MU-NLPC/Calc-aqua_rat huggingface dataset:
Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four pink stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?  Options:
A) 120  B) 350  C) 700  D) 1,960  E) 5,040

Solution: Number of ways to choose 2 colors among 8 - 8c2   Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))   Now the order,   the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4   [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]   Total number of combinations -8c2 * 2* 7c4 = 1960   1,960
Answer: D
If x > 1, which of the following decreases as x decreases?
I. x + x^2
II. 2x^2 − x
III. (x + 1)  Pick one: A) I only B) II only C) III only D) I , II and III E) II and III only

Solution: let x= 4 and 3 b old and new values   ST1: x= 4 -> 4+16 = 20   x=3-> 3+9 = 12 ...decreased   ST2:x= 4-> 2*16-4 = 28   x=3->2*9-3 = 15   decreased   St3: x=4-> 5   x=3->1/3 4   Ans: I , II and III
Answer: D
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?  Choose the correct choice.
A) 2 years
B) 4 years
C) 6years
D) 12 years
E) None

Solution: Solution   Mother's age when Ayesha's brother was born	= 36 years.   Father's age when Ayesha's brother was born   = (38+4) years.   = 42 years.   Required difference	= (42-36)= 
(42-36) = 6
6 years.   Answer 6years
Answer: C
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
Choose the correct choice from the following:
A) 6 days  B) 10 days  C) 15 days  D) 20 days  E) 25 days

Solution: Explanation:   Work done by X in 4 days = (1/20 * 4) = 1/5   Remaining work = (1 - 1/5) = 4/5   (X + Y)'s 1 day work = (1/20 + 1/12) = 2/15   Now, 2/15 work is done by X and Y in 1 day.   So, 4/5 work will be done by X and Y in (15/2 * 4/5)= 
(15/2 * 4/5) = 6
6 days.   Hence, total time taken= (6 + 4)= 
(6 + 4) = 10
10 days.   ANSWER IS 10 days
Answer: B
There is a sequence A(n) such that A(n+1)=2A(n)-1 and A(1)=3, where n is a positive integer. What is the value of A(46)-A(45)?	Choose the correct choice from the following options:
A) 2^22+1
B) 2^45
C) 2^23+1
D) 2^24
E) 2^23+1

Solution: A1= 3   A2= 2*3-1= 
2*3-1 = 5
5   A3= 2*5-1= 
2*5-1 = 9
9   A4= 2*9-1= 
2*9-1 = 17
17   We can notice that there is a squence   A2-A1= 2^1   A3-A2= 2^2   A4-A3= 2^3   Hence A46-A45= 2^45   2^45 is the answer
Answer: B
A 270 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? Choose the correct choice from the following answers: A) 230 B) 997 C) 266 D) 289 E) 179

Solution: Relative speed = 120 + 80= 
120 + 80 = 200
200 km/hr.= 200 * 5/18 = 500/9 m/sec.   Let the length of the other train be x m.   Then, (x + 270)/9 = 500/9 => x = 230.   230nswer: 230
Answer: A
Question: What is the remainder when Q=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144?  Answers:  A) 0  B) 25  C) 49  D) 81  E) 100

Solution: 144 =12 *12   (1!)^3=1   2!=2, therefore (2!)^3=2*2*2= 
2*2*2 = 8
8   3!=6, therefore (3!)^3=6*6*6= 
6*6*6 = 216
216   4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144   thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0   now the remainder when Q=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216= 
1+8+216 = 225
225 is divided by 144   now remainder when 225 is divided by 144 is 81. hence answer should be 81
Answer: D
Gauri went to the stationers 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?
Select the correct option.
A) Rs. 15
B) Rs. 15.70
C) Rs. 19.70
D) Rs. 20
E) Rs. 20.70

Solution: Let the amount taxable purchases be Rs. x.   65 of x =30/100   X = (30/100)x(100/6)   = 5   Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70   answer : Rs. 19.70
Answer: C
The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
Pick one: A) 6.09% B) 6.08% C) 6.1% D) 6.07% E) 6.05%

Solution: Amount of Rs. 100 for 1 year when compounded half-yearly   =100 x (1 + 3/100)^2 = 106.09   Therefore Effective rate = (106.09 - 100)= 
(106.09 - 100) = 6.09
6.09%   6.09%nswer 6.09%) 6.09%
Answer: A
Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
5 ~ 2 ~ 7 ~ 4 = ____
Choose the correct choice from the following.
A) 2410  B) 2910  C) 2940  D) 3749  E) 4470

Solution: 2410   2410   2410   The rule that is being followed here is   P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]   Using the same rule in the incomplete equation,   5 ~ 2 ~ 7 ~ 4 = [first digit of (5 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (5 * 4)]   = 2410   Thus 2410 is the missing number.
Answer: A
An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many meters Q long?
Choose the correct option.
A) 0.5
B) 1
C) 1.5
D) 2
E) 3

Solution: Let x be the number of desks and bookcases that are placed along the library wall.   2x + 1.5x < 15   3.5x < 15   Since x is a non negative integer, the largest number x can be is 4.   When x is 4, the desks and bookcases take up 3.5 * 4= 
3.5 * 4 = 14
14m=Q, leaving 1m of empty space.   Thus, I believe the answer is 1) 1
Answer: B
Set A consists of the integers from 4 to 15, inclusive, while set B consists of the integers from 7 to 20, inclusive. How many distinct integers do belong to the both sets at the same time?	Choose the correct choice from the following choices
A) 5	B) 7	C) 8	D) 9	E) 10

Solution: A={4,5,6,7,8,9,10,11,12}   B={6,7,8,9,10,11,12...}   Thus we see that there are 9 distinct integers that are common to both. 9 is the correct answer.
Answer: D
If the average (arithmetic mean) of the four numbers 5, 15, 30, and (N + 1) is 30, then N =	Choose the correct choice from the following answers:
A) 19
B) 20
C) 69
D) 78
E) 292

Solution: 5+15+30+N+1= 30x 4 = 120   =>N +51 = 120   =>N=69   Answer 69
Answer: C
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
Choose the most appropriate option: A) 3:4 B) 2:5 C) 6:7 D) 4:6 E) 5:2

Solution: Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i)   3:4nd, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii)   Solving (i) and (ii), we get x = 60 and y = 80   Ratio of speeds = 60:80 = 3:4   3:4NSWER 3:4
Answer: A
The present population of a town is 10000. Population increase rate is 10% p.a. Find the population of town after 2 years?	Choose the correct answer:
A) 10000 B) 11100 C) 15000 D) 12100 E) 14520

Solution: P = 10000   R = 10%   Required population of town = P(1 + R/100)^T   = 10000(1 + 10/100)^2   = 10000(11/10)^2   = 12100   Answer is 12100
Answer: D
If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 35
Select
A) 1	B) 3	C) 5	D) 7	E) 9

Solution: P Ã· 44 = 432   => P = 432 * 44= 
432 * 44 = 19_008
19008   P / 35= 19008 / 35 = 543, remainder = 3   3
Answer: B
Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 6H, which of the following represents the amount that Roberta paid?	Choose the correct choice from the following choices.
A) D + 40  B) D + H – 1  C) D + 2H  D) 6.93H  E) 1.21D

Solution: before 6.93Hiscount price was: 1.46.93H+1.5H   After 6.93Hiscount: 1.46.93H +1.5H-.426.93H-.45H   substitute 6.93H=6H   final value: 6.93H   Ans Is 6.93H
Answer: D
Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 15 kmph and 25 kmph. When will they meet for the first time any where on the track if they
are moving in the opposite direction ?
Pick one.
A) 144	B) 36	C) 124	D) 32	E) 38

Solution: Time taken to meet the first time = length of track/relative speed   = 400/ (15 +25) (5/18)   = 400/40 *(18/5)= 
400/40 *(18/5) = 36
36 sec.   Answer : 36
Answer: B
The product of digit is a Factor of a two digit number.No of such digit are:  Choose the correct choice from the following:
A) 3	B) 5	C) 9	D) 27	E) 25

Solution: 11, 1*1=1   12 , 1*2=2   15 ,1*5=5   24 ,2*4=8   36 , 3*6=18   so Ans is 5   ANSWER:5
Answer: B
On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent R of thatbeforeJuly 1 last year?	Answers
A) 90%	B) 99%	C) 100%	D) 101%	E) 110%

Solution: the total number of employees = n   the average salary = x   total salary to all emplyoees = xn   after   the total number of employees = n - 0.1n = 0.9n   the average salary = x + 10% of x = 1.1x   total salary to all emplyoees = 0.9n (1.1x)   total salary after as a % of total salary before R= [0.9n (1.1x)]/xn= 0.99 or 99%.99%
Answer: B
A vertical tower OP stands at the centre O of a square ABCD. Let h and b denote the lengths OP and AB respectively. Suppose ∠APB = 60°, then the relationship between h and b can be expressed as :	Select the correct option:  A) 2b^2 = h^2  B) 2h^2 = b^2  C) 3b^2 = 2h^2  D) 3h^2 = 2b^2  E) None of these

Solution: Explanation :   As OP is at centre of square so clearly PA = PB.   so, angle ∠PAB = ∠ PBA.   and as ∠APB = 60,so we can see that in ∆ APB, ∠ PAB = ∠ PBA = 60.   Hence, its an equilateral triangle thus making AP = PB = AB = b.   Now lets see ∆ AOB ,   O is centre of square so angle AOB=900​.   giving us AO = OB = AB/√2.   so AO= b/√2   Now in triangle AOP right angled at O,   => AO2 + OP2 = PA2 .   => b2/2 + h2 = b2 .   => h2 = b2/2   Answer : 2h^2 = b^2
Answer: B
Circles X and Y are concentric. If the radius of circle X is seven times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?	Select:
A) 13	B) Pi/3	C) Pi/2	D) 5/6	E) 48/49

Solution: Small circle radius = a, so area = PI a ^ 2   Large circle radius = 7a, so area = 9. PI a ^ 2   Area of shaded region = 49PI a^2 - PI a^2 = 48 PI a^2   So, probability = ( 48 PI a^2 ) / (49 PI a^2 )   =48/49 = Answer = 48/49
Answer: E
If x is an odd integer, which of the following is an odd integer?  Choose the correct choice from the following choices.
A) 2x
B) 3x-1
C) 5x+6
D) x+x^2
E) 6x-6

Solution: Plug in an odd integer; in this case 3   (2*3)= 
(2*3) = 6
6 Even     (3*3)-1= 
  (3*3)-1 = 8
8 Even   (5*3)+6= 15 + 6= 
15 + 6 = 21
21 Odd   3+3^2= 3 + 9= 
3 + 9 = 12
12 Even   (6*3)-6= 18 - 6= 
18 - 6 = 12
12 Even   Answer: 5x+6
Answer: C
The least perfect square, which is divisible by each of 21, 36 and 66 is:	Options
A) 213444  B) 214344  C) 214434  D) 231444  E) 23444

Solution: L.C.M. of 21, 36, 66 = 2772.   Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11   To make it a perfect square, it must be multiplied by 7 x 11.   So, required number = 22 x 32 x 72 x 112 = 213444   213444nswer: Option 213444
Answer: A
The average of first 15 natural numbers is? Choices.
A) 6 B) 5.5 C) 5.1 D) 8 E) 5

Solution: Sum of 15 natural no.   = 240/2= 
240/2 = 120
120   Average=120/15= 
120/15 = 8
8   Answer:8
Answer: D
In what time a sum of money double itself at 2% per annum simple interest?  Pick one:	A) 60%	B) 58%	C) 55%	D) 40%	E) 50%

Solution: P = (P*2*R)/100   R = 50%   ANSW50%R:50%
Answer: E
By selling an article at Rs.600, a profit of 25% is made. Find its cost price?  Choose the correct option:
A) Rs.480
B) Rs.420
C) Rs.430
D) Rs.440
E) Rs.490

Solution: SP = 600   CP = (SP)*[100/(100+P)]   = 600 * [100/(100+25)]   = 600 * [100/125] = Rs.480   Rs.480nswer:Rs.480
Answer: A
If the average (arithmetic mean) of a and b is 110, and the average of b and c is 170, what is the value of a − c?  Choose the correct choice from the following choices.
A) −120  B) −100  C) 100  D) 135  E) It cannot be determined from the information given

Solution: a+b = 220   b+c = 340   a-c = -120.   IMO option −120.
Answer: A
3 candidates in an election and received 3000, 5000 and 15000 votes respectively. What % of the total votes did the winningcandidate got in that election? Pick one
A) 65.21%	B) 50.16%	C) 57%	D) 60%	E) 65.24%

Solution: Total number of votes polled = (3000 + 5000 + 15000)= 
(3000 + 5000 + 15000) = 23_000
23000   So, Required percentage= 15000/23000 * 100 = 65.21%   65.21%
Answer: A
A corporation that had $115.19 billion in profits for the year paid out $250.10 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)
Options:
A) 50%
B) 20%
C) 5%
D) 2%
E) 0.22%

Solution: required answer = [employee benefit/profit] *100   =[(250.10 million)/(115.19 billion)]*100   =[(250.10*10^6)/(115.19*10^9)]*100   =(2.2/1000)*100= 
(2.2/1000)*100 = 0.22
0.22%   So answer is (0.22%)
Answer: E
A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)?	Choose the correct choice
A) 0  B) 20  C) 75  D) 5  E) 10

Solution: Explanation :   Gain = 50 * 11.40 - (20*10.5 + 30*12)= 
50 * 11.40 - (20*10.5 + 30*12) = 0
0   0nswer : 0
Answer: A
When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 3), the quotient is 15 and the remainder is 1. What is the value of N?  Answers
A) 151
B) 331
C) 511
D) 691
E) 205

Solution: N/P=18 7/P= 18P+7   N/(P+2)=15 1/(P+3)=15P+45+1   solving these two equations   we get P=11 N= 205 answer is 205.
Answer: E
If 15 toys cost Rs, 234, what do 35 toys cost? Choose the correct choice from the following options: A) 645 B) 564 C) 546 D) 654 E) None of them

Solution: Let the required cost be Rs. x. Then,   More toys, More cost	(Direct Proportion)   .	15 : 35 : : 234 : x = (15 x x) = (35 x 234) = x=(35 X 234)/15 =546   Hence, the cost of 35 toys is Rs. 546.   Answer is 546
Answer: C
What is the difference between the compound interest on Rs.12000 at 24% p.a. for one year when compounded yearly and half yearly? Pick:
A) 399.8
B) 383.8
C) 120.8
D) 288.8
E) 172.8

Solution: When compounded annually, interest   = 12000[1 + 24/100]1 - 12000 = Rs.2880   When compounded semi-annually, interest   = 12000[1 + 12/100]2 - 12000 = Rs.3052.80   Required difference = 3052.80 - 2880 = Rs.172.80   Answer:172.8
Answer: E
The duplicate ratio of 1:4 is?
Select the correct option
A) 1:2 B) 1:4 C) 1:8 D) 1:18 E) 1:13

Solution: 1^2: 4^2 = 2:16=1:8   ANSWER:1:8
Answer: C
Two men A and B start from place X walking at 4 Â½ kmph and 5 Â¾ kmph respectively. How many km apart they are at the end of 3 Â½ hours if they are walking in the same direction ?  Choose the most appropriate option:  A) 1 3/8 km  B) 3 3/8 km  C) 5 3/8 km  D) 4 3/8 km  E) 7 3/8 km

Solution: Explanation:   Relative Speed = 5 Â¾ - 4 Â½ = 1 Â¼   Time = 3 Â½ h.   Distance = 5/4 x 7/2 = 35/8 = 4 3/8 km.   Answer: 4 3/8 km
Answer: D
What proximate value should come in place of the question mark (?) in the following question?
6.595 × 1084 + 2568.34 – 1708.34 = ? Pick one:
A) 6,000  B) 12,000  C) 10,000  D) 8,000  E) 9,000

Solution: ? ≈ 6.6 × 1080 + 2560 – 1700 ≈ 7128 + 860 ≈ 8000   Answer 8,000
Answer: D
A man wants to sell his scooter.There are two offers,one at Rs.12,000 cash and the other at a credit of Rs. 12,880 to be paid after 8 months,money being at 18% per annum. Which is the better offer ?	Choose the most appropriate option.
A) Rs. 12,000 in cash B) Rs. 12,880 at credit C) Both are equally good D) none of these E) Cannot be determined

Solution: Solution   P.W. of Rs. 12,880 due 8 months hence   = Rs. [12880 x100/100 +( 18x8/12) ] = Rs. ( 12880x100/112)= Rs.11500.   Clearly, Rs.12,000 in cash is a better offer.   Rs. 12,000 in cashnswer Rs. 12,000 in cash
Answer: A
Noelle walks from point A to point B at an average speed of 3 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 4 kilometers per hour? Choose the correct answer
A) 5.75  B) 6  C) 7.25  D) 7.5  E) 7.75

Solution: Let's suppose that speed while returning was xkm/h   Since the distance is same, we can apply the formula of avg speed   Avg speed= 2S1S2/S1+S2   4= 2*3*x/3+x   x= 6   6 is the answer
Answer: B
c is the product of each integer from 1 to 50, inclusive and d=100^k, where k is an integer . What is the greatest value of k for which y is a factor of c?
Choose the correct choice from the following choices:
A) 7	B) 6	C) 5	D) 4	E) 9

Solution: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:   n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n   x = 1*2*3....*50 = 50!   No. of trailing zeros in 50! = 50/5 + 50/5^2 = 10+2= 
10+2 = 12
12   100^k= 10^2k → k = 12/2= 
12/2 = 6
6   6
Answer: B
The distance from City A to City B is 60 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?
Choose the correct choice from the following choices.
A) 45 B) 48 C) 50 D) 52 E) 60

Solution: The time it takes Bob to drive to City B is 60 / 40= 
60 / 40 = 3/2 = around 1.5
1.5 hours.   Alice needs to take less than 1 hour for the trip.   Alice needs to exceed a constant speed of 60 / 1= 
60 / 1 = 60
60 miles per hour.   The answer is 60.
Answer: E
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is?	Choose the correct choice from the following answers:	A) 1	B) 2	C) 6	D) 8	E) 9

Solution: Let the ten's and unit digit be x and 8 respectively.   x   Then, 10x + 8 + 18 = 10 x 8 + x   x x   10x2 + 8 + 18x = 80 + x2   9x2 + 18x - 72 = 0   x2 + 2x - 8 = 0   (x + 4)(x - 2) = 0   x = 2   Option 2
Answer: B
What could be the range of a set consisting of odd multiples of (6+1)?  Choose one.
A) 70	B) 24	C) 35	D) 62	E) 21

Solution: Range = the difference between the greatest and the smallest numbers in the sequence. Our sequence is odd and is a multiple of 7. Every number in that sequence can be represented like this: 7*(2n+1) where n is any positive integer.   Range = 7*(2m + 1) - 7*(2n + 1) = 7*2*(m-n) = 14 * (m-n).   m, n - any positive integers   The answer must be divisible by 14, which is only 70.   The correct answer is 70.
Answer: A
In a 120 meters race A beats B by 56 m or 7 seconds. A's time over the course is:	Choose the correct choice from the following
A) 22 seconds B) 12 seconds C) 10 seconds D) 8 seconds E) 28 seconds

Solution: B runs 56 m in 7 sec.   => B runs 120 m in 7/56*120= 
7/56*120 = 15
15 seconds   Since A beats B by 7 seconds, A runs 120 m in (15-7)= 
(15-7) = 8
8 seconds   Hence, A's time over the course= 8 seconds   ANSWER:8 seconds
Answer: D
The triplicate ratio of 1:3 is?	Select
A) 1:64
B) 1:62
C) 1:27
D) 3:64
E) 5:64

Solution: 1^3: 3^3 = 1:27   ANSWER:1:27
Answer: C
36 welders work at a constant rate they complete an order in 5 days. If after the first day, 12 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?  Select the correct option
A) 5 B) 2 C) 8 D) 4 E) 6

Solution: 1. We need to find out the time taken by 24 workers after day 1.   2. total no.of wokers * total time taken = time taken by 1 worker   3. Time taken by 1 worker = 36*5= 
36*5 = 180
180 days   4. But on day 1 thirty-six workers had already worked finishing 1/5 of the job. So 24 workers have to finish only 4/5 of the job.   5. Total time taken by 24 workers can be got from formula used at (2). i.e., 24* total time taken= 180. Total time taken by 6 workers to finish the complete job is 180/ 24= 
180/ 24 = 15/2 = around 7.5
7.5 days.   6. Time taken by 24 workers to finish 4/5 of the job is 4/5 * 7.5= 
4/5 * 7.5 = 6
6 days.   The answer is choice 6
Answer: E
A straight pipe 5 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard? Choose the correct choice from the following options
A) 1/6 and 1/4 only	B) 1/4 and 1/3 only	C) 1/6, 1/4, and 1/3	D) 1/12, 1/6 and 1/4	E) 1/12, 1/6, and 1/3

Solution: Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.   In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).   Distinct lengths would be: 3=3/12=1/4, 6-4=2=2/12=1/6meters long pieces.   1/6 and 1/4 onlynswer: 1/6 and 1/4 only.
Answer: A
A rectangular block 10cm by 20cm by 35cm is cut into an exact number of equal cubes. Find the least possible number of cubes?	Choose the correct choice from the following:
A) 6
B) 56
C) 15
D) 40
E) 22

Solution: Volume of the block = 10*20*35= 
10*20*35 = 7_000
7000 cm^3   Side of the largest cube= H.C.F of 10,20,35 = 5cm   Volume of the cube = 5*5*5= 
5*5*5 = 125
125 cm^3   Number of cubes= 7000/125= 
7000/125 = 56
56   Answer is 56
Answer: B
A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 500 feet. What is its area, in square feet?	Choose the correct choice from the following choices
A) 12,000  B) 19,600  C) 20,000  D) 20,400  E) 20,800

Solution: you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.   diagonal = 200   2x + 2y = 560, or x + y = 280   a^2 + b^2 = c^2 for each the sides of the triangle   using the ratio 3:4:5 for sides, and knowing c = 500, you can deduce the following   a=300   b=400   300x400=120,000   12,000 is the answer.
Answer: A
8 years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 12 years more than the present age of Anand. Find the present age of Anand? Choose the correct choice from the following choices.
A) 12
B) 13
C) 14
D) 15
E) 16

Solution: Let the present ages of Anand and Bala be 'a' and 'b' respectively.   a - 8 = 1/3 (b - 8) --- (1)   b = a + 12   Substituting b = a + 12 in first equation,   a - 8 = 1/3 (a + 4) => 3a - 24 = a + 4   => 2a = 28=> a = 14.   ANSWER:14
Answer: C