MU-NLPC/Calc-aqua_rat huggingface dataset:
Sum of the two number is 14 and difference of their square is 28. Find the numbers. Choose the most appropriate option.
A) 8 and 6  B) 9 and 5  C) 4 and 10  D) 3 and 10  E) 2 and 10

Solution: Explanation:   Let the number be x & y.   x + y = 14   x2 - y2 = 28   (x + y)(x - y) = x2 - y2   14(x - y) = 28   x - y = 2 ----------(1)   x + y = 14   x - y = 2   ------------------   2x = 16   x = 8   Therefore y = 6   x = 8 and y = 6   8 and 6nswer: Option 8 and 6
Answer: A
When x is multiplied by 3, the result is 14 more than the result of subtracting x from 26. What is the value of x? Answers: A) 10 B) -2 C) 11 D) 13 E) 22

Solution: The equation that can be formed is:   3x-14=26-x   or, 4x=40   or, x=10.   10 answer.
Answer: A
There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls?
Choose the correct choice from the following options: A) 12 B) 32 C) 5 D) 28 E) 30

Solution: number of kids playing with white color balls = 26   total number of kids in the play school = 35   number of kids playing with both white and yellow color balls = 19   we have to find,   number of kids playing with yellow color balls   35 = 26 + n(B) - 19   35 + 19 - 26= 
35 + 19 - 26 = 28
28   Hence, Answer is 28 kids play with yellow color   balls. ANSWER 28
Answer: D
One hour after Matthew started waking from r to y, a distance of 45km, Johnny started walking along the same road from y to r. Matthew's walking rate was 3 km per hour and Johnny's was 4km per hour, how many km had Johnny walked when they met?
Choose the correct choice.
A) 24  B) 23  C) 22  D) 21  E) 19.5

Solution: Just an alternative method...   After the first hour the distance r is 42 km (45-3). Now the problem can be treated as if bothof them started at the same time. Since the speeds are in the ratio 3 : 4, the distances will also be in the same ratio. Splitting 42 in that ratio we get 18 : 24. So answer is 24.   Hence 24.
Answer: A
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 37?
Choose one.
A) 3 B) 4 C) 12 D) 6 E) 35

Solution: n = 5p + 1 = 6,11,16,21,26,31   n 5  + 1= 
5  + 1 = 6
6,11,16,21,26,31   n= 7q + 3 = 3,10,17,24,31   =>n = 37m + 31   To get this, we need to take LCM of co-efficients of p and q and first common number in series.   So we need to add 6 more to make it   37m + 36   Answer - 6
Answer: D
Danny and Steve are running towards each other, each one from his own house. Danny can reach Steve's house in 27 minutes of running, which is half the time it takes Steve to reach Danny's house. If the two started to run at the same time, how much time longer will it take Steve to reach the halfway point between their houses than Danny to reach the halfway point between their houses?  Choose the correct answer.
A) 13.5 minutes B) 27 minutes C) 35 minutes D) 54 minutes E) 81 minutes

Solution: Danny's time is 27 minutes. The time to reach halfway is 13.5 minutes.   Steve's time is 54 minutes. The time to reach halfway is 27 minutes.   The time difference is   27 - 13.5= 
  27 - 13.5 = 13.5
13.5 minutes   The answer is 13.5 minutes.
Answer: A
If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before? Choose the correct choice from the following answers:
A) 27 2/23 %	B) 33 1/3 %	C) 30%	D) 19%	E) 25%

Solution: Explanation:   100   150   ------   150-------50   100-------? => 331/3%   ANSWER IS 33 1/3 %
Answer: B
If A can be complete the piece of work in 10 days and B can complete the same piece of work in 20 days.In how many days the work can be complete if both are work together?  Pick one:
A) 20/3
B) 3/20
C) 18/20
D) 9/5
E) 19/5

Solution: A's one day work=1/10   B's one day work=1/20   The question is If A and B work together, then how many days that will complete?   A+B=1/10+1/20=3/20(one day work)   20/3 days could complete their work.   The answer is option 20/3
Answer: A
Sum of two numbers is 40. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
Choose the correct choice from the following:
A) 26, 14
B) 23, 17
C) 17, 23
D) 14, 26
E) 15, 25

Solution: Explanation:   x + y = 15   3Y Ã¢â‚¬â€œ 2x = 5   x = 23 y = 17   Answer: 23, 17
Answer: B
A can do a piece of work in 8 days. He works at it for 4 days and then B finishes it in 6 days. In how many days can A and B together finish the work?
Choose the correct choice from the following.
A) 4.1 days B) 4.8 days C) 3.8 days D) 2.8 days E) 4.5 days

Solution: 4/8 + 6/x = 1 => x = 12   1/8 + 1/12 = 5/24 => 4.8 days   ANSWER:4.8 days
Answer: B
A bus stops for taking passengers. The speed of the bus with stoppages is 36 km/hr and without stoppages is 45 km/hr.For how many minutes bus stopped per hour?
Answers: A) 10 min B) 11 min C) 12 min D) 13 min E) None of these

Solution: Explanation :   It takes 9 km less due to stoppages. Time spend in stoppages=(9/45)*60= 
(9/45)*60 = 12
12 min   Answer : 12 min
Answer: C
Bert left the house with N dollars. He spent 1/4 of this at the hardware store, then $7 at the dry cleaners, and then half of what was left at the grocery store. When he got home, he had $19 left in his pocket. What was the value of N? Choose the correct choice from the following
A) $36	B) $44	C) $52	D) $60	E) $68

Solution: started to test answer D   if he had 60, then he spent 15 at hardware store   now he was left with 45$   he spent 7 dollars on cleaning, thus he remained with 38$   he then spent 1/2 of 38, or 19, and was left with 19.   hence, the only option that can be right is $36.
Answer: A
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1200 more than D, what is B's share?
Choose the correct choice from the following answers:  A) Rs. 500  B) Rs. 1500  C) Rs. 2000  D) Rs. 2400  E) none of the above

Solution: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.   Then, 4x - 3x = 1200   x = 1200.   B's share = Rs. 2x = Rs. (2 x 1200) = Rs. 2400.   Answer = Rs. 2400
Answer: D
Crew A can build a complete car in 20 minutes and Crew B can build a complete car in 25 minutes. If both crews work independently and start at the same time, what is the shortest amount of time G it could take for 10 cars to be complete? Choose the correct option.
A) 111 1/9 minutes  B) 115 2/5 minutes  C) 116 minutes  D) 120 minutes  E) 125 minutes

Solution: A builds 4 cars in 80 min   B builds 4 cars in 100 min   So A builds another car in another 20 min (i.e total 5 cars)   B builds another car in another 25 minutes (i.e, total 5 cars)   However, A can build another car in next 20 min (i.e total 6 cars)   So total time G= 125 min by B, which is > 120 min by A   B - 4 cars, A - 6 cars   Answer = 120 minutes
Answer: D
An design manager has 10patterns of chairs & 5patterns of tables. In how many ways can he make a pair of table & chair? Choose the most appropriate option:	A) 20	B) 40	C) 50	D) 90	E) 100

Solution: He has has ten patterns of chairs and eight patterns of tables   Hence, A chair can be arranged in 10 ways and   A table can be arranged in 5 ways   Hence one chair and one table can be arranged in 10 x 5 ways = 50 ways   50
Answer: C
An unbiased die is tossed .find the probability of getting a multiple of 3
Choose the correct choice from the following.
A) 4/3
B) 5/7
C) 1/3
D) 3/5
E) 2/3

Solution: Here S={1,2,3,4,5,6}   Let E be the event of getting the multiple of 3   then ,E={3,6}   P(E)=n(E)/n(S)=2/6=1/3   Ans: 1/3
Answer: C
The product of three consecutive numbers is 504. Then the sum of the smallest two numbers is ? Choose the correct option
A) 11 B) 15 C) 20 D) 38 E) 56

Solution: Product of three numbers = 504   504 = 7 * 8 * 9.   So, the three numbers are 7, 8 and 9.   And Sum of smallest of these two = 7+8= 
7+8 = 15
15.   ANSWER : OPTION 15
Answer: B
A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 37,000, what will be the amount A receives?
Choose the correct choice
A) 14700
B) 14500
C) 14900
D) 14300
E) 15540

Solution: Total amount invested = 50000   Assume that investment of C =x.   Then investment of B =5000+x,   Investment of A =4000+5000+x=9000+x   x+5000+x+9000+x=50000   ⇒3x+14000=50000   ⇒3x=50000–14000=36000   ⇒x=36000/3= 
36000/3 = 12_000
12000   Investment of C=x=12000   Investment of B =5000+x=17000   Investment of A =9000+x=21000   Ratio of the investment of A, B and C   =21000:17000:12000   =21:17:12   Share of A = Total profit ×21/50   =37000×21/50=15540   Answer is 15540
Answer: E
4 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?	Options:
A) 18:19
B) 17:19
C) 15:19
D) 18:14
E) 18:11

Solution: 4M + 12B ----- 4 days   7M + 6B ------- 5 days   16M + 48B = 35M + 30B   18B = 19M => 5M = 6B   M: B = 18:19   18:19NSWER:18:19
Answer: A
At a certain restaurant, the price of a sandwich is $ 4.00 more than the price of a cup of coffee. If the price of a sandwich and a cup of coffee is $ 7.35, including a sales tax of 5%, what is the price of a cup of coffee, EXCLUDING the sales tax?  Answers:	A) $ 1.50	B) $ 3.00	C) $ 4.00	D) $ 5.50	E) $ 7.00

Solution: Let the price of sandwich = S   price of coffee = C   S= C+4   => S - C = 4 --1   the price of a sandwich and a cup of coffee is $ 7.35, including a sales tax of 5%,   1.05(S+C) = 7.35   => S+C = 7 --2   From equations 1 and 2, we get   S=5.5$   C= 1.5$   $ 1.50nswer $ 1.50
Answer: A
At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years? Pick one
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: 150 = (750*5*R)/100   R = 4%.Answer: 4
Answer: C
60% of a number is added to 120, the result is the same number. Find the number?	Choose the correct choice from the following answers
A) 300  B) 288  C) 1687  D) 997  E) 121

Solution: (60/100) * X + 120 = X   2X = 600   X = 300   300nswer:300
Answer: A
Based on this year's costs, an orchard grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 33% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be:	Pick.
A) 15% less than N
B) 25% less than N
C) equal to N
D) 25% greater than N
E) 15% greater than N

Solution: Correct answer is (B).   This year, the price of a tree is price1=P/N.   If this price increases by 33% it becomes Price2=P/N*1.33   Then with P dollars, you can grow P/Price2 trees i.e. P/(P/N*1.33) i.e. N/1.33 i.e. 0.75N   Which is 25% less than N.
Answer: B
A sum of money on compound interest amounts to Rs. 8240 in 2 years and Rs. 9888 in 3 years. The rate of interest is	Choices.
A) 10% B) 25% C) 20% D) 12% E) 30%

Solution: Explanation:   If a certain sum of money at compound interest amounts to Rs.x in t1 years and Rs.y in t2 years, then the rate of interest per annum can be given by   R=[(y/x)^1/(t2−t1)−1]×100%   R=[(y/x)^1/(t2−t1)−1]×100=[(9888/8240)^1/(3−2)−1]×100=[(9888/8240)−1]×100   =(1648/8240)×100=(1/5)×100=20%   Answer: Option 20%
Answer: C
There is an integer, which holds a very special property. If you subtract any number from that integer, the resultant is exactly divisible by the successor of that number.
Can you find out that integer?
Choose the correct choice.
A) 1  B) 0  C) -1  D) 2  E) -2

Solution: C   The integer with the special property is -1.   To test the property, let us subtract any digit from it, let's say 5.   -1 - 5 = -6   The succeeding digit of 5 is 6.   When (-6) is divided by 6, it is completely divided.   For all other numbers as well, this stands true.
Answer: C
If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5+a^6)?	Choose one
A) -14  B) -4  C) -1  D) 4  E) 14

Solution: if a = -1, then putting values in equation   = -[ (-1)^2 + (-1)^3 + (-1^4) + (-1^5)+(-1^6) ]   = -[ 1 - 1 + 1 - 1 + 1]   = -1   Answer = -1 = -1
Answer: C
WHEN A PERSON SELLS TWO ITEMS $1656 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURS A LOSS OR GAIN OF: Pick one:
A) no loss no gain	B) 20 % profit	C) 4% loss	D) 2% profit	E) 2% loss.

Solution: The 2 items are sold at 1656 each , one at a profit of 20% and the other at a loss of 20%   So the original rates of the items are 1380 and 2070 respectively   So the total he spend for those 2 items is 3450 but he ended up in selling them with (1656*2) 3312   So the loss is 3450 - 3312= 
3450 - 3312 = 138
138   The loss percentage is   (138/3450) *100= 
  (138/3450) *100 = 4
4% loss - Answer 4% loss
Answer: C
A can do a piece of work in 11 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?  Select the correct option.
A) 15 10/31 days	B) 10 10/31 days	C) 12 10/31 days	D) 19 10/31 days	E) 13 10/31 days

Solution: 10 10/31 days   (x â€“ 5)/11 + x/20 = 1   x = 10 10/31 days
Answer: B
A man rows his boat 90 km downstream and 40 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? Answers.
A) 6
B) 7
C) 5
D) 8
E) 15

Solution: Speed downstream = d/t = 90/(2 1/2) = 36 kmph   Speed upstream = d/t = 40/(2 1/2) = 16 kmph   The speed of the stream = (36 - 16)/2   = 15 kmph   Answer: 15
Answer: E
In how many ways can 4 boys and 4 girls be arranged a ta table if 4 girls are never together?	Choose the most appropriate option
A) 3365
B) 3256
C) 4464
D) 5648
E) 2456

Solution: Total ways of arranging 8 person in a circle = 7! = 5040 ways   If we consider four women as one, then we have   4+1= 
  4+1 = 5
5 persons. Arranging these five persons in circle will take= 4! = 24 ways   And four women can arrange themselves in 4! ways   Total ways in which four women sit together in circle = 4!*4! = 576 ways   Total ways in which four women doesn’t sit together in circle = 7! - 4!*4! = 5040 - 576= 
5040 - 576 = 4_464
4464 ways   4464
Answer: C
which number need to add to 859622 to get a number exactly divisible by 456? Answers.
A) 456456 B) 576834 C) 562783 D) 634567 E) 859622

Solution: Dividend = Quotient * Divisor + Reminder   859622 / 456 gives quotient = 1885 and reminder = 62.   So, the next number divisible by 456 is 456 places infront of 456 * 1885   Which means 456 – 62 = 394 should be added to 859622.   859622
Answer: E
There were two candidates in an election. Winner candidate received 62% of votes and won the election by 312 votes. Find the number of votes casted to the winning candidate?  Choose the correct choice from the following
A) 806	B) 744	C) 912	D) 1200	E) 1400

Solution: W = 62% L = 38%   62% - 38% = 24%   24% -------- 312   62% -------- ?  62  - 38= 
 62  - 38 = 24
24%   24% -------- 312   62% -------- ?=> 806   806NSWER:806
Answer: A
In how many ways can you seat 5 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end? Choices:
A) 720 B) 1720 C) 48 D) 5040 E) 10080

Solution: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 2 chairs to sit. The remaining 4 people can sit in 4! ways. Thus the # of arrangements is 2*4! = 48.   Answer: 48.
Answer: C
Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 15 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?  Choose the correct choice from the following answers:
A) A) 6.24	B) B) 8	C) C) 29.1	D) D) 15	E) E) 24

Solution: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9   New time in minutes to cross 10 miles stretch = 10*60/15 = 10*4= 
10*4 = 40
40   Time difference= 29.1   Ans:29.1
Answer: C
How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 11? Choose the correct choice from the following choices:	A) 5	B) 6	C) 7	D) 8	E) 9

Solution: The numbers should be of the form 11c+3.   The minimum is 3 when c=0.   The maximum is 47 when c=4.   There are 5 such numbers.   The answer is 5.
Answer: A
How many times do the hands of a clock coincide in a day?	Options.
A) 22 B) 26 C) 29 D) 21 E) 27

Solution: The hands of a clock coincide 11 times in every 12 hours   (Since between 11 and 1, they coincide only once,   i.e. at 12 o'clock).   => The hands coincide 22 times in a day.   22nswer is 22.
Answer: A
If 2ab - c = 2a(b - c), which of the following must be true?  Choose the correct choice:
A) a=0 and c=0
B) a=1/2 and b=2
C) b=1 and c=0
D) a=1 or b=0
E) a=1/2 or c=0

Solution: 2ab - c = 2a(b - c)   => 2ab - c = 2ab - 2ac   => - c = - 2ac   => c = 2ac   => c - 2ac = 0   => c (1 - 2a) = 0   Either c = 0 or 1 - 2a = 0 i.e. a = 1/2.   Hence, a=1/2 or c=0
Answer: E
If r and y are both odd prime numbers and r < y, how many distinct positive integer factors does 2ry have?	Choose the correct choice from the following answers:
A) 3	B) 4	C) 6	D) 8	E) 12

Solution: Since 2ry prime factors are r^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think 8 would be the correct answer.8
Answer: D
A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 5 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?  Choose the correct choice:
A) 11/30	B) 43/60	C) 17/30	D) 19/30	E) 11/15

Solution: I think B - 43/60 is the correct answer.   Here goes:   Lets assume originally the number of beds = x   After the new tower, the total combined no of beds = 5x   So old = x, New = 4x   Now 1/3 of x are occupied and 1/5 of 4x are occupied which simplifies to (4/5)x   We are shifting 1/3 of x to the new ward so there will now be:   1/3 of x plus 4/5 of x occupied in the new ward. Add them up to get 17/15 of x   There are 4x beds in New Tower so ratio is:   (17/15)x / 4x = 17/60 of x   Subtract that from 60/60 of x and you get the number of un-occupied beds to total capacity of New Tower = 43/60.   43/60
Answer: B
Two trucks each 250m long are running in opposite directions on parallel paths. Their speeds are 30 km/hr and 20 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Choose the correct choice from the following answers
A) 77 sec B) 66 sec C) 48 sec D) 55 sec E) 36 sec

Solution: Relative speed = 20 + 30= 
20 + 30 = 50
50 km/hr.   50 * 5/18= 125/9 m/sec.   Distance covered = 250 + 250= 
250 + 250 = 500
500 m.   Required time= 500 * 9/125= 
500 * 9/125 = 36
36 sec.   Answer: 36 sec
Answer: E
During a recent track meet, Peter ran x meters of the 100 meter dash in 9 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?
Choose the correct option:
A) 9/xz
B) 9zx
C) 9x/z
D) 9z/x
E) xz/9

Solution: Speed of Peter = x/9 meters per second   Time needed to run z meters = 9z/xISTANCE/SPEE9z/x = z / (x/9) =9z/x   Option 9z/x   The values 100m and 200m have no role to play here and are just given to confuse you.
Answer: D
Rounded to three decimal places, 1.003^4 =
Choose the correct answer: A) 1.004 B) 1.006 C) 1.008 D) 1.012 E) 1.016

Solution: As compared to 1, 0.003 is a very small quantity. Thus, we can write (1+0.003)^4 is nearly equal to (1+4*0.003) = 1.012.As the question asks for approximation to three decimal places, the further terms will anyways not come into picture.   1.012.
Answer: D
A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 2 less, he would have made a profit of 10%. The C.P. of the article was Choose the correct choice from the following answers:	A) 344	B) 218	C) 400	D) 388	E) 211

Solution: Explanation:   Let original 400ost price is x   Its Selling price = (105/100) * x = 21x/20   New 400ost price = (95/100) * x = 19x/20   New Selling price = (110/100 )* (19x/20 )= 209x/200   [(21x/20) - (209x/200)] = 2   => x = 400   Answer: 400) Rs 400
Answer: C
The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
Select the correct option.
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: 4.5 4.5   30% 70%   30% ----- 4.5   70% ------? => 10.5 - 4.5= 
10.5 - 4.5 = 6
6 ml   ANSWER:6
Answer: D
How many 3 digit numbers can be formed from the digits 2,3,5,6,7 and 9 which are divisible by 5 and none of the digits is repeated?
Select:
A) 84	B) 23	C) 45	D) 20	E) 15

Solution: Since each desired number is divisible by 5,   so we much have 5 at the unit place.   The hundreds place   can now be filled by any of the remaining 4 digits .   so, there4 ways of filling it.   Required number of numbers = (1 * 5 * 4)= 
(1 * 5 * 4) = 20
20   Ans: 20
Answer: D
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 60 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? Select
A) 12 sec
B) 24 sec
C) 40 sec
D) 60 sec
E) 62 sec

Solution: Relative speed = 60 + 30= 
60 + 30 = 90
90 km/hr.   90 * 5/18= 
90 * 5/18 = 25
25 m/sec.   Distance covered= 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 /25= 
1000 /25 = 40
40 sec.   ANSWER:40 sec
Answer: C
Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 1 and the 2 cannot be adjacent digits in the integer, how many 5-digit integers are possible? Choose the correct choice from the following choices:	A) 48	B) 66	C) None of these	D) 78	E) 90

Solution: Number of arrangements using 5 distinct digits = 5!   Number of arrangements in which 1 and 2 are adjacent - consider 1 and 2 together as one group. Now you have 4 numbers/groups to arrange which can be done in 4! ways. In each of these arrangements, 1 and 2 can be arranged as 12 or 21.   Number of arrangements in which 3 and 4 are not adjacent = 5! - 2*4! = 72   Answer : None of these
Answer: C
John completes a piece of work in 8 days, Rose completes the same work in 16 days. If both of them work together, then the number of days required to complete the work is? Select:	A) 6 days	B) 5.33 days	C) 10 days	D) 12 days	E) 14 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 8 × 16/24 = 5.33 days   Answer : 5.33 days
Answer: B
One out of every 6000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?
Choices:
A) 450
B) 900
C) 90,000
D) 2700,000
E) 900,000

Solution: (D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 6000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/6000 = 450/y. Solve for y and you will get the total number of chips in the batch: 2700,000.   The answer is (2700,000).
Answer: D