MU-NLPC/Calc-aqua_rat huggingface dataset:
If n = 2×3×5×7×11×13×19, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even	Select the correct option.
A) I only  B) II only  C) III only  D) I and III  E) None of the above

Solution: Statement I: 600 = (2^3)*(3)*(5^2) this is NOT true.   Statement 2 Since n is divisible by 19 so n+19 is also divisible by 19. So this is true.   Statement 3: (n+4)/2 = n/2 + 2   So, ODD + 2 cannot be even.   So this is NOT true.   Hence option (II only).
Answer: B
From the set of numbers {p, t, u, v, w, x, y, z}, how many different combinations can we have without the t, the x, or the u in them? Ex:. (x,y), (x), (w,z,y,x), etc... and note that (x,y)=(y,x)  Choose the correct choice from the following choices:
A) 8
B) 15
C) 16
D) 31
E) 32

Solution: Any letter (p, v, w, y, z) can be included or not.   Thus there are 2^5 combinations - 1 empty combination = 31 combinations   The answer is 31.
Answer: D
An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 10%. How much will an air-conditioning unit cost in November?	Choices:
A) $434
B) $470
C) $472
D) $484
E) $491

Solution: if its previous November(before discount) then price is $470.   but if its November of next year then   16% discount on $470=470(1-16/100)=$394.8   again a corrected raised price of 10% over $394.8=394.8(1+10/100)=434.28~$434   $434ns $434
Answer: A
A basket contains Rs 216 in the form of one rupee, 50 paise and 25 paise coins in the ratio of 3 : 4 : 4. The number of 50 paise coins is ?
Choose the correct choice from the following:
A) 96  B) 128  C) 144  D) 100  E) 90

Solution: Let number of one rupee coins = 3K   Number of 50 paise coins = 4K   Number of 25 paise coins = 4K   Therefore 3K + 0.50 x 4K + 0.25 × 4K = 216   => 3K + 2K + 1K = 216   => K = 36   Therefore number of 50 paise coins = 4K = 144   ANSWER:144
Answer: C
Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 90. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test? Pick:	A) 87	B) 89	C) 90	D) 98	E) 95

Solution: Total score on 3 tests = 90*3= 
90*3 = 270
270   Jerry wants the average to be= 92   Hence total score on 4 tests should be = 92*4= 
92*4 = 368
368   Score required on the fourth test= 368 - 270= 
368 - 270 = 98
98   Option 98
Answer: D
The greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is:	Choose the most appropriate option.
A) 15 B) 18 C) 19 D) 22 E) 23

Solution: explanation:   60-6= 
60-6 = 54
54 ,190-10= 180   Highest number that divides 54 and 180 is HCF of numbers   HCF of 54 nad 180= 18   Answer:18
Answer: B
3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 48 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last?	Answers: A) 15 days B) 18 days C) 21 days D) 24 days E) 27 days

Solution: 2 oxen = 3 buffaloes = 4 cows   Also: 15 buffaloes + 8 oxen + 24 cows   = 10 oxen + 8 oxen + 12 oxen = 30 oxen   There is enough fodder for 1 oxen for 30*48 days.   60 cows + 30= 
+ 30 = 30
30 oxen + 20 oxen= 50 oxen   The new total is equal to 80 oxen instead of 30 oxen.   30*48 / 80= 
30*48 / 80 = 18
18 days   The answer is 18 days.
Answer: B
The unit digit in the product (722 * 774 * 889 * 223) is: Choose the correct answer
A) 2
B) 7
C) 6
D) 8
E) 1

Solution: Explanation:   Unit digit in the given product = Unit Digit in (2*4*9*3) = 6   ANSWER: 6
Answer: C
After playing 40 games, the Lesley basketball team had won 50% of the games. The additional games played gave the team a 20% total winning average. How many additional games must the team have won to obtain this average?  Choose the correct option:
A) 2
B) 15
C) 7
D) 10
E) 9

Solution: Explanation: Identify the parts, set up equation, and solve.   Number of games initially won by the team:   50% * 40 = 20   Additional games won by the team leaving a 20% average. (Let x represent the unknown number of additional games won.) Therefore, the total number of games played is 40+x, and the total number of games won is 20+x. This gives the equation as:   20%*(40+x)=20+x   Solve: Let's get rid of the percent sign   20/100*(40+x)=20+x   1/5 *(40+x)=20+x   Get rid of the fraction:   5[1/5 * (40+x)]=5(20+x)   1 * (40+x) =100+5x   40+x =100+5x   (40-100)+x = (100-100)+5x   -60+x= 5x   -60+(x-x)+5x-x   -60=4x   15 = x   Answer: 15
Answer: B
To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 15 hours a day?	Options:
A) 23	B) 22	C) 21	D) 20	E) 19.2

Solution: Man-hours required to asphalt 1 km road=30*12*8= 
30*12*8 = 2_880
2880   Man-hours required to asphalt 2 km road=2880*2= 
2880*2 = 5_760
5760   Man-hours available per day=20*15= 
20*15 = 300
300   Therefore number of days=5760/300= 
5760/300 = 96/5 = around 19.2
19.2 days   Ans=19.2
Answer: E
A batsman makes a score of 50 runs in the 6th inning and thus increases his average by 2. Find his average after 6th inning.  Choose one
A) 40 B) 50 C) 60 D) 70 E) 80

Solution: Let the average after 6th inning = x   Then, average after 5th inning = x-2   5(x-2)+50 = 6x   x = 10-50 = 40   40nswer is 40
Answer: A
Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 6 ½ hours if they are walking in the same direction?
Select.
A) 7 km  B) 6 km  C) 8 1/8 km  D) 9 km  E) 5 km

Solution: RS = 5 ¾ - 4 ½ = 1 ¼   T = 6 ½ h.   D = 5/4 * 13/2 = 65/8   = 8 1/8 km   Answer:8 1/8 km
Answer: C
Jacob brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20%? Select:  A) 332  B) 787  C) 500  D) 277  E) 181

Solution: Let the C.P. be Rs. x. Then, 20% of x = 1100   20/100 * x = 1100 => x = 5500   C.P. = Rs. 5500, expenditure on repairs = 10%   Actual price = Rs. (100 * 5500)/110 = Rs. 5000   Expenditures on repairs = (5500 - 5000) = Rs. 500.   Answer:500
Answer: C
1397 x 1397 = ?  Choose the correct option: A) 1951607 B) 1951609 C) 1951610 D) 1951611 E) 1951613

Solution: 1397 x 1397	= (1397)2   = (1400 - 3)2   = (1400)2 + (3)2 - (2 x 1400 x 3)   = 1960000 + 9 - 8400   = 1960009 - 8400= 
1960009 - 8400 = 1_951_609
1951609.   1951609)
Answer: B
Average of five consecutive even numbers is 35. Find the greatest number in these five numbers?	Answers:
A) 32
B) 33
C) 39
D) 40
E) 41

Solution: 39   Option '39'
Answer: C
A, B and C can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete the work? Select the correct option:
A) 12 B) 10 C) 15 D) 8 E) 13

Solution: Option 15   Explanation:   One days's work of A, B and 15 = 1/90 + 1/30 + 1/45   = (1 + 3 + 2)/90 = 1/15   A, B and 15 together can do the work in 15 days.
Answer: C
What is the remainder when (71)(73) is divided by 8? Choose the correct option
A) 1  B) 2  C) 4  D) 5  E) 7

Solution: (71)(73) = (72-1)(72+1) = 72^2 - 1 which is 1 less than a multiple of 8.   Then the remainder will be 7.   The answer is 7.
Answer: E
A shopkeeper buys two articles for Rs.1000 each and then sells them, making 30% profit on the first article and 30% loss on second article. Find the net profit or loss percent?
Select the correct option.
A) 200  B) 278  C) 282  D) 202  E) 300

Solution: Profit on first article = 30% of 1000 = 300.   This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.   Answer: 300
Answer: E
Lucia is a wonderful grandmother.Her age is b/w 50 to 70.Each of her sons have as many sons as they have brothers.Their combined number gives Lucia's present age?what is her age?
Choose the correct option:
A) 85  B) 55  C) 84  D) 64  E) 62

Solution: If she has x sons   each son has x-1 brothers.   Total no of grandchildren=x(x-1)   Total No OF Sons+Grandchildren= x+x(x-1)=x^2   =>Lucia's age is a perfect square between 50 and 70. The only number that satisfies this condition is 64.   ANSWER:64
Answer: D
Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is t, what is the difference between the probability that t is even and the probability that t is odd?
Choose the correct answer:
A) 1/9  B) 1/6  C) 2/9  D) 1/4  E) 1/2

Solution: 1/9ge of Boys t:4, 6, 7   Sum of ages taken 2 at a time: 10,13,11   1/9ges of Girls:5, 8, 9   Sum of ages taken 2 at a time: 13,17,14   9 Combinations of sum between sets(10,12,11)(13,17,14)   =23,27,24- 16,30,17- 24,28,25   Prob(Even)= 5/9   Prob(Odd) =4/9   1/9nswer=5/9 - 4/9 = 1/9
Answer: A
A picnic attracts 240 persons. There are 80 more men than women, and 80 more adults than children. How many men are at this picnic?
Select the correct option:
A) 240 B) 75 C) 110 D) 120 E) 200

Solution: Adult + Children = 240   Let, Children = y   then, Adult = y+80   i.e. y+(y+80) = 240   i.e. y =80   i.e. Adult = 80+80= 
80+80 = 160
160   Adults include only Men and Women   i.e. Men + Women= 160   Let women, W = x   then Men, M = x+80   i.e. x+(x+20) = 2x+80 = 160   i.e. x = 40   i.e. Men, M = 40+80= 
40+80 = 120
120   Answer: Option 120
Answer: D
Find four consecutive even integers such that the sum of the second and fourth integers is one and a half times the sum of the first and third integers.
Choose the correct choice from the following choices.
A) n, 2n, 4n, 6n B) n, 2, 4, 6 C) n, 2n, 3n, 4n D) n, n+2, n+4, n+6 E) n, n^2, n^4, n^6

Solution: Sum of Second and Fourth Integers: (n + 2) + (n + 6) = 2n + 8   Sum of First and Third Integers: n + (n + 4) = 2n + 4   Since sum of the second and fourth integers is twice than the sum of the first and third integers, it follows that:   2n + 8 = 1.5(2n + 4)   2n + 8 = 3n + 6   3n − 2n = 8 − 6   n = 2   Answer: n, n+2, n+4, n+6
Answer: D
A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is
Choose the most appropriate option.
A) 35.55 km/hr
B) 36 km/hr
C) 71.11 km/hr
D) 71 km/hr
E) None of these

Solution: Explanation:   Total time taken = (160/64 + 160/8)hrs   = 9/2 hrs.   Average speed = (320 × 2/9) km.hr   = 71.11 km/hr.   Answer: 71.11 km/hr
Answer: C
John went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Options.
A) 18  B) 19  C) 19.7  D) 21  E) 23

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   19.7)
Answer: C
An empty tank be filled with an inlet pipe ‘A’ in 42 minutes. After 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled. Find the time taken to fill the tank? Pick one.
A) 51.6 B) 51.5 C) 51.7 D) 51.1 E) 51.0

Solution: Assume total tank capacity = 210 Liters   Now capacity of pipe A = 210/42= 
210/42 = 5
5 Liters   Capacity of B= 210 / 30 = - 7 Liters   Capacity of C = 210 / 35= 
210 / 35 = 6
6 min   Assume tank gets filled in x min after the third pipe got opened.   So x×5+6×(−2)+4x=210x×5+6×(−2)+4x=210   ⇒48+4x=210⇒4x=162⇒x=40.5⇒48+4x=210⇒4x=162⇒x=40.5   Total time taken to fill the tank = 40.5 + 12 + 6 = 51.5   Answer:51.5
Answer: B
If a and b are positive integers and x = 4^a and y = 5^b, which of the following is a possible units digit of xy?  Pick
A) 0  B) 4  C) 5  D) 7  E) 8

Solution: The units digit of 4^a is either 4 or 6.   The units digit of 5^b is 5.   4*5= 
4*5 = 20
20 and   6*5= 
  6*5 = 30
30.   The units digit of xy is 0.   The answer is 0.
Answer: A
In a sequence of 12 numbers, each term, except for the first one, is 12^12 less than the previous term. If the greatest term in the sequence is 12^13, what is the smallest term in the sequence?
Thus, A12 = A1+12-1d
Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.
From what I undersltand the formula for an arithmetic sequence represents
some-number-in-the-sequence= first-number-in-sequence +the-place-of-that-number - 1x the-difference-of-each-#-in-the-sequence
Choose the correct choice from the following choices
A) −12^11 B) 0 C) 12^11 D) 11·12^11 E) 12^12

Solution: there are total 12 terms. andgreatestterm is 12^13. Each term is 12^12 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (NoticeEach term is 12^12 less than previous one')   Therefore, 12^13 is the first term of the AP and -12^11 is the difference between successive terms, the smallest term should be the last one.   Last term = First term + (n-1)*d   therefore, Last term = 12^13 + 11*(-12^12)   => Last term = 12^13 - 11*12^12   => Last term = 12^12 (12-11) = 12^12   Which is the smallest term.   Hence Ans 12^12 it is.
Answer: E
The probability of Sam passing the exam is 1/3. The probability of Sam passing the exam and Michael passing the driving test is 1/6. What is the probability of Michael passing his driving test?  Choose the correct option:
A) 1/24.
B) 1/2.
C) 1/3.
D) 2/3.
E) 2/5

Solution: 1/3 *1/m= 1/6 , 1/m = 1/2   Answer 1/2.
Answer: B
In the coordinate plane, one of the vertices of a square is the point (-3, -4). If the diagonals of that square intersect at point (4, 2), what is the area of that square? Choose the correct choice from the following choices:  A) 196  B) 125  C) 140  D) 128  E) 134

Solution: One point (-3-4), Intersection (4,2) so the distance from the first point -3-4=-7 is the midpoint of the square --> whole side 14, 14*14=196   196
Answer: A
A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
Choose the correct choice:
A) 4 days
B) 6 days
C) 8 days
D) 12 days
E) 15 days

Solution: Explanation:   Suppose A, B and C take x,	x/2	and	x/3	days respectively to finish the work.   Then, 1/X	+	2/X	+	3/X =	1/2   6/X	=	1/2   x = 12.   So, B takes (12/2)= 
(12/2) = 6
6 days to finish the work.   ANSWER IS 6 days
Answer: B
You frequently buy a box of dog toys for your 3 puppies to play with. Typically, the toys last 60 days before the dogs bury them all and you have to buy another box. Recently, you've started your own mini-animal shelter and now have 25 total puppies. You've just purchased a new box of dog toys, how many days until they bury all the toys?	Pick one
A) 5.6	B) 9.7	C) 75	D) 19.2	E) 7.2

Solution: First set up a ratio with all the relevant values and also the unknown variable:   3*60 = 25*x   Now solve by multiplying 3 by 60 and then dividing that product by 25:    3*60= 
 3*60 = 180
180   180/25= x   x = 7.2   The value of x represents the amount of days it takes 25 puppies to bury the toys in a box.   Answer: 7.2
Answer: E
Two employees X and Y are paid a total of Rs. 572 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?  Choose the correct choice from the following choices.
A) s.250 B) s.280 C) s.290 D) s.260 E) s.300

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 572   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 572   ⇒ y[12/10 + 1] = 572   ⇒ 22y/10 = 572   ⇒ 22y = 5720   ⇒ y = 5720/22 = 520/2 = Rs.260   s.260
Answer: D
Of the twelve participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?  Pick:	A) 3	B) 4	C) 6	D) 9	E) 20

Solution: half are male --> 6 males   half the males are under 18 --> 3 males under 18   same for females --> 3 females above 18   groups of four ( out of which 2 are males below 18 and 2 are females above 18) = 3C2 * 3C2 = 3*3= 
3*3 = 9
9   ANS:9
Answer: D
34.	The side surface of a cylinder is rolled with a rectangular plate. If the height of a cylinder tank is 10 feet and the perimeter of the circular base Is 4 feet, what is the area of the rectangular plate? Choose one:  A) 24  B) 34  C) 28  D) 40  E) 14

Solution: Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both you can multiply them together to find the area, 40. (Correct answer 40)
Answer: D
The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?	Select
A) 5	B) 8	C) 9	D) 10	E) 12

Solution: Let the number be xy.   Given xy – yx = 36.   This means the number is greater is than the number got on reversing the digits.   This shows that the ten’s digit x > unit digit y.   Also given ratio between digits is 1 : 2 => x = 2y   (10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.   Hence, (x + y) – (x – y) = 3y – y = 2y = 8   8
Answer: B
The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits G of the larger integer?  Choose the correct choice from the following answers
A) G=2	B) G=5	C) G=8	D) G=10	E) G=11

Solution: Really hard. But let's start with few concepts:   1. Square of an odd integer will be odd.   2. Difference of odd and odd will be even.   3. Any odd integer can be expressed as difference of two squares.   4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4.   Assume two odd integers to be (2x-1) and (2x+1).   Difference of their squares = (2x+1)^2 - (2x-1)^2   = 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)   = 4x^2 + 1 + 4x - 4x^2 - 1 + 4x   = 8x   Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.   8 = 2^3, so x needs to be such that itcompletesa perfect square.   If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.   Let's check the options, starting with c.   For sum to be 8, few possibilities are: 17, 35, 53, 71   If we take 17, the pair is 15 and 17, meaning x = 8.   8x = 64   root of 64 = 4 but 4 is not equal to 1+5+1+7.   Reject.   If we take 35, the pair is 33 and 35, meaning x = 17.   8x = 8*17   Reject since perfect square is not possible.   If we take 53, the pair is 51 and 53, meaning x = 26.   8x = 8*26   Reject since perfect square is not possible.   If we take 71, the pair is 69 and 71, meaning x = 35.   8x = 8*35   Reject since perfect square is not possible.   I tried each option and the possibilities and then got lost.   Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?   Starting with option a, only 2-digit odd integer whose sum is 2 is 101.   If we take 101, the pair is 99 and 101, meaning x = 50.   8x = 8*50= 
8*50 = 400
400   root of 400= 20 which is indeed equal to 9+9+1+1.   G=2nswer (G=2).
Answer: A
When a certain number X is divided by 63, the remainder is 27. What is the remainder when X is divided by 8?  Choose the correct option
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: When a certain number X is divided by 63, the remainder is 27. What is the remainder when X is divided by 8?   Putting a value say x = 27 we get remainder as 27 when divided by 63.   When 27 divided by 8 we get 3 as remainder.   3 is the answer.
Answer: B
There is a square with sides of 12. What is the circumference of the biggest circle that can be cut out of this square?
Choices: A) 75.4 B) 31.42 C) 36 D) 18.85 E) 37.7

Solution: Circumference of a circle = C=2Ï€r   Square is 12 wide, so circle's diameter would be 12, and radius would be 6   C=2Ï€6 which is approximately 37.7   Answer is 37.7
Answer: E
The average age of 36 students in a group is 14 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?
Choose the correct choice from the following answers:
A) 31  B) 36  C) 51  D) cannot be determined  E) None of these

Solution: Age of the teacher = (37 × 15 – 36 × 14) years   = 51 years.   Answer 51
Answer: C
A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 1/3 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x?	Pick:
A) x/3
B) x/2
C) 2x/3
D) 3x/2
E) 2x

Solution: x/(x+y) = 1/3   3x = x+y   2x = y   y = 2x   Answer 2x
Answer: E
The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?	Choose the correct choice from the following answers.
A) s.4528	B) s.4520	C) s.5436	D) s.4530	E) s.4521

Solution: Area of the four walls = 2h(l + b)   Since there are doors and windows, area of the walls   = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)   = 906 sq.ft.   Total cost = 906 * 6   = Rs.5436   Answer:s.5436
Answer: C
The ratio, by volume, of soap to alcohol to water in a certain solution is 2:40:70. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?	Pick: A) 500 B) 600 C) 650 D) 700 E) 720

Solution: soap:alcohol   Initial ratio soap:alcohol: water --> 2:40:70   Initial soap:alcohol = 2/40 =2:40   after doubled soap:alcohol =2* 2/40 = 4:40   Initial soap:water = 2/70=2:70   after halved soap:water: 1/2 * 2/70 = 1/70 = 1:70   After soap: alcohol:water --> 4:40:280-->1:10:70   given alcohol 100 cubic centimeter.   ratio is 10:100:700(1:10:70)   For 100 cubic centimeter of Alcohol --- 700cubic cm water is required.   Answer-700
Answer: D
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 130 sq cm. Find the area of the square?
Select.
A) 482
B) 268
C) 260
D) 480
E) Cannot be determined

Solution: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .   Area of the square cannot be found.   Answer: Cannot be determined
Answer: E
If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 63. By how much do the two digits differ?  Pick one:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Given that (10a + b) - (10b + a) = 63 --> 9a - 9b =63 --> a - b 63 --  9  - 9= 
63 --  9  - 9 = 63
63 --> a - b= 7.   Answer: 7.
Answer: E
Ken and Shen are workers in a department that has a total of 10 employees. Their boss decides that two workers from the department will be picked at random to participate in a company interview. What is the probability that both Jim and John are chosen?
Choose the correct choice from the following choices:
A) 2/45
B) 1/45
C) 11/45
D) 12/45
E) 1/45

Solution: Probability = 2c2/10c2   = 1/45   Answer 1/45
Answer: B