increase by 10%. It could be the case that small number of higher end incomes increased a little or many low end incomes increased - it cannot be identified.
Answer: E
An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 44$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold?
Choose the correct choice from the following answers: A) 52 B) 75 C) 92 D) 136 E) 150

Solution: w1/w2 = (A2 - Aavg)/(Aavg - A1) = (44 - 40)/(40 - 36) = 4/4= 
4/4 = 1
1/1= Number of MicroTron stocks/Number of Dynaco stocks   So for every 1 MicroTron stock, she sold 1 Dynaco stock.   So out of 300 total stocks, (1/1)th i.e. 300/2 = 150 must be Dynaco stock.   Answer (150)
Answer: E
The simple form of the ratio 2/3:2/5 is? Choose the correct choice from the following options:  A) 5:6  B) 5:1  C) 5:7  D) 5:3  E) 1:3

Solution: 2/3 : 2/5 = 10:6   =5:3   Answer:5:3
Answer: D
A box contains 4 red chips and 5 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?	Choices.
A) 1/2	B) 5/9	C) 7/12	D) 2/3	E) 7/10

Solution: Total selection ways: 9C2=9!/5!4!=36   Selecting one blue chip out of two: 5C1=5!/4!1!=5   Selecting one red chip out of four: 4C1=4!/1!3!=4   Thus, (5C1*4C1)/9C2=(5*4)/36=20/36=5/9=5/9
Answer: B
Walking at 8KMPH From Point R to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point R to Railway station? Answers.
A) A)9KM
B) B)6.66KM
C) C)7.25KM
D) D)12.40KM
E) E)13KM

Solution: Since time differences given are in minutes so let's convert speed in Km per minute   8 kmph = 8/60 km per minute = (2/15) km per minute   10 kmph = 10/60 km per minute = (1/6) km per minute   Let, Time of train to depart from station = t minutes   Distance between Point R and Railway Station = Speed*Time = (2/15)*(t+5)   Distance between Point R and Railway Station = Speed*Time = (1/6)*(t-5)   i.e. (2/15)*(t+5) = (1/6)*(t-5)   i.e. 12t+60 = 15t - 75   i.e. 3t = 135   i.e. t = 45 minutes   i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km   Answer: Option 6.66KM
Answer: B
A shop sells bicycles and tricycles. In total there are 10 cycles (cycles include both bicycles and tricycles) and 23 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.
Select the correct option:
A) b=7,t=3
B) b=5,t=3
C) b=8,t=2
D) b=2,t=5
E) b=6,t=4

Solution: Let b be the number of bicycles and let t be the number of tricycles.   Set up the equations   b+t=10............(1)   2b+3t=23............(2)   Let b be the number of bicycles and let t be the number of tricycles.   Set up the equations   b+t=8............(1)   2b+3t=19............(2)   Rearrange equation (1) and substitute into equation (2)   2b+30-3b=23   -b=-7   b=7   Calculate the number of tricycles t   t=10−b   =10−7   =3   There are 3 tricycles and 7 bicycles.   b=7,t=3nswer is b=7,t=3.
Answer: A
12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?	Select the correct option.
A) 8
B) 15
C) 16
D) 18
E) None

Solution: Solution   Capacity of the tank	= (12×13.5) litres   = 162 litres.   Capacity of each bucket	= 9 litres.   Number of buckets needed	= (162/9)= 
(162/9) = 18
› 18.   Answer 18
Answer: D
On average, the boys in the class have 20 pencils and the girls have 38 pencils. If the overall class average is 30 pencils, what is the ratio of boys to girls in the class?
Choose the most appropriate option:
A) 1/2	B) 2/3	C) 3/4	D) 4/5	E) 5/6

Solution: (38G + 20B) / (G+B) = 30   38G + 20B = 30(G+B)   8G=10B   B/G = 4/5   The answer is 4/5.
Answer: D
What is the ratio of 12 minute to 1 hour ?
Choose the correct answer.
A) 1/4
B) 3/4
C) 1/5
D) 2/2
E) 3/1

Solution: 1/5   1/5
Answer: C
Tough and Tricky questions: Work/Rate Problems.
If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 20 workers to do this same job?  Choices.
A) 40/3	B) 10.5	C) 7	D) 7/3	E) 9/7

Solution: 70 Workers = 3 hours then,   1 Worker = 3*70 Hours   20 Workers = (3*70) /(20)= 
(3*70) /(20) = 21/2 = around 10.5
10.5 Answer. 10.5
Answer: B
The moon revolves around the earth at a speed of approximately 1.02 kilometers per second. This approximate speed is how many kilometers per hour?  Choose the correct choice from the following choices:
A) 60  B) 61.2  C) 62.5  D) 3,600  E) 3,672

Solution: moon revolves around the earth at a speed of 1.02kilometers per second.   one hour equal to 60 minutes.   one minute equals to 60 seconds. so one hour equals to 3600 seconds.   so one hour, speed= 1.02*3600= 
1.02*3600 = 3_672
3672 kilometers per hour.   Option 3,672 is correct
Answer: E
Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 7 muffins remained. How many guests did Monica plan on? Choose the correct choice from the following answers
A) 3.	B) 4.	C) 1.	D) 6.	E) 7.

Solution: 5N +2 = 7 + 6(N-1)   Solving N5  +2= 
5  +2 = 7
7 + 6(N-1)   Solving N= 1   Hence 1.
Answer: C
A man rows his boat 72 km downstream and 30 km upstream, taking 3 hours each time. Find the speed of the stream?
Choose the correct choice from the following answers.
A) 6 kmph  B) 5 kmph  C) 2 kmph  D) 8 kmph  E) 7 kmph

Solution: Speed downstream = d/t = 72/(3)= 
72/(3) = 24
24 kmph   Speed upstream= d/t = 30/(3)= 
30/(3) = 10
10 kmph   The speed of the stream= (24 - 10)/2= 
(24 - 10)/2 = 7
7 kmph   Answer:7 kmph
Answer: E
A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 39,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?	Pick one.
A) Rs. 2000
B) Rs. 4000
C) Rs. 3500
D) Rs. 3000
E) None of these

Solution: Explanation:   A's capital : B 's capital   20000 : 40000 = 1 : 2   Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2   Profit of A = (1/3) * 39,000 = Rs. 13,000   Salary of A = Rs. (15000 – 13000) = Rs. 2000   Rs. 2000NSWER: Rs. 2000
Answer: A
Jack and Jill work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?  Select
A) 1/3 B) 1/4 C) 1/15 D) 3/8 E) 2/3

Solution: Total number of ways to choose 2 out of 6 workers= 6!/2!4!= 15   Number of ways to choose both jack and jill= 1   probability= 1/15   1/15 should be the answer
Answer: C
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?  Choose the correct choice:  A) 5.77 km  B) 5.98 km  C) 5.76 km  D) 5.96 km  E) 5.12 km

Solution: Explanation:   M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2= 
2.88 * 2 = 5.76
5.76   Answer: Option 5.76 km
Answer: C
How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? Choose the correct answer:
A) 120  B) 121.1  C) 13  D) 156  E) 148

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec   Total distance covered= 110 + 132= 
110 + 132 = 242
242 m.   Required time= 242/20= 
242/20 = 121/10 = around 12.1
12.1 sec.   Answer: Option 121.1
Answer: B
The sum of ages of 5 children born 2 years different each is 50 yrs. What is the age of the Elder child?  Choose the correct choice from the following options
A) 8
B) 14
C) 16
D) 17
E) 18

Solution: Let the ages of children be x, (x + 2), (x + 4), (x + 6) and (x + 8) years.   Then, x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 50   5x = 30   x = 6   x+8= 6+8= 
6+8 = 14
14   Answer : 14
Answer: B
If x and y are prime numbers, which of the following CANNOT be ( x + Y )? Choose the correct option.
A) 5
B) 23
C) 13
D) 16
E) 3

Solution: All answer choices but B are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd.   Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers.   Answer: 23
Answer: B
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	Choose the correct choice from the following answers.
A) 22	B) 66	C) 48	D) 77	E) 21

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 6/125= 
1000 * 6/125 = 48
48 sec.   Answer:48
Answer: C
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 50, the dividend is:
Choose the correct choice from the following answers:
A) A)5322 B) B)5330 C) C)6300 D) D)5340 E) E)5342

Solution: Divisor = (5 * 50)= 
(5 * 50) = 250
250= 10 * Quotient = Divisor   => Quotient = 250/10= 
250/10 = 25
25   Dividend= (Divisor * Quotient) + Remainder   Dividend = (250 * 25) + 50= 
(250 * 25) + 50 = 6_300
6300.   6300
Answer: C
Which of the following is equal to (x+1)!/x!  Choose the correct choice.
A) x-1 B) 1+(1/x) C) x+1 D) 1 E) x

Solution: (x + 1)! = (x + 1) * x!   (x + 1)!/x! = x + 1   Answer: x+1
Answer: C
There are 47 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?	Choose the correct choice:
A) 39	B) 40	C) 51	D) 58	E) 63

Solution: {Total} = {M} + {N} - {Both}   {Total} = 47 + 28 - 12= 
47 + 28 - 12 = 63
63.   Answer: 63.
Answer: E
which of the following will not give an integer on taking square root?  Choose the correct choice from the following answers: A) 64 B) 529 C) 441 D) 484 E) 450

Solution: square root(64)=8   square root(529)=23   square root(441)=21   square root(484)=22   square root(450) is not an integer   so the answer is 450
Answer: E
In how many different number of ways 4 boys and 2 girls can sit on a bench?
Options.
A) 700  B) 710  C) 720  D) 800  E) 820

Solution: npn = n!   6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720   720)
Answer: C
A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 140 kilometers? Choose the correct choice from the following: A) 4.5 B) 5.5 C) 6.5 D) 7.5 E) 3.5

Solution: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 140 kilometers?   140 ÷ 40 = 3.5 × 1 gallon = 3.5 gallons   correct answer 3.5
Answer: E
Charlie's lawn service fills up all their gas cans every Friday at Zeb's store. They have to get enough gas for 10 lawn mowers and 10 weed-eaters. The weed-eaters use 5 liters of gas each. The mowers us 60% more than the weedeaters.
Zeb charges .75 cents service per item. Fuel is .40 cents per liter. How much will it cost to fill all mowers and weed-eaters? Choose the correct choice from the following choices
A) $77
B) $60
C) $67
D) $62
E) $55

Solution: Lots of calculations.   .75*20 + 10*.40*5+ 5*(8/5)*10*.40= 
.75*20 + 10*.40*5+ 5*(8/5)*10*.40 = 67
$67   The correct option is $67
Answer: C
A tin of oil was 4/5full.when 6 bottles of oil were taken out and four bottles of oil were poured into it, it was ¾ full. how many bottles of oil can the tin contain?	Choose the correct answer: A) 40 B) 30 C) 20 D) 50 E) 60

Solution: Suppose x bottles can fill the tin completely   Then4/5x-3/4x=6-4   X/20=2   X=40   Therefore required no of bottles =40   40nswer is 40.
Answer: A
A goods train runs at a speed of 72 kmph and crosses a 270 m long platform in 26 seconds.What is the length of the goods train?
Choose the correct option:
A) 230 m	B) 250 m	C) 260 m	D) 270 m	E) 240 m

Solution: s=270+x/t   72*5/18=270+x/26   x=250   ANSWER:250 m
Answer: B
The cost price of 20 books is the same as the selling price of ’X’ books. If the profit is 25%, then the value of X is ? Choose the correct choice: A) 25 B) 18 C) 16 D) 15 E) 14

Solution: let S.P. of X books = Rs 100 = C.P. of 20 books   Therefore, C.P. of one book = Rs 5   Profit = 25 %   Therefore, S.P of one book = 6.25   S.P of X articles = 6.25 X   6.25 X = 100 => X = 16   ANSWER:16
Answer: C
he average of 10 numbers is zero. Of them, at the most, how many may be greater than zero?	Choose the correct choice from the following answers:
A) 0 B) 1 C) 10 D) 9 E) 8

Solution: Average of 10 numbers = 0.   Sum of 10 numbers (0 x 10) = 0.   It is quite possible that 9 of these numbers may be positive and if their sum is a the 10th number is (-a).   Answer: Option 9
Answer: D
Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Select the correct option
A) 378
B) 277
C) 375
D) 287
E) 279

Solution: A+B+375 = 1500   A = 1/3(B+375); B = 2/3(A+375)   A/(B+375) = 1/3   A = 1/4 * 1500= 
1/4 * 1500 = 375
> 375   Answer: 375
Answer: C
Consider two statements
Statement 1 => If X is an integer and X=2p+1 where p is not an integer.
Statement 2 => If Y is an integer and Y=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of X and Y respectively
Choose the correct choice:
A) Odd,Even	B) Odd,Odd	C) Even,Odd	D) Even,Even	E) Cannot be determined

Solution: x = integer   x = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out   if n were even x would odd   if n odd x would be even   Similarly other   answer will be Cannot be determined
Answer: E
Martin has a business washing cars. Last year he washed 20 cars a
week. This year, he wants to increase his business to 1,200 cars a year.
How many cars will he have to wash each month on average?
Pick:
A) 200 cars B) 500 cars C) 300 cars D) 100 cars E) 400 cars

Solution: The last year part is extra information. 1200÷12 (months in a year)= 100   He will have to wash 100 cars each month.   correct answer 100 cars
Answer: D
A train speeds past a pole in 23 seconds and a platform 125 m long in 33 seconds. Its length is?	Answers:
A) 275
B) 287.5
C) 288
D) 233.5
E) 245.6

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 23 => y = x/23   x + 125 / 33 = x / 23   x = 287.5 m.   Answer:287.5
Answer: B
A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.2, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?  Pick.
A) $16.60
B) $20.75
C) $22.50
D) $42.75
E) $45.00

Solution: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .   A= 2O   S= 2G   A= 2S   A= 4G   A+O+S+G = 90   =>A + A/2 + A/2 +A/4 = 90   => 9A/4 = 90   => A = 40   O = 20   S = 20   G = 10   Cost of each candy = .2 $   Mininum amount of money required to guarantee that you would buy at least three of each type of candy   We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .   Total = 83 candies   $16.60mount required = 83 * .2= 
83 * .2 = 16.6
16.60 $   $16.60nswer $16.60
Answer: A
What is the remainder when 14,451 × 15,654 × 16,783 is divided by 5?	Choices.
A) 1
B) 3
C) 2
D) 4
E) 5

Solution: Only the unit's digit of the product will decide the remainder when divided by 5.   Hence, 1*4*3= will give units digit as 2   So, whatever be the number, if it ends in 2, the remainder after dividing with 5 will be 2.   Option 2
Answer: C
In a public show 75 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?
Answers:
A) 100
B) 110
C) 120
D) 140
E) 150

Solution: 75 % of 600   = 75/100 × 600   = 450   Therefore, the number of vacant seats = 600 - 450= 
600 - 450 = 150
150.   Answer:150
Answer: E
In a group of 120 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20?  Choose the correct choice from the following answers:
A) 60/ 120 B) 15 / 120 C) 30 / 120 D) 80 / 120 E) 40/ 120

Solution: Number of people whose age is less than 20 is given by   120 - 90= 
120 - 90 = 30
30   Probability P that a person selected at random from the group is less than 20 is gieven by    30 / 120= 
 30 / 120 = 1/4 = around 0.25
0.25   correct answer 30 / 120
Answer: C
Find the one which does not belong to that group? Choose the correct choice from the following answers:  A) 16  B) 36  C) 77  D) 64  E) 4

Solution: Explanation:   16, 36, 64 and 4 are perfect squares but not 77.   Answer:77
Answer: C
If one positive integer is greater than another positive integer by 4, and the difference of their cubes is 316, what is their sum?  Answers:
A) 6  B) 8  C) 10  D) 12  E) 14

Solution: 1^3 = 1   2^3 = 8   3^3 = 27   4^3 = 64   5^3 = 125   6^3 = 216   7^3 = 343   The two numbers are 3 and 7.   The answer is 10.
Answer: C
A car X takes 3 hours more than a bus Y in covering 40 km. If the car triples its speed it takes 1 hour less than bus. What is the speed of the car?
Choose the correct answer: A) 6 km/hr B) 6.25 km/hr C) 6.67 km/hr D) 7 km/hr E) None of these

Solution: Explanation :   Let the car's speed be x km/hr.   => 40/x-40/(3x)=4   => 80/3x=4   => 12x=80   => x=6.67 km/hr   Answer : 6.67 km/hr
Answer: C
A can finish a piece of work in 4 days. B can do it in 12 days. They work together for two days and then A goes away. In how many days will B finish the work?  Choose the most appropriate option.
A) 6 days	B) 5 days	C) 7 days	D) 4 days	E) 3 days

Solution: 2/4 + (2 + x)/12= 1 => x =6 days   6 daysnswer: 6 days
Answer: A
If k is the greatest positive integer such that 4^k is a divisor of 32! then k =  Choose the most appropriate option.
A) 3 B) 4 C) 5 D) 6 E) 10

Solution: 32/4= 
32/4 = 8
8   32/16= 
32/16 = 2
2   8+2= 
8+2 = 10
10=k   Answer:10
Answer: E
A local bank that has 9 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 9 codes? Choose the correct choice from the following answers:
A) 9 codes 3 integers
B) 4
C) 5
D) 6
E) 7

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   Total = 9 Codes.. 9 codes 3 integersnswer: 9 codes 3 integers
Answer: A
If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be
Choose the most appropriate option:  A) 7  B) 9  C) 12  D) 14  E) 15

Solution: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.   x = 7.   7)
Answer: A
If the number 5 * 2 is divisible by 6, then * = ? Choose the correct answer.
A) 8  B) 6  C) 2  D) 1  E) 5

Solution: C   2   6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x.   Then, (5 + x + 2) must be divisible by 3. So, x = 2.
Answer: C
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 ?	Select the correct option:  A) 160  B) 175  C) 180  D) 195  E) 166

Solution: Explanation:   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: B