MU-NLPC/Calc-aqua_rat huggingface dataset:
Two dice are thrown simultaneously. What is the probability of geƫng two numbers whose product is
even ?	Select:
A) 3/4	B) 1/4	C) 7/4	D) 1/2	E) None of these

Solution: Explanation:   Total number of cases = 6*6= 
6*6 = 36
36   Favourable cases=   [(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,2),(5,4)   ,(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)] = 27   So Probability = 27/36 = 3/4   3/4nswer: 3/4
Answer: A
The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 40 cents more than the commodity Y?
Choose the correct choice
A) 2007 B) 2008 C) 2009 D) 2010 E) 2011

Solution: The cost of commodity X increases by 10 cents per year relative to commodity Y.   The price of X must gain  20 + 40= 
 20 + 40 = 60
60 cents on commodity Y, which will take 6 years.   The answer is 2007.
Answer: A
√0.0081 is equal to :
Choose the correct choice from the following:
A) 0.09  B) 0.9  C) ±0.08  D) 0.81  E) None of these

Solution: √0.0081 = √0.0081/10000 = √81/10000 = 9/100= 
9/100 = 9/100 = around 0.09
0.09   0.09nswer: 0.09
Answer: A
I bought two books; for Rs.490. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss? Choose the correct choice from the following choices.
A) 337.83
B) 285.83
C) 284.83
D) 266.83
E) 299.83

Solution: x*(85/100) = (490 - x)119/100   x = 285.83   Answer: 285.83
Answer: B
Oranges are bought at 11 for a rupee and an equal number more at 9 a rupee. If these are sold at 10 for a rupee, find the loss or gain percent? Answers.
A) 22
B) 87
C) 65
D) 20
E) 28

Solution: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20   Answer: 20
Answer: D
37.	If the cost price of 15 tables be equal to the selling price of 20 tables, the loss per cent is ?	Choose the correct option
A) 20%
B) 30%
C) 25%
D) 37.5%
E) 38 %

Solution: Let C.P. of each table = Re. 1   C.P. of 20 tables = Rs. 20   S.P. of 20 table = C.P. of 15 tables = Rs. 15   loss = (5/20) x 100 % = 25%   answer :25%
Answer: C
Souju's age is 130% of what it was 10 years ago, but 81% of what it will be after 10 years. What is her present age? Choose the correct option: A) 63 years B) 54 years C) 56 years D) 36 years E) 43years

Solution: Let the age before 10 years =x. Then,   130x/100=x+10   â‡’130x=100x+1000   â‡’x=1000/30=33   Present age =x+10=33+10= 
33+10 = 43
43   ANSW43yearsR:43years
Answer: E
(469 + 174)^2 - (469 - 174)^2 /(469 x 174)= ?  Select
A) 643
B) 2
C) 295
D) 4
E) 185

Solution: Given exp. =(a + b)^2 - (a - b)^2/ab   =4ab/ab   = 4 (where a = 469, b = 174.)   Answer is 4.
Answer: D
Of the three-digit positive integers whose three digits are all different and nonzero, how many are odd integers greater than 700?
Choose one:
A) 84
B) 91
C) 100
D) 105
E) 243

Solution: Number of combinations for type 1 : 1*7*4= 
1*7*4 = 28
28   Number of combinations for type 2: 1*7*5= 35   Number of combinations for type 3 : 1*7*4= 
1*7*4 = 28
28   Thus, total numbers possible= 28+35+28= 
28+35+28 = 91
91.   91 is thus the correct answer
Answer: B
In what ratio should a variety of rice costing Rs. 6.5 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg? Choose one
A) 5/6 B) 5/9 C) 5/4 D) 5/3 E) 7/6

Solution: Let us say the ratio of the quantities of cheaper and dearer varieties   = x : y   By the rule of allegation, x/y   = (8.75 - 7.50) / (7.50 - 6.5) =5/4   Answer: 5/4
Answer: C
Joe drives 360 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour?	Choices:
A) 42	B) 53	C) 50	D) 54	E) 56

Solution: t1= 360/60= 
360/60 = 6
6 hours   t2=120/40= 
120/40 = 3
3 hours   T=t1+t2=9 hours   Avg speed = Total Distance/T   = 480/9 = 53mph=53
Answer: B
If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:  Answers
A) 2.87  B) 2.965  C) 3.876  D) 3.9  E) 4.526

Solution: log5 512 = log 512/ log 5   = log 2^9/log(10/2)   =9 log 2 /log 10 - log 2   =(9*0.3010)/1-0.3010   =2.709/0.699 = 2709/699   = 3.876   ANSWER 3.876
Answer: C
John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/2 the number of cans that Karen collected and 1/3 the number of cans that Luke collected. The number of cans that Karen collected was what fraction of the total number of cans that John, Karen, and Luke collected? Choose one:
A) 1/5
B) 1/3
C) 2/5
D) 1/2
E) 2/3

Solution: John = (1/2)Karen --> Karen = 2(John)   John = 1/3(Luke) --> Luke = 3(John)   Total = 6(John)   Karen/Total = 2/6 = 1/3   Answer: 1/3
Answer: B
From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 25 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?
Choose one:	A) 36	B) 39	C) 40	D) 41	E) 42

Solution: 1.25x=45 --> 5/4*x=45 --> x=45*4/5=180/5= 
180/5 = 36
36.   36nswer: 36.
Answer: A
James can finish a job in 20 dasy he worked for 10 days alone and completed the remaining part working with David 2 days how many days would both David and James together take to complete the entire job?	Options:  A) 4  B) 5  C) 10  D) 12  E) 14

Solution: Explanation:   James and David complete half work in 2 days   => they can complete whole work in 4 days   4nswer: Option 4
Answer: A
The difference between the local value and face value of 7 in the numeral 657903 is:	Options:
A) 0
B) 7896
C) 6993
D) 903
E) 897

Solution: (Local value)-(Face value)= (7000-7)= 
(7000-7) = 6_993
6993.   Answer: 6993
Answer: C
A shopkeeper sold 50articles at the cost price of 60 articles. Then find the profit% or lost% Select.
A) 20%	B) 22%	C) 25%	D) 30%	E) 35%

Solution: here 50 articles selling price = 60 articles cost price   so the difference = 60-50= 
60-50 = 10
10   % of profit= 10*100/50= 
10*100/50 = 20
20%   correct option is 20%
Answer: A
x is a positive integer of S less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?	Choose the correct choice from the following choices
A) 21
B) 22
C) 23
D) 24
E) 25

Solution: Took me more than 2 mins to solve.   That's how I did it.   x is between 1-499 included.   Smallest number that can be written as 7n+1 (7*0+1) is 1   Largest number that can be written as 7n+1 is (7*71 +1) is 498   So there are total 72 numbers that can be written as 7n+1   Because x can also be written as 3m+2, we have to see how many numbers that can be written as 7n+1 also can be written as 3m+2   7*0+1 can not be written in the form 3m+2   7*1+1 can be written in the form 3m+2   7*2+1 can not be written in the form 3m+2   7*3+1 can not be written in the form 3m+2   7*4+1 can be written in the form 3m+2   Here we see a sequence that one out of every 4 numbers can be written as 3m+1   72/4= 24 numbers can be written as 3m+1   24 is the answer
Answer: D
Rs.200 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?	Choose the correct choice from the following choices
A) 388 B) 266 C) 120 D) 150 E) 267

Solution: 4x 5x 6x   100 50 25   400x + 250x + 150x = 20000   x = 25   6x = 150   Answer: 150
Answer: D
If m > 0, y > 0, and x is m percent of 2y, then, in terms of y, m is what percent of x?
Choose the correct choice from the following answers:  A) y/200  B) 2y  C) 50y  D) 50/y  E) 5000/y

Solution: y/200nswer:   y/200 = Y/200,   Done this by taking numbers:   Let 10 (x) be 5% (m) of 2 * 100 (y)   Then m/x*100 = 5/10*100= 
5/10*100 = 50
50% or 1/2   50% or 1/2 in terms of Y= 100/200 = Y/200   y/200NSWER:y/200
Answer: A
A boat running downstream cover a distance of 16km in 2 hr while covering the same distance upstream it takes 4 hr then the speed of the boat still in the water	Choose the correct choice from the following answers.
A) 43km/hr
B) 78km/hr
C) 9km/hr
D) 7km/hr
E) 3km/hr

Solution: rate down stream=(16/2)= 
(16/2) = 8
8 kmph   rate upstream=(16/4)= 
(16/4) = 4
4 kmph   speed still water=1/2(8+4)kmph=km/hr   Answer(9km/hr)
Answer: C
If the two-digit integers G and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of G and N?
Select the correct option
A) 181  B) 165  C) 121  D) 99  E) 44

Solution: Since the question asks for the answer that CANNOT be the sum of G and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.   We're told that G and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of M and N.   Let's start with the 'easiest' answer first:   44. Can we get to 44 in the manner described?   Yes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E   Now let's work through the rest of the list....   Can we get to 99 in the manner described?   Yes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D   Can we get to 121 in the manner described?   Yes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C   Can we get to 165 in the manner described?   Yes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B   There's only one answer left....   181
Answer: A
The ratio of daily wages of two workers is 4 : 3 and one gets daily Rs 9 more than the other, what are their daily wages?  Choose the correct choice from the following
A) Rs 32 and Rs 24
B) Rs 60 and Rs 45
C) Rs 80 and Rs 60
D) Rs 36 and Rs 27
E) Rs 36 and Rs 24

Solution: let us take second worker wages= x   so from the given data   first worker wages= x+9   from the qstn we know that wages of first/ wages of second=4/3   so (x+9)/x = 4/3   ==> 3x+27=4x   ==> x=27   so x+9= 36   so the answer is 36rs and 27rs   ANSWER:Rs 36 and Rs 27
Answer: D
In an election between two candidates, one got 60% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 2000, the number of valid votes that the other candidate got, was: Answers
A) 1200  B) 750  C) 800  D) 600  E) 900

Solution: Number of valid votes = 80% of 2000 = 1600.   Valid votes polled by other candidate = 40% of 2000   =(40/100)X2000 =800   ANSWER = 800
Answer: C
If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x? Choose the correct choice from the following
A) 9,827
B) 10,816
C) 11,433
D) 12,908
E) 13,482

Solution: The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9.   The answer is 10,816.
Answer: B
If the selling price of 7 Candle is same as the cost price of 14 candle. Find the gain or loss percentage?
Pick one:  A) 85%  B) 65%  C) 75%  D) 35%  E) 100%

Solution: Let the C.P of each candle be Re 1. Then,   S.P of 7 candle = C.P of 14 candle= Rs. 14   Now, C.P of 7 candle= Rs.7, S.p of 7 candle= Rs 14   Gain = Rs ( 14 -7 )= 
( 14 -7 ) = 7
Rs 7.   Gain%= ( 7/7× 100 ) % = 100%   Answer : 100%
Answer: E
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?  Choose the correct answer
A) 207
B) 209
C) 300
D) 305
E) 307

Solution: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).   Required number   of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)   = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)   = (24 + 90 + 80 + 15)= 
(24 + 90 + 80 + 15) = 209
209   ANSWER 209
Answer: B
By selling 99 pens, a trader gains the cost of 11 pens. Find his gain percentage?
Choose the correct choice from the following:
A) 11 1/3%	B) 11 7/3%	C) 11 1/8%	D) 11 1/3%	E) 11 1/9%

Solution: Let the CP of each pen be Rs. 1.   CP of 99 pens = Rs. 99   Profit = Cost of 11 pens   = Rs. 11   Profit% = 11/99 * 100   = 11 1/9%   Answer: 11 1/9%
Answer: E
How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?
Pick.
A) 36 kg  B) 42 kg  C) 54 kg  D) 63 kg  E) 60 kg

Solution: S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.   C.P. of 1 kg of mixture = Rs.((100/110) x 9.24) = Rs. 8.40   C.P. of 1 kg sugar of 1st kind Rs.9   Cost of 1 kg sugar of 2nd kind Rs.7   Mean Price Rs. 8.40   Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.   Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind.   Then, 7 : 3 = x : 27   x =	(7 x 27)/3	= 63 kg.   Answer:63 kg
Answer: D
Find the principle on a certain sum of money at 5% per annum for 2 years if the amount being Rs.1120? Choices: A) 1018 B) 1067 C) 1977 D) 1056 E) 1097

Solution: 1120 = P [1 + (5*2)/100]   P= 1018   1018nswer: 1018
Answer: A
Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 64 hours and 121 hours respectively. The ratio of their speeds is
Choose the correct choice from the following:  A) 8 : 7  B) 11 : 8  C) 6 : 7  D) 9 : 16  E) None

Solution: Sol.   Let us name the trains as A and B. Then,   (A's speed) : (B's speed) = √b : √a   = √121 : √64   = 11 : 8.   Answer 11 : 8
Answer: B
The average age of a family of 5 was 32 . It fell to 18 when the grandmother died.How old was she ?
Choose the correct choice:	A) 86	B) 87	C) 88	D) 89	E) 90

Solution: Avg of 5 = 32   total/5=32   Total age of 5 = 160   After grandma died, total ll be   total/4=18   Total age of 4 = 72   Age of grandma ll be => 160-72= 
160-72 = 88
88   ANSWER:88
Answer: C
How many times the keys of a writer have to be pressed in order to write first 250 counting no's?	Choose the correct choice from the following options: A) 632 B) 642 C) 652 D) 662 E) 672

Solution: 1 to 9 = 9 * 1= 
9 * 1 = 9
9   10 to 99= 90 * 2= 
90 * 2 = 180
180   100 to 250= 151 * 3= 
151 * 3 = 453
453   -----------   642   642
Answer: B
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
Choose the correct choice from the following answers.
A) 3/8 B) 3/2 C) 3/5 D) 3/6 E) 3/7

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train   = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23   ==> 27 x + 17 y   = 23 x + 23 y   ==> 4 x = 6 y   ==> x/y   = 3/2.   Answer: 3/2
Answer: B
Raju age after 45 years will be 5 times his age 5 years back, What is the present age of Raju Choose the correct choice from the following answers
A) 28.5 B) 17.2 C) 10.2 D) 17.5 E) 66.2

Solution: Clearly,   x+45 = 5(x-5)   <=> 4x = 70 => x = 17.5   Answer:17.5
Answer: D
The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 60%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?	Choose one
A) 20%  B) 24%  C) 30%  D) 43%  E) 79%

Solution: take it as original output =100.   to meet demand increase by 10%, then output=110.   to meet holiday demand , new output increase by 60% then output equals 176   To restore new holidy demand output to original 100.   final -initial/final*100   =76/176*100=8/33*100=43% approxiamately.   option 43% is correct.
Answer: D
When positive integer x is divided by 12, the quotient is y and the remainder is 3. When 2x is divided by 11, the quotient is 3y and the remainder is 6. What is the value of 21y – x? Pick one.
A) 3	B) 2	C) -1	D) -2	E) -3

Solution: (1) x = 12y+3   (2) 2x = 33y+6   (2)-(1): x=21y+3   21y-x=-3   The answer is -3.
Answer: E
What is the remainder when 5632 is divided by 6?  Choose the correct choice from the following: A) 2 B) 1 C) 0 D) 4 E) 3

Solution: f the number is divisible by both 2 and 3, then number will be divisible by 6.   As there is 2 an even number in units place it is divisible by 2.   sum of digits is:  5+6+3+2= 
  5+6+3+2 = 16
16. 16 is not divisible by 3 hence number is not divisible by 3.   The nearest multiple of 6 is 5630.   5632-5630= 
5632-5630 = 2
2.   2nswer:2
Answer: A
The cost to park a car in a certain parking garage is $20.00 for up to 2 hours of parking and $1.75 for each hour in excess of 2 hours. What is the average (arithmetic mean) cost per hour to park a car in the parking garage for 9 hours?
Choose the correct answer:  A) $3.58  B) $1.67  C) $2.25  D) $2.37  E) $2.50

Solution: Total cost of parking for 9 hours = 20$ for the first 2 hours and then 1.75 for (9-2) hours = 20+7*1.75= 
20+7*1.75 = 32.25
32.25   Thus the $3.58VER$3.58GE parking price= 32.25/9 = 3.58 $   $3.58 is the correct answer.
Answer: A
For dinner at a restaurant, there are x choices of appetizers, y + 1 main courses, and z+1 choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?
Choose the correct choice from the following answers
A) x + y + z + 1
B) xyz + xz
C) xy + z + 1
D) xz+x+xyz+xy
E) xyz + 1/2

Solution: x appetizers,   y + 1 main courses,   z+1 dessert   Required: 1 appetizer, 1 main course, and 1 dessert   Number of ways possible = xC1*(y+1)C1*(z+1)C1 {NC1 = N! / (N-1)!*1! = N}   Hence, number of ways = x(y+1)(z+1) = (x + xy)(z+1)=xz+x+xyz+xy   Correct Option: xz+x+xyz+xy
Answer: D
A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 36 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used?  Pick.
A) 3  B) 4  C) 6  D) 9  E) 12

Solution: yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as:   A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 36 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used?   So for a job to be done in 2 hours R = 1/2   R_a(Rate of Machine R) = 1/36   R_s(Rate of Machine S) = 1/36   Lets say x machines are used to attain the desired rate, thus   x/36+x/36 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours)   (x+x)/36 = 1/2   2x/36 = 1/2   x = 9.   QA = 9 (ANSWER 9)
Answer: D
At a certain college 25% of the students join a band, 25% play a sport and 20% both join the band and play a sport. if a randomly selected student is a member of the band, what is the probablility that the student also plays a sport?	Options:
A) 1) 3/4
B) 2)1/5
C) 3)2/5
D) 4)1/2
E) 5)4/5

Solution: This is the way to approach the question:   25% of the students join a band => 25% of the students either only join a band or both join a band and play sports   25% of the students play sports => 25% of the students either only play sports or both play sports and join a band   If a randomly selected student is a member of the band, then probability that the student also plays a sport = percentage of cases in which the student can do both/percentage of cases in which the student can just play sports or do both   =20%/25% = 4/5   The answer is therefore (5)4/5)
Answer: E
A trumpet section includes five musicians. If they hold an audition to determine chair order within the section, and there are to be no ties, how many distinct chair orders can result?  Choose the correct choice from the following answers:
A) 240
B) 125
C) 120
D) 100
E) 25

Solution: We have a word problem using permutations. We must identify the number of total items in the group. There are five possible musicians who could be placed in the first chair, four possible musicians for the second, three for the third, two for the fourth, and one for the fifth. To determine the number of possible orderings, we multiply these numbers, which we can express as 5!. Now 5! = (5)(4)(3)(2)(1) = 120.   ANS:120
Answer: C
There are four temples, one plant of flower and a pond.
A boy goes there and before entering the first temple he plucks the flower and has to take a bath in the pond before entering into every temple.
The specialty of the pond is that if a person is carrying flowers with him and he takes a dip in the pond the number of the flowers gets doubled.
He takes a dip and offers some flowers in the first temple, then he again takes a dip and offers flowers in second temple , again the same in the third temple, and again the same in the fourth temple
The boy offers EQUAL number of flowers in all the four temples and goes back with EMPTY hand after offering flower in the fourth temple..How many flowers could he have offered in each temples?	Choose one:	A) 20	B) 24	C) 30	D) 48	E) 60

Solution: Note : all temples received equal flowers   lets start with the 4th temple , lets say all x flowers were given, then before dip x/2 flowers must have been left after offering in the 3rd temple. ( only then x/2 flowers could be doubled to become x and all offered in the 4th temple with nothing left over )   so x/2 flowers were left after offering made in the 3rd temple   going backwards .....   (x/2) left after 3rd temple + x given in the 3rd temple =(3x/2) {after dip, total flowers just before offering in the 3rd temple}   so before dip (3x/4)   (3x)/4 left after 2nd temple + x given in the 2nd temple = (7x)/4{after dip, total flowers just before offering in the 2nd temple}   so before dip (7x)/8   (7x)/8 left after 1st temple + x given in the 1st temple = (15x)/8{after dip, total flowers just before offering in the 1st temple}   so before dip (15x)/16   now since number of flowers have to be an integer then x has to be a multiple of 2,4,8 and 16   only 48 satisfies   Hence Answer = 48
Answer: D
How many times are the hands of a clock at right angle in 5 days?  Pick one
A) 202	B) 220	C) 210	D) 212	E) 222

Solution: In 1 day, they are at right angles 44 times.   In 5 days, they are at right angles 220 times. Answer: Option 220
Answer: B
10 men and 15 women together can complete a work in 4 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?	Choices:  A) 100 days  B) 667 days  C) 177 days  D) 187 days  E) 225 days

Solution: 1 man's 1 day work = 1/100   (10 men + 15 women)'s 1 day work = 1/4   15 women's 1 day work = (1/4 - 10/100) = 3/20   1 woman's 1 day work = 1/100   1 woman alone can complete the work in 100 days.   100 daysnswer:100 days
Answer: A
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?	Choose the correct choice from the following answers
A) 20/66	B) 20/63	C) 20/87	D) 20/98	E) 20/12

Solution: Required probability = (5C3 . 4C1)/9C4   = (10 * 4)/126   = 20/63   Answer:20/63
Answer: B
Two cars are traveling towards each other. If car A is traveling at a speed of 50 mph and car B is traveling 12% slower, how much time will it take the cars to meet if the initial distance between the two is 705 miles?  Select the correct option:  A) Six hours and 30 minutes.  B) Seven hours and 30 minutes.  C) Eight hours and 20 minutes.  D) Nine hours and 15 minutes.  E) Ten hours and 20 minutes.

Solution: since they are travelling towards each other, the total speed is 50 mph + 50*0.88 = 94 mph (0.88 since, the other car is 12% less than first one)   Distance to be covered is 705, so time taken = distance/speed = 705/94= 
705/94 = 15/2 = around 7.5
7.5 hours or 7 hours and 30 mins.   Answer is Seven hours and 30 minutes.: Seven hours and 30 minutes.
Answer: B