MU-NLPC/Calc-aqua_rat huggingface dataset:
Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 40 minutes earlier than usual. How much time did the man spend walking?
Choose the correct choice from the following:	A) 45 minutes	B) 50 minutes	C) 40 minutes	D) 55 minutes	E) 35 minutes

Solution: As they arrived 40 minutes earlier than usual, they saved 40 minutes on round trip from home to station (home-station-home) --> 20 minutes in each direction (home-station) --> wife meets husband 20 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent waking the rest of the time before their meeting, which is hour-20 minutes=40minutes.   Answer: 40 minutes
Answer: C
Difficulty:
There are five sales agents in a certain real estate office. One month Andy sold five as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold five times as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month? Choose the correct choice from the following answers:
A) Andy	B) Bob	C) Cary	D) Dora	E) Ellen

Solution: a= 5e   b =3 +e   c = 5b = 15+ 5e (highest of all)   d = b + e = 3+ e +e = 3 + 2e   Ans. Cary
Answer: C
A man can row his boat with the stream at 18 km/h and against the stream in 8 km/h. The man's rate is?
Choose the correct choice from the following choices
A) 5 kmph
B) 2 kmph
C) 7 kmph
D) 8 kmph
E) 3 kmph

Solution: DS = 18   US = 8   S = ?   S = (18 - 8)/2= 
(18 - 8)/2 = 5
5 kmph   5 kmphnswer:5 kmph
Answer: A
In how many ways can be 4 boys and 4 girls sit around circular table so that no two boys sit next to each other?
Choose the correct choice from the following:
A) (5!)^2  B) (6!)^2  C) 3!4!  D) 11!  E) (5!)^2*6!

Solution: first fix one boy and place other 3 in alt seats so total ways is 3!   now place each girl between a pair of boys... total ways of seating arrangement of girls 4!   total is 4!*3!   ANS 3!4!
Answer: C
In a bag, there are three 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?	Pick.
A) 60  B) 61  C) 64  D) 84  E) 960

Solution: As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited:   1) The minimum number on any given die is 1   2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each.   With 4 dice, we could end up with any SUM between:   4 (if we rolled 1s on all 4 dice)   to   64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice).   Thus, there are only 61 possible sums.   61
Answer: B
If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 40 minutes?	Choose the correct choice from the following
A) 80	B) 100	C) 160	D) 240	E) 300

Solution: Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 40 minutes the population increases by 40 x 4 = 160 people.   Answer. 160.
Answer: C
In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest? Choose one: A) 5 years B) 6 years C) 7 years D) 9 years E) 15 years

Solution: (4000*T*5)/100 = (5000*5*4)/100   T = 5 years   5 yearsNSWER:5 years
Answer: A
Replace X with the appropriate number in
1 , 2 , 3 , 4 , 7 , 10 , 11 , X  Choose the most appropriate option
A) 12	B) 13	C) 15	D) 16	E) 18

Solution: 12   list of consecutive numbers that does not contain a 'i' in the spelling
Answer: A
In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 182 votes. Find the total number of valid votes?	Choose the correct choice from the following answers
A) 455 B) 570 C) 480 D) 520 E) 550

Solution: Let the total number of valid votes be x.   70% of x = 70/100 * x = 7x/10   Number of votes secured by the other candidate = x - 7x/100 = 3x/10   Given, 7x/10 - 3x/10 = 182 => 4x/10 = 182   => 4x = 1820 => x = 455.   455NSWER:455
Answer: A
Rahim bought 50 books for Rs.1000 from one shop and 40 books for Rs.800 from another. What is the average price he paid per book ?	Choose the correct choice from the following choices
A) 28  B) 20  C) 27  D) 29  E) 21

Solution: Average price per book   = (1000+ 800) / (50 + 40)   = 1800 / 90   = Rs.20   Answer:20
Answer: B
By selling a house for Rs.55000, it was found that 1/10 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?  Choose the correct choice
A) 38020 B) 38000 C) 38028 D) 38019 E) 47500

Solution: CP + CP/10 = 55000   CP = 50000   SP = 50000*(95/100)= 
50000*(95/100) = 47_500
47500   Answer: 47500
Answer: E
Ratio of the ages of Mahesh and Nilesh is 5 : x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x?  Choices
A) 13.9	B) 16.5	C) 14.7	D) 12.5	E) 14.5

Solution: Let the present ages of Mahesh, Nilesh and Ramesh be m, n and r respectively.   m/n = 5/x ------ (1)   m = r - 18 ------ (2)   r + 9 = 47 ------ (3)   m - n = r ----- (4)   (3) => r = 47 - 9= 
47 - 9 = 38
38 years   (2)=> m = 38 -18= 
38 -18 = 20
20 years   (1)=> 20/n = 5/x => n = 4x   (4) => 4x - 20 = 38   => 4x = 58 => x = 14.5   Answer:14.5
Answer: E
If [x] is the greatest integer less than or equal to x, what is the value of [-11.6]+[13.4]+[12.7]?  Choose the correct option.
A) 3 B) 10 C) 13 D) 16 E) 17

Solution: You are asked what the closest lesser integer value to [x] is.   [-11.6] = -12.0   [13.4] = 13.0   [12.7] = 12.0   Therefore , answer is: -12.0 + 13.0 + 12.0= 
-12.0 + 13.0 + 12.0 = 13
13.0   Option A.
Answer: C
A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is? Choose the correct choice from the following answers:
A) 28	B) 21	C) 29	D) 27	E) 13

Solution: 20 15 5   25 20 8   500 + 300 + 40= 
500 + 300 + 40 = 840
840/40= 
840/40 = 21
21   Answer:21
Answer: B
A question paper has 2 parts, A & B, each containing 5 questions. If a student has to choose 3 from part A & 4 from part B, in how many ways can he choose the questions?	Options
A) 50	B) 100	C) 152	D) 150	E) 55

Solution: There 3 questions in part A out of which 4 question can be chosen as = 5C3.   Similarly, 5 questions can be chosen from 10 questions of Part B as = 5C4.   Hence, total number of ways,   =5C3*5C4   =[5!/(2!3!)]*[5!/(4!*1)]   = {10}*{5*4!/(4!)}   = 10*5= 
10*5 = 50
50.   50
Answer: A
The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 14.56 years. What was the average age of five new men?
Answers
A) 15.5	B) 15.4	C) 15.25	D) 10.4	E) 15.6

Solution: Total age of 20 men = 15.6 x 20 = 312   Now, total age of 25 men = 364.   Total age of five men added later = 364 - 312= 
364 - 312 = 52
52.   Hence, the total average of five men= 52/5= 
52/5 = 52/5 = around 10.4
10.4   ANSWER:10.4
Answer: D
In What proportion must flour at $0.8 per pound be mixed with flour at $0.9 per pound so that the mixture costs $0.865 per pound? Select:
A) 1:3
B) 1:2
C) 1:1
D) 2:1
E) 3:1

Solution: Using weighted average method:   Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.   Thus 0.8*x + 0.9*(1-x) = 0.865   0.9 – 0.1x = 0.865   x = 0.35   Thus ratio of both flours is 1:2   1:2
Answer: B
The average number of printing error per page in a book of 512 pages is 4. If the total number of printing error in the first 302 pages is 1,208, the average number of printing errors per page in the remaining pages is	Options:
A) 0 B) 4 C) 840 D) 90 E) 80

Solution: Remaining pages = 512 – 302 = 210   Let average printing error in remaining pages = x   Then, 1208+210×x /512=4   ⇒ 210x = 840 ⇒ x = 4   Answer 4
Answer: B
X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 60 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is :  Choose the correct choice from the following choices:	A) 45	B) 43	C) 40	D) 38	E) 29

Solution: Solution: 45verage speed = 2XY / X+Y   = 2*60*36 / 60+36   = 45   45nswer : 45
Answer: A
If c and d are unique prime integers, which of the following must be odd?	Pick one
A) a−b B) a−2b C) 2c−2d D) 2c/2d E) c-d

Solution: The answer is C. Let's assume that a is an even prime integer and b is an odd prime integer, their subtraction results in an odd integer and an odd integer multiplied by an even integer yields an even integer.   Answer 2c−2d
Answer: C
When the positive integer C is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer Dis divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of C-D? Pick one: A) 12 B) 24 C) 35 D) 16 E) 30

Solution: If I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:   n = 5c + 3   n = 7d + 4   I will need to check for the smallest such number.   I put d= 1. n = 11. Is it of the form 5c + 3? No.   Put d= 2. n = 18. Is it of the form 5c + 3? Yes.   When 18 is divided by 5, it gives a remainder of 3. When it is divided by 7, it gives a remainder if 4.   Next such number will be 35 + 18 because 35 will be divisible by 5 as well as 7 and whatever is the remainder from 18, will still be the remainder   Next will be 35*2 + 18   and so on...   Difference between such numbers will be a multiple of 35 so   your answer is 35
Answer: C
What is the difference between the compound interests on $5000 for 1 years at 4% per annum compounded yearly and half-yearly? Choose the correct option:
A) $2.04	B) $3.06	C) $4.80	D) $8.30	E) $9.30

Solution: A.   $. 2.04   B.   $. 3.06   C.   $. 4.80   D.   $. 8.30   Answer: Option A   Explanation:   C.I. when interest   compounded yearly = $ 5000 x 1 +	4 x 1 + x 4   100 100   = $. 5000 x	26	x	51   25 50   = $. 5304.   C.I. when interest is   compounded half-yearly	= $ 5000 x 1 +	2 3   100   = $ 5000 x	51	x	51	x	51   50 50 50   = $5306.04   Difference = $. (5306.04 - 5304) =$. 2.04   $2.04NSWER : $2.04 $2.04
Answer: A
Find the invalid no.from the following series 3, 7, 15, 27, 63, 127, 255  Choose the most appropriate option
A) 18 B) 19 C) 27 D) 29 E) 31

Solution: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong.   27
Answer: C
A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 147 km downstream.
Choose the most appropriate option:
A) 4 hours	B) 5 hours	C) 6 hours	D) 7 hours	E) 8 hours

Solution: Explanation:   It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.   Lets see the question now.   Speed downstream = (16 + 5)= 
(16 + 5) = 21
21 kmph   Time= distance/speed = 147/21= 
147/21 = 7
7 hours   Option 7 hours
Answer: D
Find the number of ways of arranging the host and 5 guests at a circular table so that the boy always sits in a particular seat? Choose the correct choice from the following choices:  A) 5!  B) 8!  C) 11!  D) 12!  E) 14!

Solution: Ans.(A)   Sol. Total number of persons = 6 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 5 places => 5! Ways ... The number of required arrangements = 5! x 1= 5! = 5! ways
Answer: A
A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:  Pick:
A) 3  B) 5  C) 9  D) 11  E) None of these

Solution: Let the ten's digit be x and unit's digit be y.   Then, number = 10x + y.   Number obtained by interchanging the digits = 10y + x.   (10x + y) + (10y + x) = 11(x + y), which is divisible by 11.   ANSWER : 11
Answer: D
The ratio by weight, measured in pounds, of books to clothes to electronics in a suitcase initially stands at 7:5:3. Someone removes 5 pounds of clothing from the suitcase, thereby doubling the ratio of books to clothes. How many pounds do the electronics in the suitcase weigh? Choose one:
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: The weights of the items in the suitcase are 7k, 5k, and 3k.   If removing 5 pounds of clothes doubles the ratio of books to clothes, then 5 pounds represents half the weight of the clothes.   2.5k = 5 pounds and then k = 2 pounds.   The electronics weigh 3(2) = 6 pounds.   The answer is 6.
Answer: D
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?  Choose the most appropriate option:  A) 22  B) 88  C) 48  D) 99  E) 12

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.9= 
1.10 + 0.9 = 2
2 km= 2000 m.   Required time = 2000 * 3/125= 
2000 * 3/125 = 48
48 sec.   Answer: 48
Answer: C
One half of a two digit number exceeds its one third by 5. What is the sum of the digits of the number? Choose the correct choice from the following answers:  A) A)3  B) B)5  C) C)7  D) D)9  E) E)11

Solution: x/2 – x/3 = 5 => x =30   3 + 0= 
3 + 0 = 3
3   3NSWER:3
Answer: A
If the price of sugar rises from Rs. 10 per kg to Rs. 13 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by  Choose the correct choice from the following answers
A) 15%
B) 20%
C) 23%
D) 30%
E) none

Solution: Sol.   Let the original consumption = 100 kg and new consumption = x kg.   So, 100 x 10 = x × 13 = x = 77 kg.   ∴ Reduction in consumption = 23%.   Answer 23%
Answer: C
If x > y^5 > z^6, which of the following statements could be true? I.x=y II. x>y III.x>y>z  Choose the correct answer:	A) I only	B) II only	C) II,III only	D) III only	E) I,III only

Solution: Answer : II,III only
Answer: C
Ram, who is half as efficient as Krish, will take 30 days to complete a task if he worked alone. If Ram and Krish worked together, how long will they take to complete the task? Pick.
A) 16 days B) 10 days C) 8 days D) 6 days E) 18 days

Solution: Number of days taken by Ram to complete task = 30   Since Ram is half as efficient as Krish , Amount of work done by Krish in 1 day = Amount of work done by Ram in 2 days   If total work done by Ram in 30 days is 30w   Amount of work done by Ram in 1 day = w   Amount of work done by Krish in 1 day = 2w   Total amount of work done by Krish and Ram in a day = 3w   Total amount of time needed by Krish and Ram to complete task = 30w/3w = 10 days   Answer 10 days30 /3= 
30 /3 = 10
10 days   Answer 10 days
Answer: B
trisha bakes 6 cookies for 6 friends. 4 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies?
Options:
A) 6  B) 0  C) 4  D) 3  E) 1

Solution: trisha made 6*6= 
6*6 = 36
36 cookies. 4 friends eat 3 cookies, leaving 24 remaining for 2 friends.   24 is divisible by 2. The 2 friends ate a cumulative number of cookies divisible by 2, because the number is the same.   24-24= 
24-24 = 0
0;   0 is the correct answer
Answer: B
A can do a piece of work in 12 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in	Choose the most appropriate option:  A) 5days  B) 6days  C) 7.5days  D) 8.5days  E) 9days

Solution: Explanation:   6days's 5 days work =   1/10∗5=1/2   Remaining work =1−1/2=1/2   A can finish work =12∗1/2= 6 days   Option 6days
Answer: B
From the given equation find the value of x: x² − 3x + 2	Choose the correct choice from the following.
A) 0 B) 2 C) 4 D) 5 E) 6

Solution: (x − 1)(x − 2)   x = 1 or 2.   2
Answer: B
Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 4 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? Select the correct option.
A) 1 ≤ n ≤23  B) 7 ≤ n ≤17  C) 5 ≤ n ≤19  D) 6 ≤ n ≤18  E) 9 ≤ n ≤15

Solution: ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-4+3= 
12+6-4+3 = 17
17 for the maximum, and   12-6+4-3= 
  12-6+4-3 = 7
7 for the minimum, so 7 ≤ n ≤17 is the answer
Answer: B
The average of five numbers is 18. The average of first two numbers is 14 and the average of last two numbers is 19. What is the middle number?
Answers:	A) 24	B) 27	C) 29	D) 32	E) 34

Solution: The total of seven numbers = 5X18 = 90   The total of first 2 and last 2 numbers is = 2 X 14+2 X 19 = 66   So, the middle number is  (90 - 66 )= 
 (90 - 66 ) = 24
24   24
Answer: A
About the number of pairs which have 16 as their HCF and 125 as their LCM, the conclusion can be Choose the correct choice from the following
A) only one such pair exists	B) no paid is exists	C) many such pairs exist	D) pair exists	E) None of these

Solution: Explanation:   HCF is always a factor of LCM. ie., HCF always divides LCM perfectly.   Correct Option:no paid is exists
Answer: B
Ram, who is half as efficient as Krish, will take 24 days to complete a task if he worked alone. If Ram and Krish worked together, how long will they take to complete the task? Choose the most appropriate option
A) 16 days
B) 12 days
C) 8 days
D) 6 days
E) 18 days

Solution: Answer   Ram takes 24 days to complete the task, if he works alone.   Krish is twice as efficient as Ram is. So, working alone, Krish will take half the time to complete the task.i.e., 12 days.   Ram will complete 1/24th of the task in a day.   Krish will complete 1/12th of the task in a day.   When they work together, they will complete 1/24+1/12=1/8th of the task in a day.   Therefore, when they work together they will complete the task in 8 days.   8 dayshoice 8 days
Answer: C
Find the fraction which has the same ratio to 1/13 that 5/34 has to 7/48. Answers.
A) 110/1547  B) 120/1547  C) 140/1547  D) 160/1547  E) 220/1547

Solution: P : 1/13 = 5/34 : 7/48   As the product of the means is equal to the product of the extremes.   P*7/48 = 1/13 * 5/34   P*7/48 = 5/442   P = 240/3094 => P = 120/1547   ANSWER:120/1547
Answer: B
The measurements obtained for the interior dimensions of a rectangular box are 100 cm by 100 cm by 150cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements? Choose the correct choice:
A) 50,000	B) 40,000	C) 45,000	D) 50,000	E) 60,000

Solution: The options are well spread so we can approximate.   Changing the length by 1 cm results in change of the volume by 1*100*150 = 15,000 cubic centimeters;   Changing the width by 1 cm results in change of the volume by 100*1*150 = 15,000 cubic centimeters;   Changing the height by 1 cm results in change of the volume by 100*100*1 = 10,000 cubic centimeters.   So, approximate maximum possible difference is 15,000 + 15,000 + 10,000 = 40,000 cubic centimeters.   Answer: 40,000.
Answer: B
At Company X senior sales representatives visit the home office once every 30 days, and junior sales representatives visit the home office once every 20 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period? Answers.
A) 10%  B) 25%  C) 33%  D) 50%  E) 67%

Solution: When you say Senior is 1/30, what do you mean by it? It is the rate of visit. The time of visit is 30 days. The rate is 1/30. Similarly, the rate of visit for junior is 1/20.   The 2 yrs has no significance in this case. The rate stays the same for every time interval.   {1/20} - {1/30}/ {1/30} * 100 = 50%   ANSWER:50%
Answer: D
In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?	Choose the correct option
A) 12  B) 14  C) 36  D) 38  E) 40

Solution: There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.   Let us mark these positions as under:   (1) (2) (3) (4) (5) (6)   Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.   Number of ways of arranging the vowels = 3P3 = 3! = 6.   Also, the 3 consonants can be arranged at the remaining 3 positions.   Number of ways of these arrangements = 3P3 = 3! = 6.   Total number of ways = (6 x 6) = 36.   ANSWER 36
Answer: C
A rectangular grass field is 65 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
Choose the correct choice from the following options.
A) 1350
B) 1971
C) 9676
D) 1679
E) 1250

Solution: Area = (l + b +2d) 2d   = (65 + 55 +2.5 * 2) 2*2.5 => 625   625 * 2 = Rs.1250   Answer:1250
Answer: E
A mobile battery in 1 hour charges to 20 percent.How much time (in minute) will it require more to charge to 60 percent.  Answers:
A) 145
B) 150
C) 175
D) 180
E) 130

Solution: 1 hr =20 percent.Thus 15 min=5 percent .Now to charge 60 percent 180 min.Answer:180
Answer: D
How long does a train 250 meters long running at the rate of 72km/hr take to cross a bridge 150 meters in length?  Choose the correct choice from the following answers.
A) 10sec B) 20sec C) 25sec D) 30sec E) 35sec

Solution: Distance = length of train + length of bridge = 250+150= 
250+150 = 400
400   speed= 72km/hr = 72*5/18= 
72*5/18 = 20
20m/s   Required time= 400/20= 
400/20 = 20
20 seconds   Answer is 20sec
Answer: B
The average length of 6 strings is 80 cm. If the average length of one third of the strings is 70 cm, what is the average of the other strings?
Choose the most appropriate option:
A) 75.
B) 85.
C) 90.
D) 94.
E) 100.

Solution: Edit:   Given ( X1 + X2 ... + X6 ) / 6 = 80   ( X1 + X2 ... + X6 ) = 480 --> Eq 1.   Now given avg length of one third strings is 70. That means out  6 / 3= 
 6 / 3 = 2
2 strings.   let the avg length of two strings be ( X1 + X2 ) / 2= 70 .   ( X1 + X2 ) = 140. --> eq 2.   Now we are asked to find the average of the remaining i.e. ( X3 + X4 + X5 + X6 )   Substitute eq 2 in eq 1 then we get   140 + X3 + X4 + X5 + X6 = 480   => X3 + X4 + X5 + X6 = 340   Now divide 340 by 4 we get 85.   => ( X3 + X4 + X5 + X6) / 4 = 85 = avg length of remaining strings.   IMO correct option is 85..
Answer: B
A sum of money is distributed among w,x,y,z in the proportion of 1:6:2:4. If X gets $1500 more than Y, what is the W's share?	Choose the most appropriate option:
A) $1500 B) $150 C) $375 D) $200 E) $450

Solution: Let the shares of w,x,y,z are 1a,6a,2a,4a   6a-2a = 1500   4a = $1500, A=375   W's share = 1a = $375   Answer is $375
Answer: C