MU-NLPC/Calc-aqua_rat huggingface dataset:
A project manager needs to select a group of 4 people from a total of 4 men and 4 women. How many possible group combinations exist such that no group has all men or all women? Choose the correct choice from the following answers.
A) 72
B) 68
C) 74
D) 82
E) 48

Solution: First list all the possible combinations of Groups wit F = Female and M = Male:   MMMF   Total Combinations of 16 (4*3*2/3! *4)   FFFM   Total Combinations of 16 (same as above)   FFMM   Total Combinations of 36 (4*3/2! * 4*3/2!)   Altogether that makes 68.   Answer Choice 68
Answer: B
If the ratio of the roots of the equation 2x2-6x+q=0 is equal to that of the roots 3x2-6x+s=0, then:  Choose the correct choice from the following choices
A) 2s=q	B) s=q	C) 2q=s	D) 4s-q	E) None

Solution: 2x2-6x+q=0 for this eqn... roots are R1=6/2= 
6/2 = 3
3 R2=-q/2   3x2-6x+s=0 for this eqn... roots are R3=6/3= 
6/3 = 2
2 R4=-s/3   As per Question, 3/(-q/2)=2/(-s/3)   => s=q   ANSWER:s=q
Answer: B
a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a+b+c)]?  Choose the correct choice from the following choices:
A) 524
B) 693
C) 731 is answer
D) 970
E) None of the above

Solution: Is the answer bank correct? Shouldn't option 731 is answer be 713? 731 is answer
Answer: C
A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box?
Choices:  A) 2 m  B) 3 m  C) 4 m  D) 7 m  E) 8 m

Solution: Let radius of the outer circle be R and radius of the inner circle be r.   Circumference of the outer circle =   Circumference of the inner circle =   But,   or, R - r =   Thus, width of the road = 7 m   7 m
Answer: D
A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 8 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?  Choose the most appropriate option.
A) 2  B) 9  C) 6  D) 21  E) 30

Solution: Let the duration, in minutes, for which the company charges the same under plan A and plan B be t minutes.   Then under plan A the cost would be $0.6+0.06(t-8) and under plan B the cost would be $0.08t. We want these amount to be equal: 0.6+0.06(t-8)=0.08t --> 60+6(t-8)=8t --> t=6.   Answer: 6.
Answer: C
A man has about 4 children and 16 apples.He cuts the apple into quarter pieces and distribute them among the Children.One of the children eats one apple and returns remaining to the father.The father now distribute it among remaining.How many pieces does each of remaining child have?
Choose the correct choice from the following
A) 24
B) 25
C) 20
D) 36
E) 30

Solution: Each one gets 4 apples at first.One of them is eaten and 3 gets returned to father who distribute it again .So 3 apples get distributed among 3 children who get total of 5 apples.The apple is cut into a quarter.Thus   5*4= 
  5*4 = 20
20 pieces.Answer:20
Answer: C
If Q= x^4 + y^4 = 100, then the greatest possible value of x is between  Choose the correct answer.
A) 0 and 3	B) 3 and 6	C) 6 and 9	D) 9 and 12	E) 12 and 15

Solution: My attempt:   If Q=x^4+y^4=100, then the greatest possible value of x would be when y is minimum.   Let y^4 be 0. Now x^4 = 100. x should be definitely greater than 3 but less than 4. The only option that fits this range is 3 and 6   Hence answer is --   b) 3 and 6.
Answer: B
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture? Choose the correct choice from the following:
A) 12 liters.
B) 10 liters.
C) 10 liters.
D) 16 liters.
E) 15 liters.

Solution: Explanation:   Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150= 
20/100 * 150 = 30
30 liters.   P liters of water added to the mixture to make water 25% of the new mixture.   Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).   (30 + P)= 25/100 * (150 + P)   120 + 4P = 150 + P => P = 10 liters.   Answer: Option 10 liters.
Answer: C
2ab5 is a four digit number divisible by 25. If a number formed from the two digits ab is a multiple of 13, then ab is Choose the correct choice from the following choices.
A) 52  B) 27  C) 20  D) 26  E) 201

Solution: For a number to be divisible by 25, last two digits of that number should be divisible by 25. So b must be either 2 or 7   it is given that ab must be divisible by 13 and in the options only 52 is divisible by 13.   52nswer:52
Answer: A
Find the value for m?
19(m + n) + 17 = 19(-m + n) - 173 Select the correct option:
A) 0
B) -1
C) -5
D) 2
E) 3

Solution: 19m + 19n + 17 = -19m + 19n - 173   38m= -190 => m = -5   0
Answer: A
A water tank has three taps A, B and C. Tap A, when opened,can fill the water tank alone in 4 hours. Tap B, when opened, can fill the water tank alone in 6 hours and tap C, when opened, can empty the water tank alone in 3 hours. If taps A, B and C are opened simultaneously, how long will it take to fill the tank completely?
Select the correct option:
A) 10 hours
B) 8 hours
C) 18 hours
D) 12 hours
E) None of these

Solution: Required time to fill the tank   = 1 /(1/4+1/6)−1/3=1 /5/12−1/3=1 /1/12=12h   Answer 12 hours
Answer: D
Martha has 3 dogs and 4 cats. She takes each animal separately for a daily walk. She can take the animals for a walk to the park or to the barber shop. How many different options for a walk with a single animal does Martha have?
Select:
A) 8	B) 9	C) 10	D) 14	E) 20

Solution: 5 dogs, 4 cats; park/barber shop   1 dog - 2 options - either park or barber shop, so, 3 dogs - 6 options and 4 dogs - 8 options.   Total = 14 options.   14
Answer: D
The average age of 20 men in the class is 17.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men?  Choose the correct choice from the following
A) 15.5 B) 7.4 C) 15.25 D) 15.3 E) 15.6

Solution: Total age of 20 men = 17.6 x 20 = 352   Now, total age of 25 men = 389.   Total age of five men added later = 389 - 352= 
389 - 352 = 37
37.   Hence, the total average of five men= 37/5= 
37/5 = 37/5 = around 7.4
7.4   ANSWER:7.4
Answer: B
The average age of three boys is 25 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?	Choose the correct choice from the following options:
A) 6  B) 9  C) 6  D) 4  E) 15

Solution: 3x + 5x + 7x = 75   x =5   3x = 15   Answer:15
Answer: E
A train covers a distance of 100km in 1 hour. If its speed is decreased by 25km/hr, the time taken by the car to cover the same distance will be? Pick one: A) 1hr B) 1hr 20min C) 50min D) 1hr 30min E) 1hr 45min

Solution: Speed = 100/1= 
100/1 = 100
100km/hr   New speed= 100-25= 
100-25 = 75
75 km/hr   Time taken= 100/75 = 1hr 20min   Answer is 1hr 20min
Answer: B
Danny drove his old car 100 kilometers, from his home to a friend. To prevent the engine from overheating, he stopped his car for 12 minutes every time he completed 40 kilometers of continuous driving. When the car was moving, Danny drove it at an average speed of 60 kilometers per hour. What was Danny's average speed on that trip?
Choose the correct answer.
A) 37.5 kilometers per hour	B) 48.4 kilometers per hour	C) 50 kilometers per hour	D) 75 kilometers per hour	E) 100 kilometers per hour

Solution: Time taken to reach first 40 km is 40/60 = 2/3 hr   Time taken to reach next 40 km is 40/60 = 2/3 hr   Time taken to reach next 20 km is 20/60 = 1/3 hr   Danny stopped twice on his way at 40 km from starting point and at 80km from the starting point...   Each stop was of 12 min , so two 12min break = 2*1/5 => 2/5 hr   Total time taken to reach 100 km is (2/3 + 2/3 + 1/3+2/5 ) = 31/15 hrs   So, Average speed is 100/(31/15) = 48.4km/hour   Answer will be 48.4 kilometers per hour
Answer: B
November 2, 1962, fell on a Friday. On which day of the week did November 2, 1985, fall? (Note: 1964 was a leap year and every succeeding fourth year were leap years.)
Choose the correct choice from the following answers.
A) Sunday B) Tuesday C) Thursday D) Friday E) Saturday

Solution: There are 365 days in a non-leap year and 366 in a leap year. In the period in question, there are 17 non-leap years and 6 leap years, thus the number of days in the period is (17 * 365) + (6 * 366)= 
(17 * 365) + (6 * 366) = 8_401
8401. Dividing by 7 yields 1200 and a remainder of 1. Since the first date was a Friday, we advance the day of the week by the remainder of 1 and thus the second date is a Saturday. The answer is Saturday.
Answer: E
A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?	Choose the most appropriate option:  A) 1000  B) 1526  C) 5625  D) 1090  E) 1829

Solution: 90%   104%   --------   14% ---- 140   100% ---- ? => Rs.1000   1000nswer: 1000
Answer: A
The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class? Choose the correct choice:	A) 176.5 cm	B) 175.5 cm	C) 174.5 cm	D) 173.5 cm	E) 172.5 cm

Solution: The total height was 45 cm too much.   The average height should be reduced by 45 cm/30 = 1.5 cm   The answer is 175.5 cm.
Answer: B
A, B and C can do a work in 7 , 14 and 21 days respectively. They completed the work and got $242. What is the share of C?	Choose the correct choice:
A) $25  B) $48  C) $44  D) $49  E) $40

Solution: C   $44   The ratio of their working rates = 1/7 : 1/14 : 1/21 = 6 : 3 : 2.   Since, they work together, the share of $44   = 2/11 * 242= 
2/11 * 242 = 44
$44
Answer: C
How many cubes of 2cm edge can be cut out of a cube of 24cm edge Pick one:  A) 1136  B) 1728  C) 1216  D) 1484  E) None of these

Solution: Explanation:   number of cubes=(24 x 24 x 24) / (2 x 2 x 2) = 1728   Answer: 1728
Answer: B
Working together at their respective constant rates, Machine A and Machine B can produce 1,800 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, what percent of the 1,800 unit total would it produce?	Choose the correct choice from the following choices:  A) 25  B) 33  C) 30  D) 67  E) 75

Solution: 1/A+1/B= 1/T   1/A +1/12= 1/8 (50% more of 8 is 12)   1/A= 1/24   Machine A can produce 1800 units in 24 hrs, so it can produce  1800*8/24= 
 1800*8/24 = 600
600 units is 8 hrs.   600 is 30% of 1800.   30 is the answer
Answer: C
Set A: {1, 3, 4, 6, 9, 12, 15}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 2?	Choices: A) 3/14 B) 2/7 C) 9/14 D) 5/7 E) 1/35

Solution: using probability you can solve: 3/7*2/6*1/5=1/35.   Ans 1/35
Answer: E
A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by f meteres, What is the area of the rug in square meters? Pick one
A) mn - p(m+n)
B) mn – 2p(m+n)
C) mn – p^2
D) (m - p)(n - p)
E) (m - 2p)(f - 2p)

Solution: The answer must be E.   Plug in M 100   N 50   f 10.
Answer: E
A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 10%. Their gross income from sales for one month decreases by what percent?
Select the correct option:
A) 1%  B) 3%  C) 5%  D) 7%  E) 9%

Solution: Let P be the original price and let x be the number of items sold originally.   The original income is P*x.   After the changes, the income is 0.9P*1.1x = 0.99*(P*x), a decrease of 1%.   The answer is 1%.0.9 *1.1= 
0.9 *1.1 = 0.99
0.99*(P*x), a decrease of 1%.   The answer is 1%.
Answer: A
If 5 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
Choose the correct choice from the following answers:  A) 2:5  B) 2:3  C) 2:8  D) 2:1  E) 2:2

Solution: 5M + 2B = 4(1M + 1B)   5M + 2B = 4M + 4B   1M = 2B   The required ratio of work done by a man and a boy = 2:1   Answer:2:1
Answer: D
A train 100 meters long completely crosses a 300 meters long bridge in 30 seconds. What is the speed of the train is? Choose the correct option
A) 32 kmph B) 48 kmph C) 34 kmph D) 43 kmph E) 40 kmph

Solution: S = (100 + 300)/30   = 400/30 * 18/5= 
400/30 * 18/5 = 48
48   Answer:48 kmph
Answer: B
In how many different ways can the letters of the word ‘ARMOUM’ be arranged?  Select
A) 200 B) 210 C) 220 D) 250 E) 360

Solution: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360   360
Answer: E
The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly three elements each?	Options:	A) 24	B) 42	C) 54	D) 72	E) 84

Solution: nC2 = 36   => n*(n-1)/2 = 36   => n = 9   nC3 = 9C3 = 84   So, Answer is 84.
Answer: E
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?	Choose the correct answer
A) 96 B) 720 C) 120 D) 6 E) 64

Solution: Consonants = L D N G (4)   Vowels = E A I (3)   No of ways the all vowels can be together is arranged by , -   we can arrange EAI together , this can be done by 3! = 6 ways   Now arrange consonants LNDG   LNDG can arrange in 5! = 120 ways   Required no of ways = 120 * 6= 
120 * 6 = 720
720   Ans- 720
Answer: B
Find the number of ways in which four men, two women and a child can sit at a table if the child is seated between two women.	Choose the correct choice from the following:
A) 12 B) 24 C) 36 D) 48 E) 60

Solution: The number of arrangements of n distinct objects in a row is given by n!n!.   The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.   We have M, M, M, M, W, W, C --> glue two women and the child so that they become one unit and the child is between women: {WCW}. Now, these 5 units: {M}, {M}, {M}, {M}, {WCW} can be arranged around the table in  (5-1)= 
 (5-1) = 4
4! ways and the women within their unit can be arranged in 2 ways {W1, C, W2} or {W2, C, W1} so total # of arrangement is 4!*2=48.   Answer: 48. ANSWER:48
Answer: D
P and Q started a business investing Rs. 54,000 and Rs. 18,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
Choose the correct option.
A) 3:1	B) 4:3	C) 5:4	D) 6:5	E) 17:4

Solution: P:Q = 54000 : 18000   = 3:1.   3:1nswer:3:1
Answer: A
The sum of the two numbers is 13 and their product is 35. What is the sum of the reciprocals of these numbers? Choose the most appropriate option: A) 12/35 B) 13/35 C) 35/8 D) 7/32 E) None of these

Solution: Let the numbers be a and b. Then, a+b=13 and ab =35.   a+b/ab=13/35; (1/b+1/a)=13/35   Sum of reciprocals of given numbers=13/35.   Correct Option: 13/35
Answer: B
Three numbers are in the ratio 3 : 4 : 8. The sum of its longest and smallest numbers equals the sum of the third number and 42. Find the third number?  Choose the correct choice
A) A)54 B) B)75 C) C)24 D) D)46 E) E)63

Solution: Let the numbers be 3x, 4x, 8x.   Largest number = 8x.   Smallest number = 3x.   Third number = 4x.   8x + 3x = 4x + 42   7x = 42 =>x=6   4x=24 =>third number is 24.   Answer:24
Answer: C
Tough and Tricky questions: Distance/Rate.
On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 500 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 2.5 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey?  Choose the correct choice from the following answers.
A) 40  B) 30  C) 60  D) 80  E) 100

Solution: Say, if speed is 40, 500/40 = 12.5 hrs and 500/50= 
500/50 = 10
10 hrs (a reduction of 12.5 hr -> Correct answer)   40nswer (40)
Answer: A
When n is divided by 48, the remainder is 6. What is the remainder when 4n is divided by 8?
Choose one:
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: Let n=6 (leaves a remainder of 6 when divided by 48)   4n = 4(6) =24, which leaves a remainder of 0 when divided by 8.   0nswer 0
Answer: A
Each side of a certain parallelogram has length 6. If the area of the parallelogram is 24. Which of the following is the measure of one of its angles? Answers:
A) 30 B) 42 C) 60 D) 90 E) 120

Solution: Ans is 30deg   area of a parallelogram = b*h   b*h=24   h=24/6= 
24/6 = 4
4   sin theta=opp/hyp= 4/6 = 2/3   theta = sin inv of 2/3=42 deg   42
Answer: B
In a Quiz the points in each round for the first,second,third and fourth position were 100,50,20,10 . No other points were given. Rachel participated in several rounds in the competition and the product of her score was 10000. In How many rounds did she participate?
Select
A) 2  B) Cannot be determined  C) 4  D) 6  E) 10

Solution: Correct answer is B because we are given that there won't be any points awarded for rounds other than 1st four position.   Thus, it may happen that she played 150 rounds out of only 8 rounds were there in which she was awarded some points.
Answer: B
How many integers less than 100 have exactly 4 odd factors but no even factors?
Choose the correct choice from the following answers:
A) 11	B) 13	C) 15	D) 17	E) 19

Solution: Two cases are possible:   x1y1=xy=odd<100x1y1=xy=odd<100, where xx and yy are odd prime numbers, then # of factors will be (1+1)(1+1)=4(1+1)(1+1)=4;   If x=3, then y can be: 5, 7, 11, 13, 17, 19, 23, 29, 31 - 9 numbers.   If x=5, then y can be: 7, 11, 13, 17, 19 - 5 numbers.   If x=7, then y can be: 11, 13 - 2 numbers.   OR:   x3=odd<100x3=odd<100, where xx is odd prime number, then # of factors will be (3+1)= 
(3+1) = 4
4(3+1)=4.   x can be only 3 - 1 number.   Total 9+5+2+1=179+5+2+1=17 .   Answer: 17.
Answer: D
A fort had provision of food for 150 men for 45 days. After 10 days, 50 men left the fort. The number of days for which the remaining food will last, is:	Choose the most appropriate option
A) 29 1/5 B) 37 1/4 C) 42 D) 5 1/4 E) 48

Solution: After 10 days : 150 men had food for 35 days.   Suppose 100 men had food for x days.   Now, Less men, More days (Indirect Proportion)   Therefore 100 : 150 :: 35 : x <=> 100 x x = 150 x 35   => x =150 x 35/100   => x = 5 1/4.   Correct answer is 5 1/4
Answer: D
If q = 20! + 17, then q is divisible by which of the following?
I. 15
II. 17
III. 19
Choose the correct answer:
A) None
B) I only
C) II only
D) I and II
E) II and II

Solution: Another crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included.   So q!+17 = xxxx00 +17= 
00 +17 = 17
xxxx17 which is only possibly divisible by 17. Hence Option II only is the answer.
Answer: C
The average marks scored by Ganesh in English, Science, Mathematics and History is less than 15 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?	Options:
A) 40 B) 50 C) 60 D) Data inadequate E) None of these

Solution: E+H+G+M/4−E+S+M+H/4=15   ⇒ G - S = 60   Answer 60
Answer: C
When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 4. If 1 < m < 200, what is the greatest possible value of m? Choices:	A) 47	B) 65	C) 103	D) 117	E) 173

Solution: Looking at the choices, options BD can be eliminated as they are divisible by 13   Starting from the highest number 164;   173 = 171 + 2 (171 divisible by 9)   173 = 169 + 4 (169 divisible by 13)   it fits the result   Answer = 173
Answer: E
For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum m of all the even integers between 99 and 301?
Choose the correct answer
A) 10,100  B) 20,200  C) 22,650  D) 40,200  E) 45,150

Solution: I would solve it in a different way.   First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2= 
202/2 = 101
101   Average= (301+99)/2 = 400/2= 
400/2 = 200
200   Sum m= Average*total count = 200*101 = 20,200   Answer is 20,200
Answer: B
A computer can perform x calculations in s seconds. How many minutes will it take the computer to perform k calculations?
Choose the correct choice from the following answers: A) 60ks/x B) ks/x C) ks/60x D) 60x/ks E) k/60xs

Solution: As 'thick' as this question might look, it's actually a fairly straight-forward Rate question and can be solved by TESTing VALUES.   We're told that a computer can perform X calculations in S seconds.   Let's TEST....   x = 2   S = 3   2 calculations every 3 seconds =   40 calculations every 1 minute   We're asked how many MINUTES it will take to perform K calculations.   Since we already know that the computer can perform 40 calculations in 1 minute, let's TEST...   K = 80   So we're looking for an answer that = 2 when C = 2, S = 3 and K = 80   Answer A: 60KS/x = 60(80)(3)/2 = 7200 This is NOT a match   Answer B: KS/x = (80)(3)/2 = 120 This is NOT a match   Answer C: KS/60x = (80)(3)/(60)(2) = 2 This IS a match   Answer D: 60x/KS = 60(2)/(80)(3) = 1/2 This is NOT a match   Answer E: K/60xS = 80/(60)(2)(3) = a fraction. This is NOT a match   ks/60x
Answer: C
If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 348, the cost of the article is	Options.
A) 289
B) 231
C) 200
D) 40
E) 111

Solution: Explanation:   Let C.P. be Rs. x.   Then, 5% of x = 350 - 348= 
350 - 348 = 2
2   x/20= 2 => x = 40   Answer: 40
Answer: D
Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?  Choose one:
A) 17 1/7 days  B) 5 days  C) 6 days  D) 9 days  E) 10 days

Solution: Explanation:   1/30 + 1/40 = 7/120   120/7 = 17 1/7 days   17 1/7 daysnswer: 17 1/7 days
Answer: A
Solve below question 2x - 1 = 17	Choices:
A) -8 B) -9 C) -5 D) -4 E) 9

Solution: 1. Add 1 to both sides: 2x - 1 + 1 = 17 + 1 2. Simplify both sides: 2x = 18 3. Divide both sides by 2: 4. Simplify both sides: x = 9 9
Answer: E
Car Dealership X, the total profit from sales increased by 15 percent over the previous years, while the number of cars sold decreased by 15 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.  Options
A) 18%  B) 20%  C) 22%  D) 35.29%  E) 55%

Solution: Let Profit be x and cars sold be y   Originally Profit/Car = x/y   Now it is 1.15x / 0.85 y = 115/85 (x/y)   Increase in profit per car = ((30/85) (x/y)) / (x/y) * 100 = 35.29%   Answer = 35.29%
Answer: D
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 5 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?	Choose the correct choice from the following options.
A) 5  B) 6  C) 15  D) 20  E) 25

Solution: Audery and Ferris collective Work rate:   1/4 + 1/3 = 7/12   Collective work Time = 12/7 = 1.7 Hrs   Job Was actually done in = 2 (Includes breaks)   6reaks = Actual time taken - Collective work time   = 2 - 1.7= 
2 - 1.7 = 0.3
.3 Hrs= 1/2   so ferrais took 5 breaks   =.3/5= 
.3/5 = 0.06
.06 hrs= 6 m   so Answer is 6) 10 mins
Answer: B
In a G6 summit held at london. A french, a german, an italian, a british, a spanish, a polish diplomat represent their respective countries. (i) Polish sits immediately next to british (ii) German sits immediately next to italian, British or both (iii) French does not sit immediately next to italian (iv) If spanish sits immediately next to polish, spanish does not sit immediately next to Italian Which of the following does not violate the stated conditions?  Select the correct option: A) DKSOO B) UDFHD C) DKJHIU D) FSPBGI E) OIHDSD

Solution: FSPBGI   Answer:FSPBGI
Answer: D