MU-NLPC/Calc-aqua_rat huggingface dataset:
In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes. Choose the correct answer:
A) 11
B) 12
C) 14
D) 16
E) 18

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 24   => 2x = 24 => x = 12   12
Answer: B
A shoe store sells Adidas shoes for $60 each and Puma shoes for $50 each. On every Adidas shoe the restaurant makes a profit of $10 while on every Puma shoe it makes a profit of $8. If on a given day the storest's sales amounted to $1600, which of the following cannot be the profit made on that day?
Choose the correct choice from the following answers.
A) 262
B) 260
C) 258
D) 256
E) 254

Solution: $254 is the only option that does not fit into a combination of Adidas and Puma sales profits, given the total sales of the day. Answer: 254
Answer: E
The price of 357 mangoes is Rs. 1517.25. What will be the approximate price of 49 dozens of such mangoes?	Choose the correct answer
A) Rs. 3000	B) Rs.2500	C) Rs 2700	D) Rs 2900	E) None of these

Solution: Explanation :   More mangoes, more cost (Direct)357 : 49 * 12 :: 1517.25 : xor 375 * x= 49 * 12 * 1517.25.49 * 12 * 15l7.25 / 357 = 2499Approximate cost = Rs. 2500.   Answer : Rs.2500
Answer: B
Suraj has a certain average of runs for 16 innings. In the 17th innings he scores 92 runs thereby increasing his average by 4 runs. What is his average after the 17th innings?	Choose one:
A) 48  B) 64  C) 28  D) 72  E) 27

Solution: To improve his average by 4 runs per innings he has to contribute 16 x 4 = 64 runs for the previous 16 innings.   Thus, the average after the 17th innings   = 92 - 64= 
92 - 64 = 28
28.   ANSWER:28
Answer: C
The length of a fabric needed for a dress is cut into two pieces. If the total length of the fabric is 200 inches and the shorter side is 10 inches less than half the length of the other fabric, what is the length of the shorter fabric?  Choose one:
A) 60  B) 140  C) 400  D) 200  E) 80

Solution: length one as L1, and length two as L2.   L1=(L2/2)-10 as eq.a   L1+L2=200 as eq.b   Substitute equation a into equation b, (L1/2)-10 +L1=200   Transpose like terms, (L1/2) + L1= 200 + 10   Get rid of fraction, L1+ L1*2= 400+20   reduces to 3*L1= 40, L1 results to 140.   Shorter fabric is (140/2)-10= 
(140/2)-10 = 60
60   60nswer is 60.
Answer: A
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
Choose the correct option:
A) 10 years
B) 12 years
C) 14 years
D) 16 years
E) 18 years

Solution: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.   (2x + 2) + 2x + x = 27   5x = 25   x = 5.   Hence, B's age = 2x = 10 years.   10 years)
Answer: A
Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 6. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased? Answers.
A) 3, 8, 24
B) 7, 9, 17
C) 6, 9, 12
D) 5, 15, 18
E) 9, 10, 13

Solution: I didnt get your point on eliminating A.   The number of stamps only one purchased was divisible by 6.Could that not be Cecilia with 9 stamps.   I choose this and marked 3, 8, 24.
Answer: A
A hiker walked for 3 days. She walked 21 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
Choose the correct choice from the following answers.
A) 73  B) 44  C) 58  D) 60  E) 62

Solution: She walked 21 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 21/3= 
21/3 = 7
7 Hours   Second day time of walk= 7-1= 
7-1 = 6
6 hours and Speed= 3+1= 
3+1 = 4
4 miles per hour i.e. Distance walked on second day= 6*4= 
6*4 = 24
24 miles   Third day time of walk= 7 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 7*4= 
7*4 = 28
28 miles   Total Distance travelled on three days= 21+24+28= 
21+24+28 = 73
73   73nswer: Option 73
Answer: A
The old lady who lived in a shoe was having some real trouble buying Christmas presentsfor her enormous family. Although she bought the least expensive stocking stuffers she couldfind, the bill was high. Of course, both a 15 percent sales tax and a 5 percent luxury tax wereadded to the original price. She paid a total of Rs.100. What was the cost of the stuffers before taxes? Choose the correct choice from the following choices:	A) 82.333rupees	B) 83.333rupees	C) 84.333rupees	D) 85.333rupees	E) 86.333rupees

Solution: let the cost before taxes=x   x+15x/100+5x/100=100   120x/100=100   x=83.333rupees   ANSWER:83.333rupees
Answer: B
The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 9 years hence?	Choose the correct choice:
A) 22	B) 77	C) 78	D) 98	E) 71

Solution: A + B = 60, A = 2B   2B + B = 60 => B = 20 then A = 40.   9 years, their ages will be 49 and 29.   Sum of their ages = 49 + 29= 
49 + 29 = 78
78.   Answer: 78
Answer: C
x and y are positive integers of h. If 1/x + 1/y < 2, which of the following must be true?
Select:  A) x + y > 4  B) xy>1  C) x/y + y/x < 1  D) (x - y)^2 > 0  E) None of the above

Solution: Answer is B:   1/X + 1/Y < 2   The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.   So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.   Another way of putting it is:   X*Y>1.xy>1
Answer: B
Find the odd man out. 24,36,52,72,96	Pick one
A) 72	B) 52	C) 36	D) 24	E) 34

Solution: Explanation :   All except 52 are multiples of 6. Answer : Option 52
Answer: B
20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 08:10 in the morning?
Options:
A) 27 B) 36. C) 42. D) 46. E) 50.

Solution: @ 6:30 - 2   @ 7 - 4+7 =11   @ 7:30 - 2   @ 8 - 12   totals to 27=27
Answer: A
Ben left a job paying $75,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change?
Choose the correct choice from the following:
A) 40
B) 200
C) 266
D) 267
E) 600

Solution: In order not to lose money because of the change Ben's total commission must beat least$75,000-$45,000=$30,000, so total sales must beat least$30,000/0.15=$200,000. Which means that he must makeat least$200,000/750=800/3=266.6 sales, so 267 sales.   Answer: 267.
Answer: D
When the integer p is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6 ?
I. 2p
II. 6p
III. 4p + 6 Choose the most appropriate option.
A) I only B) II only C) III only D) I and II only E) I, II, and III

Solution: is it E.   p = 12*a + 3   2p = 12*2*a + 6   6p = 12*6*a + 18 ( 18 = 12+6)   4p + 6 = 12*4*a + 18 (18 = 12 + 6)
Answer: E
A merchant sells an item at a 10% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?
Options:	A) 30%	B) 40%	C) 50%	D) 60%	E) 75%

Solution: original SP = X   Cost =C   current selling price = .9x ( 10% discount)   .9x = 1.2C (20% profit)   x= 1.2/.9 *C   x= 4/3 C   Original selling price is 1.3C which is 30% profit   30%nswer 30%
Answer: A
There are 13 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have?
Choose the correct choice from the following answers:
A) 17/52
B) 14/39
C) 12/31
D) 9/23
E) 7/17

Solution: P(first stamp is different) = 8/13   P(second stamp is different) = 7/12   P(both stamps are different) = 8/13*7/12 = 14/39   The answer is 14/39.
Answer: B
If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area ?  Choose the most appropriate option.
A) 108 sq.cm B) 112 sq.cm C) 116 sq.cm D) 120 sq.cm E) NONE OF THESE

Solution: Explanation:   The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.   Area of the triangle =1/2 x base x height => 1/2 x 24 x 10 = 120 sq.cm   ANSWER IS 120 sq.cm
Answer: D
A dozen eggs and 10 pounds of apples are currently at the same price. If the price of a dozen eggs rises by 10 percent and the price of apples rises by 2 %. How much more will it cost to buy a dozen eggs and 10 pounds of apples. Pick one
A) 2% B) 6% C) 10% D) 12% E) 12.2%

Solution: Say currently both a dozen eggs and 10 pounds of apples cost $50 (they are at the same price). So, to buy a dozen eggs and 10 pounds of apples we need $100.   After the increase, the price of a dozen eggs will be $55 and the price of 10 pounds of apples will be $51. So after the increase, to buy a dozen eggs and 10 pounds of apples we'll need $106.   Increase = 6%.   Answer: 6%
Answer: B
A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 50,000 and at the same time n is a perfect square and a perfect cube?  Pick:
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: If n is a perfect square and a perfect cube, then n = a^6 for some integer a.   The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625, 6^=46,656.   The answer is 6.
Answer: D
If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is: Choose the correct choice from the following choices.
A) 53.33 B) 54.68 C) 55 D) 56 E) None of these

Solution: Explanation:   Required average = (55 × 50 + 60 × 55 + 45 × 60/55 + 60 + 45)   = (2750 + 3300 + 2700/160)   = 8750/160   = 54.68   Answer: 54.68
Answer: B
A sock drawer contains two socks, each one a different solid color. The colors of the socks are Indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made?	Choose the correct answer.
A) 24  B) 240  C) 1,024  D) 2,520  E) 2

Solution: I see no condition for arrangement.   So 2! ways - IMO option 2 is correct answer..
Answer: E
A car was initially traveling at an average speed of 36 miles per hour. During each of ten successive 5-minute intervals, the car decreased its average speed by 2 miles per hour. How many miles did the car travel in the fourth 5-minute interval?	Choose the correct option:
A) 1.32	B) 5.32	C) 4.56	D) 2.33	E) 1.44

Solution: The question does not specifically mentioned whether 36miles/h is the speed in first interval or before that... So I got confused.   If former is the case, then average speed of the car in 4th interval will be 28. This gives 28 * (5/60) = m = 2.33 miles   correct option is 2.33
Answer: D
The average of 7 consecutive numbers is 20. The largest of these numbers is Choices
A) 20
B) 22
C) 23
D) 24
E) 25

Solution: Let the first number be x, Then the last number is ( x+6)   Average = (x+(x+1)+(x+2)+(x+3)+(x+3)+(x+4)+(x+5)+(x+6))/7 = 20   7x + 21 = 20*7= 
20*7 = 140
140, 7x=119, x = 17   The largest number =x+6 =17+6= 
17+6 = 23
23   ANSWER:23
Answer: C
A combustion reaction forms carbon dioxide. A carbon dioxide molecule contains one carbon and two oxygen atoms. If, over a period of 15 minutes, a combustion reaction creates 15,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute?	Select:
A) 1,000
B) 500
C) 250
D) 50
E) 0

Solution: Solution:   15,000 carbon dioxide molecules are created over a period of 15 minutes. Therefore 15,000/15 = 1,000 carbon dioxide molecules are created on average per minute   Each carbon dioxide molecule contains one carbon atom and two oxygen atoms. So 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms. The difference is 2,000 – 1,000 = 1,000.   The correct answer is 1,000.
Answer: A
Two dice are tossed. The probability that the total score is a prime number is:
Choose the correct answer:
A) 1/6	B) 5/12	C) 1/2	D) 7/9	E) 9/4

Solution: Clearly, n(S) = (6 x 6) = 36.   Let E = Event that the sum is a prime number.   Then E	= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),   (5, 2), (5, 6), (6, 1), (6, 5) }   n(E) = 15.   P(9/4) =	n(9/4)/n(S)   =	15/36	=	5/12
Answer: E
Twenty four men can do a work in 14 days. How many men are required to complete the work in 10 days? Select: A) 33.6 B) 10.12 C) 50 D) 14.2 E) 60

Solution: A   33.6   We have M1 D1 = M2 D2   So, 24 * 14 = M2 * 10 => M2 = 33.6.   33.6nswer is 33.6
Answer: A
In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards Q will he need to gain this Sunday if he wants to keep his season average above 100 yards?
Answers:
A) 101	B) 116	C) 130	D) Q=131	E) Q=141

Solution: Sorry Q=141 the answer is Q=131.
Answer: D
Boy sells a book for Rs. 540 he gets a loss of 10 %, To gain 10%, what should be the SP?  Select:
A) 430
B) 450
C) 550
D) 590
E) 660

Solution: Cost price = 540/90 x 100 = 600   To gain 10% = 600 x 10/100 = 60   SP = CP + gain = 600 + 60= 
600 + 60 = 660
660   Answer :660
Answer: E
Three unbiased coins are tossed. What is the probability of getting 1 heads and 1 Tail?	Options.
A) 3/4	B) 1/4	C) 3/8	D) 7/8	E) 1/8

Solution: Let, H --> Head , T --> Tail   Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}   Let E = event of getting 3 heads   Then E = {THT, HTH }   P(E) = n(E)/n(S) =2/8 = 1/4   Answer is 1/4
Answer: B
Starting with the initial speed of 30 km/hr, the speed is increased by 4 km/hour every two hours. How many hours will it take to cover a distance of 288 km?
Answers:
A) 4
B) 6
C) 12
D) 8
E) None of these

Solution: Hour Speed (km/h) 8istance travelled (in km)   =2x30=60   =2x34=68   =2x38=76   =2x42=84   =2+2+2+2= 
2+2+2+2 = 8
8=60+68+76+84= 
60+68+76+84 = 288
288   Hence, the required time= 8 hours   Answer 8
Answer: D
There are between 140 and 150 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?	Choose the correct choice from the following.
A) 141
B) 143
C) 145
D) 147
E) 149

Solution: The numbers with the form 4n+1 are 141, 145, and 149.   Only 149 has the form 3k+2.   The answer is 149.
Answer: E
A is twice as good a workman as B and together they finish a piece in 18 days. In how many days will A alone finish the work?	Choose the most appropriate option.
A) 15 days B) 3 days C) 12 days D) 27 days E) 18 days

Solution: Sol. (A’s 1 day’s work):)(B’s 1 days work) = 2 : 1.   (A + B)'s 1 day's work = 1/18   Divide 1/18 in the ratio 2 : 1   A’s 1 day's work =(1/18*2/3)=1/27   Hence, A alone can finish the work in 27 days.   Ans: 27 days
Answer: D
List R contains five numbers that have an average value of 50. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list? Choose the correct choice from the following options: A) 18 B) 22 C) 26 D) 30 E) 34

Solution: The middle number is 50.   Let the smallest number be x. Then the largest number is 2x+20.   To make x as small as possible, let's make the remaining numbers as large as possible.   So the second largest = the largest = 2x+20.   The second smallest should be equal to the median.   The numbers are x, 50, 50, 2x+20, 2x+20.   x + 50 + 50 + 2x + 20 + 2x + 20 = 5*50= 
5*50 = 250
250   5x= 110   x = 22   The answer is 22.
Answer: B
Set Q consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set Q by 50, set Y is derived by multiplying each term in set Q by 1.5, and set Z is derived by dividing each term in set Q by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?	Choices:
A) X, Y, Z B) X, Z, Y C) Y, Z, X D) Y, X, Z E) Z, Y, X

Solution: Set Q - {2, 4, ..., 100};   Set X - {-48, -46, ..., 50};   Set Y - {3, 6, ..., 150};   Set Z - {-2/4, -4/4, ..., -100/4} = {-1/2, -1, -3/2, ..., -25}.   If we add or subtract a constant to each term in a set the SD will not change, so sets Q and X will have the same SD.   If we increase or decrease each term in a set by the same percent (multiply by a constant) the SD will increase or decrease by the same percent, so set Y will have 1.5 times greater SD than set Q and set Z will have 4 times less SD than set Q (note SD can not be negative so SD of Z wil be SD of Q divided by 4 not by -4).   So, the ranking of SD's in descending order is: Y, Q=X, Z.   Answer: Y, X, Z.
Answer: D
A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 5 years ago?  Choose the correct choice from the following:
A) 8  B) 10  C) 9  D) 14  E) 16

Solution: Let's say   Age of Richard is "R"   Age of David is "D"   Age of Scott is "S"   Now   Richard is 6 years older than David,   i.e. R = D +6   David is 8 years older than Scott   i.e. D = S +8   If in 8 years, Richard will be twice as old as Scott   i.e. R+8 = 2x(S+8)   i.e. R+8 = 2S + 16   i.e. R = 2S+8   But R = D+6 = (S+8)+6 = S+14   therefore, 2S + 8 = S +14   i.e. S = 6   i.e. R = 20   i.e. D = 14   Now,   how old was David 5 years ago?   i.e. D-5 = 14-5= 
14-5 = 9
9 years   ANSWER:9
Answer: C
A and B started a business by investing Rs.4000/- and Rs.5000/- respectively. Find the A’s share out of a total profit of Rs.1800:
Choose one.
A) Rs.600/-  B) Rs.660/-  C) Rs.800/-  D) Rs.820/-  E) Rs.840/-

Solution: A = Rs.4000/-   B = Rs.5000/-   A share 4 parts & B share 5 parts   Total 9 parts -----> Rs.1800/-   ----> 1 part -------> Rs.200/-   A share = 4 parts -----> Rs.800/-   Rs.800/-
Answer: C
There are 6 people and 3 chairs. In how many different ways people can occupy the chairs?  Options:
A) 330
B) 340
C) 350
D) 360
E) 370

Solution: number of ways = 6*5*4*3= 
6*5*4*3 = 360
360   Answer is 360
Answer: D
How many 3 digit integers can be chosen such that none of the digits appear more than twice and none of the digits equal zero ?	Pick one:
A) 729	B) 720	C) 648	D) 640	E) 57

Solution: number of ways without restriction = 9*9*9= 
9*9*9 = 729
729   number of ways that break restriction= 9*1*9 = 9   so the answer is   729-9= 
  729-9 = 720
720   ANS:720
Answer: B
Before 4 years, dog A’s age was 4 times of dog B’s age and after 4 years, dog A’s age will be 3 times of dog B’s age. What is the difference of dog A’s age and dog B’s now?	Choose one.
A) 36
B) 42
C) 52
D) 60
E) 64

Solution: A - 4 = 4(B - 4) --> A - 4B = -12.............1   A + 4 = 3(B + 4) --> A - 3B = 8.............2   (2) - (1) --> B = 20 --> A = 3(24) = 72   A - B = 72 - 20= 
72 - 20 = 52
52   Answer: 52
Answer: C
A certain number X when divided by 223 leaves a remainder of 93. Which of the following can be subtracted from X to make X divisible by 85?
Choose the correct choice from the following options.
A) 17
B) 27
C) 37
D) 47
E) 71

Solution: Least possible value of the number is 233 + 93= 
233 + 93 = 326
326   Further it is given the number must be divisible by 85 .   326/85= Gives remainder as 71   So, 71 must be subtracted from the number , answer is (71)
Answer: E
If x + y = 9 and x – y = 3, then x^2 - y^2 = Choose the most appropriate option:  A) -4  B) 4  C) 10  D) 27  E) 40

Solution: The fastest approach has already been shown. Here's one more option.   Given:   x + y = 9   x – y = 3   Add the two equations to get: 2x = 12, which means x = 6   If x = 6, we can plug that value into either equation, to conclude that y = 3   If x = 6 and y = 3, then x² - y² = 6² - 3² = 27   Answer: 27
Answer: D
If candy bars that regularly sell for $0.40 each are on sale at two for $0.75, what is the percent reduction in the price of two such candy bars purchased at the sale price?	Pick
A) 2 1/2 %
B) 6 1/4 %
C) 6 2/3 %
D) 8%
E) 12 %

Solution: Regular price is $0.80, sales price is $0.75.   So, 80-(80 * x%)=75   5 = 80*x%   x% = 5/80 = 1/16 = 6.25%   ANSWER:6 1/4 %
Answer: B
What is the units digit of the expression 14^7−18^4?  Options:
A) 0 B) 3 C) 4 D) 6 E) 8

Solution: Units digit of 14^7−18^4:   Consider the following unit digits:   4^1: 4   4^2: 6   4^3: 4   4^4: 6   ⇒ unit digit of 4^7 is: 4   The unit digit of 14^7 will also be 4   Also:   8^1: 8   8^2: 4   8^3: 2   8^4: 6   ⇒ unit digit of 8^4 is: 6   The unit digit of 18^4 will also be 6   Finally, 4-6 (or 14-6) = 8   Answer: 8)
Answer: E
The ages of two persons differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages.	Choose the correct answer:
A) 14 years B) 17 years C) 24 years D) 29 years E) None

Solution: Solution   Let the age of the younger person be x years.   Then, age of the elder person	= (x + 16) years.   Therefore	‹=› 3 (x - 6) =(x + 16 - 6)   ‹=› 3x-18 = x+10   ‹=› 2x = 28   x= 14 years.   14 yearsnswer 14 years
Answer: A
The present ages of three persons in proportions 2 : 2 : 6. Eight years ago, the sum of their ages was 56. Find their present ages (in years). Choose the correct choice from the following answers:
A) 8, 20, 28	B) 16, 16,48	C) 20, 35, 45	D) 18, 24, 32	E) None of these

Solution: Explanation:   Let their present ages be 2x, 2x and 6x years respectively.   Then, (2x - 8) + (2x - 8) + (6x - 8) = 56   10x = 80   x = 8   Their present ages are 2x = 16 years,2x = 16 years and 6x = 48 years respectively.   Answer: 16, 16,48
Answer: B
Find the sum of first 100 odd numbers Select:
A) 5500  B) 2005  C) 10000  D) 5800  E) 4960

Solution: Explanation:   n2 = 1002 = 10000   Answer: Option 10000
Answer: C
A can do a piece of work in 5 days, and B can do it in 6 days. How long will they take if both work together?  Choose the correct option: A) 2 8/11 B) 2 8/198 C) 2 8/7 D) 2 8/18 E) 2 8/112

Solution: Sol. A’s 1 day’s work =   1   th   5   part of whole work and   B’s 1 day’s work =   1   th   6   part of whole work   ? (A + B)’s one day’s work =   1 1 11 5 6 30 th part of whole work. So, both together will finish the work in 30 days 2 8/ 11 days.   2 8/11nswer:2 8/11
Answer: A
Jack and Jill are marathon runners. Jack can finish a marathon (42 km) in 5.5 hours and Jill can run a marathon in 4.2 hours.What is the ratio of their average running speed? (Jack: Jill) Pick one:
A) 14/15  B) 15/14  C) 4/5  D) 42/55  E) Cannot be determined

Solution: Average Speed of Jack =42/55istance/ Time   = 42 /(11/2) = 84/11   Average Speed of Jill = 42/(4.2)= 
42/(4.2) = 10
10   Ratio of Average speed of Jack to Jill= (84/11)/10 = 84/110 = 42/55   Answer 42/55
Answer: D