MU-NLPC/Calc-aqua_rat huggingface dataset:
List L: ABC, BCA, CAB
In list L above, there are 7 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
Pick.
A) 47  B) 114  C) 152  D) 161  E) 488

Solution: Let's try to sum the 3 given numbers taking their place values into account:   (100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B)   = 100(A + B + C) + 10(A + B + C) + (A + B + C)   = 111*(A + B + C)   We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152   Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases.   Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3   A, B and C are all even. 2+4+8 = 14. Factors 2 and 7   Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get.   488
Answer: E
(32^32^32)/9 will leave a remainder?????
Options:
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: 32^32^32=(2^5)^32^32=2^5120.   2^5120/9   =((2^3)^1706*2^2)/9   =((9-1)^1706*2^2)/9   =(-1)^1706*4   =4   ANSWER:4
Answer: C
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 15. The larger of the two numbers is:	Choose the correct choice from the following options:
A) 276	B) 299	C) 322	D) 345	E) 354

Solution: Clearly, the numbers are (23 x 13) and (23 x 15).   Larger number = (23 x 15) = 345.   Answer: Option 345
Answer: D
The food in a camp lasts for 40 men for 50 days. If ten more men join, how many days will the food last?  Choose the correct answer
A) 20days B) 30days C) 40days D) 50days E) 60days

Solution: one man can consume the same food in 40*50= 
40*50 = 2_000
2000 days.   10 more men join, the total number of men= 50   The number of days the food will last = 2000/50= 
2000/50 = 40
40 days.   Answer: 40days
Answer: C
There are 8 girls and 8 boys. If they are to be seated in a row, what is the probability that no two girls sit together?
Select:
A) A)1/16!
B) B)6!5!/16!
C) C)6!6!/16!
D) D)2∗8!8!/16!
E) E)6!7!/12!

Solution: If girls are alternate, then only no 2 girls can be together.   So among 16 places, girls can be seated in 8 alternate places in 8! ways.   And boys can be seated in the remaining 8 places in 8! ways.   Therefore total number of ways = 8! * 8!   But there could be 2 such arrangements-->   1. When first place is filled by a girl   2. When first place is filled by a boy   Therefore total number of ways = 2*8! * 8!   Also total number of ways to fill 16 places = 16!   Hence probability =2∗8!8!/16!   Answer:2∗8!8!/16!
Answer: D
Rajesh can finish 1/6 of his home work in one hour. Seema can finish 3/7 of
her homework in 70 minutes and Ramya can finish 3/4 of her homework in
three and a half hours. If all of them start their home work at 12.00 PM and can
go to play as soon as they all finish their homework. When can they start to
play, if they take a break at 3.30 PM for 30 minutes?  Choose the correct choice from the following choices:	A) 4:30pm	B) 5:10pm	C) 6:30pm	D) 5:30pm	E) 3:30pm

Solution: rajesh can finish his work in 6 hr,   ramya can finish her work in 2.7 hr   seema can finish in 3.5 hr   so 6:30pm they can go to play   ANSWER:6:30pm
Answer: C
Out of 7 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?  Choose the most appropriate option.
A) A)3/7
B) B)5/4
C) C)5/7
D) D)5/6
E) E)5/3

Solution: P(at least one graduate) = 1 - P(no graduates)   = 1 - ⁶C₃/¹⁰C₃   = 1 - (6 * 5 * 4)/(7 * 6 * 5)   = 3/7   3/7nswer:3/7
Answer: A
A code is to be made by arranging 8 letters. four of the letters used will be the letter A, two of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?
Choose the correct choice from the following choices.
A) 42
B) 210
C) 420
D) 840
E) 10080

Solution: we have 8 letters out of which 2 are of one kind, 2 are of another kind..   so total ways = 8!/2!2!=420   ans 10080
Answer: E
A car moves at 102 km/hr. What is the speed of the car in meters per second ?
Choose the correct choice from the following choices:
A) 20 2/9m sec B) 28 1/3m sec C) 24 1/9m sec D) 26 2/3m sec E) 28 2/9m sec

Solution: Explanation:   Speed=(102∗5/18)m/sec   =85/3 m/sec   =28 1/3msec   Option 28 1/3m sec
Answer: B
x percent of y percent of z is decreased by y percent. What is the result?  Choose the most appropriate option.
A) (100xyz - xy^2z) / 1000000 B) (xz - y) / 100 C) (xz - y) / 10,000 D) (xyz - 2y) / 100 E) (xyz - 2y) / 10,000

Solution: We're told that X percent of Y percent of Z is DECREASED by Y percent. We're asked for the result of all of this math.   IF....   X = 10   Y = 50   Z = 100   First, 50% of 100 = 50   Next, 10% of 50 = 5   Finally, 5 decreased by 50% of itself is 2.5   So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.   Answer A. (100xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 = 2,500,000/1,000,000 = 2.5 This is a MATCH   Answer B. (xz - y) / 100 = (1,000 - 50)/100 = 950/100= 
950/100 = 19/2 = around 9.5
9.5 NOT a match   Answer C. (xz - y) / 10,000= 950/10,000 = .095 NOT a match   Answer D. (xyz - 2y) / 100 = (50,000 - 100)/100 = 49,900/100 = 499 NOT a match   Answer E. (xyz - 2y) / 10,000 = 49,900/10,000 = 4.99 NOT a match   (100xyz - xy^2z) / 1000000
Answer: A
A hall 36m long and 15m broad is to be paved with stones, each measuring 4dm by 5 dm. The number of stones required is: Answers.
A) 180 B) 2700 C) 18 D) 18000 E) 1.8

Solution: Area of the hall= 3600*1500   Area of each stone= (40*50)   Therefore, number of stones= (3600*1500/ 40*50)= 2700   ANSWER:2700
Answer: B
The market value of a certain machine decreased by 10 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later?
Choose the correct answer
A) $8,000
B) $5,600
C) $3,200
D) $6,400
E) $800

Solution: $6,400   Market value in 1982= $ 8000   Market value in 1983 = $ 8000- ($ 8000 x 10/100) = 8000-800= 
8000-800 = 7_200
$ 7200   Market value in 1984= Market value in 1983 - (10 % of $8000)= 7200-800= 
7200-800 = 6_400
$6400
Answer: D
On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1⁄3 of the total distance and again after she traveled 1⁄2 of the distance remaining between her first stop and her destination. She then drove the remaining 100 miles and arrived safely at her destination. What was the total distance, in miles, from Traci’s starting point to Seal Beach?	Choose the correct choice from the following answers.
A) 250	B) 300	C) 350	D) 400	E) 550

Solution: Let D = total distance   Traci traveled 1/3 = D/3   i.e. remaining distance = 2D/3   She traveled 1/2 th of 2D/3 = D/3   Thus:   D = (D/3) + (D/3) + 100   D = 300   ANSWER: 300
Answer: B
In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 21 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
Choose one:
A) 2/1
B) 4/1
C) 6/5
D) 3/4
E) 3/2

Solution: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.   Thus Milk=4x=36 liters and Water=x=9 liters.   New ratio = 36/(9+21) = 36/30 = 6/5.   Answer: 6/5.
Answer: C
In how many different number of ways a combination of 3 persons can be selected from 4 men and 2 women?  Choose the correct choice from the following options:
A) 200	B) 220	C) 240	D) 260	E) 280

Solution: 6C3 × 5C2   6C3   = 6!/(3! . 3!)   = (6 × 5 × 4)/(3 × 2)   = 5 × 4 = 20.   5C2   = 5!/(3! . 2!)   = 5 × 2 = 10   = 20 × 10 = 200.   200)
Answer: A
A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 34 per kg. His profit percent is:  Options:
A) No profit, no loss  B) 5%  C) 19%  D) 10%  E) None of these

Solution: Explanation :   C.P. of 56 kg rice = (26 * 20 + 30 * 36) Rs. = (520 + 1080) Rs. = 1600 Rs.   S.P. of 56 kg rice = (56 * 34) Rs. = 1904 Rs.   Profit % = (1904−1600/1600∗100)% = 19%   Answer : 19%
Answer: C
John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?  Choose the correct choice from the following options:
A) 3/5	B) 2/3	C) 7/10	D) 3/4	E) 4/5

Solution: X(1+10/100) + Y(1-15/100) = X+Y   this gives 2X = 3Y   or X/Y = 3/2   So, fraction invested in X = 3/5   3/5NSWER:3/5
Answer: A
The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
Choose the correct choice from the following answers.
A) 1/3 B) 3/4 C) 3/5 D) 3/7 E) 4/7

Solution: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D   1 2 3 1 =iXiX71=4;   1 3 Required probability 3/4   3/4
Answer: B
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is? Choose one:	A) 50	B) 267	C) 26	D) 87	E) 62

Solution: Let the actual distance traveled be x km. Then,   x/10 = (x + 20)/14   4x - 200 =>x = 50 km.   50nswer:50
Answer: A
The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher. Choose the correct choice from the following:
A) 22 Yrs	B) 25 Yrs	C) 26 Yrs	D) 32 Yrs	E) 34 Yrs

Solution: Sol. Total age of 39 persons = (39 x 15) years   = 585 years.   Average age of 40 persons= 15 yrs 3 months   = 61/4 years.   Total age of 40 persons = (_(61/4 )x 40) years= 610 years.   :. Age of the teacher = (610 - 585)= 
(610 - 585) = 25
25 yANSWER 25 Yrs
Answer: B
Three consecutive even numbers are such that thrice the first number exceeds double the third number by three. What is the third number?
Choose the correct choice from the following answers:	A) 7	B) 9	C) 11	D) 13	E) 15

Solution: Let the three numbers be x, x+2, and x+4.   3x = 2(x+4) + 3   x = 11 and then the third number is x+4 = 15.   The answer is 15.
Answer: E
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?	Select: A) 3 9/97 hrs B) 3 9/77 hrs C) 3 9/17 hrs D) 3 9/27 hrs E) 3 9/19 hrs

Solution: Net part filled in 1 hour = 1/5 + 1/6 - 1/12   = 17/60   The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.   Answer:3 9/17 hrs
Answer: C
In what time will a train 250 metres long cross an electric pole, if its speed be 162 km/hr?  Pick:
A) 4 sec  B) 5 sec  C) 5.55 sec  D) 6.55sec  E) 4.55 sec

Solution: Solution   Speed	= (162 x 5 /18) m/sec   = 45 m / sec   Time taken	= (250 /45) sec   = 5.55 sec.   Answer 5.55 sec
Answer: C
At an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1⁄3 of the men are single, what fraction of the men are married?  Select
A) 1/2
B) 1/3
C) 2/3
D) 3/5
E) 2/7

Solution: --------------------M------W--------Total   Marrried----------20-----20---------40   Not married-----10-----50---------60   Total-------------30-----70--------100   need married man/total man, so 20/30=2/3   2/3
Answer: C
A manâ€™s current age is (2/5) of the age of his father. After 10 years, he will be (1/2) of the age of his father. What is the age of father at now?	Choices:
A) 40	B) 45	C) 38	D) 50	E) 39

Solution: Let, fatherâ€™s current age is A years.   Then, Manâ€™s current age =[ (2/5)A ]years.   Therefore, [ (2/5)A + 10 ]= (1/2)(A + 10)   2(2A + 50) = 5(A + 10)   A = 50   50
Answer: D
A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Select.
A) 65 km B) 88 km C) 55 km D) 66 km E) 20 km

Solution: Let the distance between A and B be x km.   Total time = x/(9 + 1) + x/(9 - 1) = 4.5   => x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.   Answer: 20 km
Answer: E
When 52416 is divided by 312, the quotient is 168. what will be the quotient when 52.416 is divided by 0.12510168?  Choose the correct choice from the following answers.
A) 5 B) 6 C) 10 D) 3 E) 8

Solution: for the 1st no. there are 2 digits after decimal   for the 2nd no. there are 9 digits after decimal   total no. of decimals = 11   req. no. of digits=(n-1)=(11-1)= 
(11-1) = 10
10   ANSWER :10
Answer: C
If (a-b) is 6 more than (c+d) and (a+b) is 3 less than (c-d), then (a-c)	Pick one
A) 0.5
B) 1
C) 1.5
D) 2
E) 2.5

Solution: (a-b)-(c-d)=6 and (c-d)-(a+b)=3   (a-c)-(b+d)=6 and (c-a)-(b+d)=3   (b+d)= (a-c)-6 and (b+d)=3-(c-a)   2(a-c)=3   (a-c)=1.5   ANSWER 1.5 1.5
Answer: C
James took a 3-hour bike ride. In the second hour he traveled 30 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride?  Choose the correct choice from the following answers
A) 54.0	B) 54.9	C) 92.5	D) 57.0	E) 63.0

Solution: Let the distance travelled in the first hour be x. Thus, 1.2x = 30 , x = 25. Now, the distance travelled in the 3rd hour = 30+1/4âˆ—30= 37.5 The only option ending with a 0.5 in the decimal place is C.   ANSWER:92.5
Answer: C
If 3 people can do 3 times of a particular work in 3 days, then how many days would it take 6 people to do 6 times of that particular work?
Choose the correct answer:
A) 1	B) 2	C) 3	D) 6	E) 9

Solution: 3 people can do the work one time in one day.   1 person can do 1/3 of the work in one day.   6 people can do 6/3 of the work in one day.   6 people can do 6 times the work in 3 days.   The answer is 3.
Answer: C
Mary is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of white, and 1 morsel of waffle. The pattern repeats after she leaves the morsel of waffle. If Mary drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?	Select the correct option:
A) waffle − wheat − wheat
B) wheat − wheat − white
C) white − waffle − wheat
D) white − white − white
E) white − white − waffle

Solution: In a single round Mary drops 6 morsels.   Remainder (2000/6) = 2   Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated   waffle − wheat − wheatnswer: waffle − wheat − wheat
Answer: A
Average of five numbers is 30 . If one number is excluded the average becomes 26. The excluded number is  Choices:
A) 35 B) 45 C) 55 D) 46 E) 67

Solution: Explanation:   Number is (5*30) - (4*26) = 150-104= 
150-104 = 46
46   Answer: Option 46
Answer: D
Insert the missing number. 2, 7, 8, 17, 16, 27, 22
Pick one:
A) 42 B) 52 C) 46 D) 62 E) 37

Solution: Explanation :   There are two series here   2, 8, 16, 22 ... (Increase by 6)   7, 17, 27, 37 ... (Increase by 10)   Hence, next term is   27+10= 
  27+10 = 37
37   Answer : Option 37
Answer: E
Ron scored 344 marks out of 400 marks and his elder brother Ben scored 582 marks out of 600 marks. Who scored percentage is better?
Choose the correct choice from the following answers: A) 2333 B) 2778 C) 1000 D) 2776 E) 2881

Solution: An alloy contains 26 % of copper. What quantity of alloy is required to get 260 g of copper?   Solution:   Let the quantity of alloy required = m g   Then 26 % of m =260 g   ⇒ 26/100 × m = 260 g   ⇒ m = (260 × 100)/26 g   ⇒ m = 26000/26= 
26000/26 = 1_000
1000 g   Answer:1000
Answer: C
The seats in an Engineering college for Computer science, electronics and civil are in the ratio of 5 : 7 :
8. There is a proportion to increase these seats by 40%, 50% and 75% respectively. What will be the
ratio of increased seats ?  Choose the correct choice from the following answers
A) 2 : 3 : 4
B) 6 : 7 : 8
C) 6 : 8 : 9
D) none of these
E) Insufficient data

Solution: Expl : Originally, let the number of seats for Computer science, electronics and civil   are 5x : 7x : 8x respectively.   Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)   7x : 21x/2 : 14x = 14x : 21x : 28x = 2 : 3 : 4.   2 : 3 : 4nswer: 2 : 3 : 4
Answer: A
What is the perimeter of a rectangular field whose diagonal is 10m and length is 3m ?	Select
A) 12 m
B) 5 m
C) 10 m
D) 8 m
E) 6 m

Solution: Sol:   Breadth of the rectangular plot is=10^2-3^2=1m   Therefore,   Perimeter of the rectangular plot= 2(3+1)=8m   8 m) 8m
Answer: D
The average of a set of five distinct integers is 400. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers?  Choose the correct choice.
A) -4,494 B) -3,994 C) -3,494 D) -3,194 E) The answer cannot be determined from the information given

Solution: Sum of the set = 400*5= 
400*5 = 2_000
2000 Each number is less than 2000 and median of the set is the greatest possible value.   Therefore last 3 numbers can be 1999,1998 and 1997. Their sum=5994.   Therefore sum of two smallest numbers= 2000-5994= -3994   Answer=-3,994
Answer: B
A can complete a journey in 1 hours. He travels first half of the journey at the rate of 21km/hr and second half at the rate of 24km/hr. Find the total journey in km? Select the correct option.
A) 120km	B) 150km	C) 200km	D) 224km	E) 287km

Solution: Let the total distance be xkm   x/2/21 + x/2/24 = 10   x/21 + x/24 = 20   15x = 168*20   x = 224km   Answer is 224km
Answer: D
The average age of an adult class is 40years. 15new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class?	Pick one.
A) 8 B) 12 C) 15 D) 17 E) 18

Solution: Let original strength = y   Then , 40y + 15 x 32 = ( y + 15) x 36   â‡’ 40y + 480 = 36y + 540   â‡’ 4y = 60   âˆ´ y = 15   15
Answer: C
the cyclist going at a constant rate of 18 miles per hour is passed by a motor-cyclist traveling in the same direction along the same path at 48 miles per hour. the motor-cyclist stops to wait for the cyclist 15 minutes after passing cyclist, while the cyclist continues to travel at constant rate, how many minutes must the motor-cyclist wait until the cyclist catches up?
Choose the correct choice from the following choices:
A) 25
B) 30
C) 35
D) 40
E) 45

Solution: For the 15 minutes the motor-cyclist continues to overtake the cyclist, she is going at 30 miles per hour faster than the cyclist.   Once the motor-cyclist stops, the cyclist is going at 18 miles per hour while the motor-cyclist is at rest   So the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds. 30/18 * 15 or 25 minutes   25nswer is (25)
Answer: A
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Choose the correct choice from the following: A) 10 kmph B) 5 kmph C) 20 kmph D) 22 kmph E) 25 kmph

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20   ANSWER:20 kmph
Answer: C
A and B can do a piece of work in 12 days. With the help of C they finish the work in 6 days. C alone can do that piece of work in?
Choose the correct choice
A) 33 B) 878 C) 30 D) 88 E) 12

Solution: C = 1/6 â€“ 1/12 = 1/12 => 12 days   Answer: 12
Answer: E
If a – 8 = b, then determine the value of | a - b| - | b - a|.	Choose the correct option:
A) 16	B) 0	C) 4	D) 2	E) 1

Solution: Sol.(b) | a - b| = |8| = 8   => | b - a| = |-8| = 8   => | a - b| - | b - a| = 8 - 8= 
8 - 8 = 0
0.   Answer 0
Answer: B
Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance. Options.
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: Let the total distance be x km . Then,   =(2 x/3)/4 + (1x/3)/5   = 7/5 = x/6 + x/15 = 7/5   = 7x = 42   = x = 6   Answer is 6.
Answer: E
A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 7 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?  Choose the correct answer: A) 62 B) 63 C) 64 D) 65 E) 72

Solution: I will make an equation in x and then make educated guesses. Here's how:   Assuming x motorcycles were sold every month initially.   (568000/x + 1000)(x-7) = 594000   (568/x + 1)(x-7) = 594   Now 568 = 8*71   Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.   We get  9*66= 
 9*66 = 594
594 (matches)   So he will sell  71 - 7= 
 71 - 7 = 64
64 bikes this month   Answer (64)
Answer: C
What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3? Choose the correct choice from the following answers
A) 30  B) 42  C) 45  D) 49  E) 51

Solution: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).   In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.   i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0   or −27+36+21+12=k−27+36+21+12=k   or k=k= 42   42
Answer: B
Two pipes can fill a tank in 8 minutes and 5 minutes. An outlet pipe can empty the tank in 12 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
Choose the correct option
A) 30 minutes  B) 17 minutes  C) 15 minutes  D) 10 minutes  E) 14 minutes

Solution: Part of the filled by all the three pipes in one minute   = 1/8 + 1/5 - 1/12 = (15 + 24 - 10)/120 = 29/120   So, the tank becomes full in 14 minutes.   Answer: 14 minutes
Answer: E
What is the positive difference between the sum of the squares of the first 3 positive integers and the sum of the prime numbers between the first square and fourth square?
Pick
A) 11
B) 12
C) 13
D) 24
E) 27

Solution: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.   the sum of the squares of the first 4 positive integers = 1^2 + 2^2 + 3^2 = 14   the sum of the prime numbers between the first square(=1) and fourth square(=16) = 2+3+5+7+11+13= 
2+3+5+7+11+13 = 41
41.   So the difference between 41 and 14 is 27.   So the answer is (27).
Answer: E
Three rugs have a combined area of 200 square meters. By overlapping the rugs to cover floor area of 138 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?
Choose the correct choice from the following options:
A) 18 square meters  B) 19 square meters  C) 24 square meters  D) 28 square meters  E) 30 square meters

Solution: Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs}   138 = 200 - 24 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 19.   Answer: 19 square meters.
Answer: B
Two employees X and Y are paid a total of Rs. 590 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 options
A) s.268
B) s.288
C) s.298
D) s.300
E) s.388

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 590   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 590   ⇒ y[12/10 + 1] = 590   ⇒ 22y/10 = 590   ⇒ 22y = 5900   ⇒ y = 5900/22 = 500/2 = Rs.268   s.268)
Answer: A