MU-NLPC/Calc-aqua_rat huggingface dataset:
Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 30 days.
Answers.
A) 16 days.
B) 17 days.
C) 18 days.
D) 19 days.
E) 20 days.

Solution: They together completed 4/10 work in 4 days.   balance 6/10 work will be completed by Arun alone in   30*6/10= 
  30*6/10 = 18
18 days.   ANSWER:18 days.
Answer: C
During a sale of 20% on everything in a store, a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies. The store still makes a profit of 10% on this sale. What is the mark up percentage on each candy?  Pick one
A) 100%  B) 80%  C) 75%  D) 66+2/3%  E) 55%

Solution: Hi Akhil, I can share the way I solved it..   Let's say Marked price = M   So, there's a discount of 20% on M So, new S.P. = 80% of M   Now, the child convinces the owner to sell 20 candies for the price of 14 candies .   Let's say each candy after discount is 1$. So, S.P. of 20 candies = 20$. THe child bought it for 14 $ So, he got a discount of  6/20 *100= 
 6/20 *100 = 30
30%   So, the latest S.P.= 70% of 80% of M = 0.7* 0.8 M   Now, we are given that the shopkeeper still makes a profit of 12%. So we have ,   0.7 * 0.8 * M = 1.12 C.P   So, we get, M= 2 C.P.   i.e. Marked price was kept 100% above C.P.   75%
Answer: C
Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 4 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off?
Choose the correct choice from the following:
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: Let x be the total time it takes for the cistern to fill.   4/12 + x/15 = 1   x/15 = 2/3   x = 10   After the first pipe is turned off, it takes 6 more minutes to fill the cistern.   The answer is 6.
Answer: A
Gaurav spends 30% of his monthly income on food articles, 40% of the remaining on conveyance and clothes and saves 50% of the remaining. If his monthly salary is Rs. 18,400, how much money does he save every month ?	Select:  A) 3864  B) 2338  C) 3799  D) 1267  E) 2991

Solution: Explanation:   Saving = 50% of (100 - 40)% of (100 - 30)% of Rs. 18,400   = Rs. (50/100 * 60/100 * 70/100 * 18400) = Rs. 3864.   3864nswer: 3864) 3864
Answer: A
4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how
many days will 10 women working together finish it ?
Choose the correct choice from the following options
A) 30 days B) 40 days C) 50 days D) 60 days E) None of these

Solution: Explanation:   Let 1 man's 1 day work = x   and 1 woman's 1 days work = y.   Then, 4x + 6y = 1/8   and 3x+7y = 1/10   solving, we get y = 1/400 [means work done by a woman in 1 day]   10 women 1 day work = 10/400 = 1/40   10 women will finish the work in 40 days   Answer: 40 days
Answer: B
In a company of 15 employees, 6 employees earn $37,000, 5 employees earn $42,000, and the 4 highest-paid employees earn the same amount. If the average annual salary for the 15 employees is $45,000, what is the annual salary for each of the highest-paid employees?
Choose the correct choice from the following options:
A) $56,250	B) $57,750	C) $59,250	D) $60,750	E) $62,250

Solution: 6*37,000+5*42,000+4x=15*45,000   4x=675,000-222,000-210,000   4x=243,000   x=60,750   The answer is $60,750.
Answer: D
$500 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is
Choose the correct choice from the following choices
A) $100 B) $150 C) $125 D) $200 E) $250

Solution: A:(B+C) = 2:3   A's share = 500*2/5= 
500*2/5 = 200
$200   Answer is $200
Answer: D
Eight years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages Pick:
A) A)35	B) B)28	C) C)45	D) D)25	E) E)26

Solution: Explanation:   Let the present age of P and Q be 3x and 4x respectively.   Eight years ago, P was half of Q in age   => 2(3x – 8) = (4x – 8)   => 6x – 16 = 4x – 8   => 2x = 8   => x = 4   7x=7*4= 
7*4 = 28
28   Answer: Option 28
Answer: B
28 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
Choose the correct choice from the following options.
A) 13.25  B) 38.25  C) 33.25  D) 12.25  E) 31.25

Solution: x/7 = y/9 => x:y = 7:9   7/16 * 28= 
7/16 * 28 = 49/4 = around 12.25
12.25   ANSWER:12.25
Answer: D
If the number is divided by 3, it reduced by 24. The number is
Answers:
A) A)51
B) B)50
C) C)45
D) D)40
E) E)36

Solution: Explanation:   Let the number be x. Then,   x - (x/3) = 24 => 2x/3 = 24   => x = 36   Answer: Option 36
Answer: E
A grocer has a sale of Rs. 3435, Rs. 3927, Rs. 3855, Rs. 4230 and Rs. 3562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 3500? Pick
A) s. 1991
B) s. 2991
C) s. 3991
D) s. 4991
E) s. 5991

Solution: Explanation:   Total sale for 5 months = Rs. (3435 + 3927 + 3855 + 4230 + 3562) = Rs. 19009.   Required sale = Rs. [ (3500 x 6) â€“ 19009 ]   = Rs. (21000 â€“ 19009)   = Rs. 1991.   s. 1991nswer s. 1991
Answer: A
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.74 less, he could have gained 25%. What is the cost price?	Choose the correct answer:
A) s.370
B) s.375
C) s.375
D) s.350
E) s.300

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   74 ----- ?=> 370   s.370NSWER:s.370
Answer: A
Ian is paid an hourly wage, totaling $400 for h hours of work in a week, where h >0. If Ian's hourly wage increases by 25% and Ian decides to work 25% fewer hours each week, how much will Ian be paid in a week?  Choices: A) $200 B) $375 C) $400 D) $425 E) $600

Solution: let No of hours ian worked = h   and wage per hour = w   therefore w*h = 400   if he decides to work 25% fewer hours = 0.75 * h   and 25% more age is paid = 1.25 * w   therefore 1.25*w*0.75*h = 1.25*0.75*400= 
1.25*0.75*400 = 375
375   ANSWER:$375
Answer: B
A and B go around a circular track of length 400 m on a cycle at speeds of 36 kmph and 36 kmph. After how much time will they meet for the first time at the starting point?	Choose the correct choice from the following answers.
A) 40 sec
B) 198 sec
C) 178 sec
D) 665 sec
E) 276 sec

Solution: Time taken to meet for the first time at the starting point   = LCM { length of the track / speed of A , length of the track / speed of B}   = LCM { 400/ (36 * 5/18) , 400/ (36 * 5 /18) }   = LCM (40, 40) = 40 sec.   40 secnswer:40 sec
Answer: A
If 821562 is to be divisible by 5, what is the least whole number that should be added to it?
Choose the correct choice from the following.
A) 6  B) 4  C) 5  D) 2  E) 3

Solution: A number is divisible by 8 if the number formed by the last three digits is divisible by 8.   Here, 821562 =562,   the next multiple of 9 is 568.   6 must be added to 821562 to make it divisible by 8   6
Answer: A
If a:b=2:3 and b:c=2:4 find a:b:c? Choose the correct choice from the following options.
A) 6:2:3 B) 2:6:3 C) 2:3:6 D) 3:2:6 E) 6:3:2

Solution: a:b = 2:3, b:c = 2:4   2:3   2:4   (a = a × b, b = b × b and c = b × c)   a:b:c = 2:3:6   2:3:6
Answer: C
If x = -2 and y = -4, what is the value of 5(x-y)^2 - xy ?  Choose the correct choice from the following choices
A) 12	B) 13	C) 15	D) 18	E) 22

Solution: x = -2 and y = -4   x-y = -2 - (-4) = -2+4= 
-2+4 = 2
2   x*y= -2 * -4= 
-2 * -4 = 8
8   Now we apply it in the equation 5(x-y)^2 - xy=5 (2)^2-8   ==>5*4 -8 = 20-8= 
20-8 = 12
12   12nswer : 12
Answer: A
Country X taxes each of its citizens an amount equal to 11 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income? Choose one.
A) $40,000 B) $56,000 C) $64,000 D) $58,000 E) $80,000

Solution: Equation is correct, so math must be a problem.   0.11*40,000+0.2*(x-40,000)=8,000 --> 4,400+0.2x-8,000=8,000 --> 0.2x=11,600 --> x=58,000.   Answer: $58,000.
Answer: D
A sum fetched a total simple interest of Rs. 4016.25 at the rate of 8% p.a. in 5 years. What is the sum?	Answers.
A) Rs. 10060.625 B) Rs. 10040.62 C) Rs. 12040.62 D) Rs. 20040.625 E) Rs. 10030.625

Solution: Principal = (100 * 4016.25) / (8 * 5) = Rs. 10040.625.   ANSWER:Rs. 10040.62
Answer: B
If any amount is distributed among A ,B and C so that the part of A is doubled that of the part of B and part of b is 3 time the part of C .Find the ratio among their parts. Pick one:
A) 1:2:4	B) 1:4:1	C) 8:4:1	D) 2:4:1	E) 6:3:1

Solution: By the assumptions as mentioned we have A=2B and B=3C. So A=2(3C) and we get A=6C. We have, therefore, A:B:C = 6C:3C:C. By cancelling the ratio with C we have 6:3:1. The answer is, therefore, 6:3:1.
Answer: E
An antique shop has four different vases (vase 1, vase2, vase3, vase4) which are valued at different prices. If vase2 is 30% less in value than vase1, vase3 is 10% less than vase2, and vase4 is 5% less than vase3. what percent of vase1's cost is a vase3?
Options:
A) 50.85%
B) 59.85%
C) 60.85%
D) 40.5%
E) 39.85%

Solution: Let the cost of vase1 be $100   I) vase2 is 30% less in value than vase1--100-30=70   II) vase3 is 10% less than vase2--70-7=63   III) vase4 is 5% less than vase3--63-3.15=59.85   what percent of vase1's cost is a vase3=59.85*100/100   Answer is 59.85%
Answer: B
A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
Choose the most appropriate option:  A) 200  B) 962  C) 267  D) 258  E) 268

Solution: Profit on first article   = 20% of 1000   = 200.   This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.   200nswer:200
Answer: A
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 5/6 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?	Choose the correct choice
A) 4/7  B) 5/9  C) 6/11  D) 7/12  E) 8/13

Solution: Let x be the number of workers on the day crew.   Let y be the number of boxes loaded by each member of the day crew.   Then the number of boxes loaded by the day crew is xy.   The number of boxes loaded by the night crew is (5x/6)(3y/4) = 5xy/8   The total number of boxes is xy + 5xy/8 = 13xy/8   The fraction loaded by the day crew is xy / (13xy/8) = 8/13   The answer is 8/13.
Answer: E
A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? Choose one:
A) 1.8 B) 1.5 C) 1.3 D) 1.2 E) 1.6

Solution: 72 --- 9 DS = 8   ? ---- 1   45 ---- 9 US = 5   ? ---- 1 S = ?   S = (8 - 5)/2= 
(8 - 5)/2 = 3/2 = around 1.5
1.5   Answer: 1.5
Answer: B
The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x5x cents per day while the price of wheat is decreasing at a constant rate of 2√∗x−x2∗x−x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat? Choose one:
A) $4.50
B) $5.10
C) $5.30
D) $5.50
E) $5.60

Solution: Let yy be the # of days when these two bushels will have the same price.   First let's simplify the formula given for the rate of decrease of the price of wheat: 2√∗x−x=1.41x−x=0.41x2∗x−x=1.41x−x=0.41x, this means that the price of wheat decreases by 0.41x0.41x cents per day, in yy days it'll decrease by 0.41xy0.41xy cents;   As price of corn increases 5x5x cents per day, in yy days it'll will increase by 5xy5xy cents;   Set the equation: 320+5xy=580−0.41xy320+5xy=580−0.41xy, solve for xyxy --> xy=48xy=48;   The cost of a bushel of corn in yy days (the # of days when these two bushels will have the same price) will be 320+5xy=320+5∗48=560320+5xy=320+5∗48=560 or $5.6.   Answer: $5.60.
Answer: E
If C + D = 12 and C and D are positive integers, which of the following is a possible value for 5C + 8D?	Select the correct option:
A) 111  B) 121  C) 150  D) 171  E) 180

Solution: c + d = 11   5c + 8d = 5c + 5d + 3d = 5(c+d) + 3d = 60 + 3d=D=30   D=30   c+d=12=150+30=9=150=12-30=-18   150=-18   5150 + 8D=5(-18)+8(30)=-90+240= 
-90+240 = 150
150   Hence, 150 is the right answer.
Answer: C
Two years ago, Ram put $1,000 into a savings account. At the end of the first year, his account had accrued $200 in interest bringing his total balance to $1,200. The next year, his account balance increased by 20%. At the end of the two years, by what percent has Ram's account balance increased from his initial deposit of $1,000 ?	Choose one:
A) 19%
B) 30%
C) 42%
D) 45%
E) 25%

Solution: investment 1000 dollars   1 st year total gained = 200   total amount end of first year = 1200   second year account increased by 20 % = 1200*0.2= 
1200*0.2 = 240
240   therefore total amount by second year end= 1420   so total percentage increase in money = (1420-1000)*100/1000= 
(1420-1000)*100/1000 = 42
42 %   42%orrect Answer 42%=42%
Answer: C
A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
Choose one
A) 16 hours  B) 28 hours  C) 18 hours  D) 19 hours  E) 10 hours

Solution: 1/A + 1/B + 1/C = 1/8 (Given)   Also given that A = 2B and B = 2C   => 1/2B + 1/B + 2/B = 1/8   => (1 + 2 + 4)/2B = 1/8   => 2B/7 = 8   => B = 28 hours.   Answer:28 hours
Answer: B
How many positive integers P less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ? Options.
A) 19	B) 18	C) 17	D) 16	E) 15

Solution: We're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?   The first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?   1, 3, 5, 7   None of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15 = 15
Answer: E
In Town X, 64 percent of the population are employed, and 38 percent of the population are employed males. What percent of the employed people in Town X are females?
Choose the correct choice from the following options.
A) 16%
B) 25%
C) 32%
D) 40%
E) 52%

Solution: We are asked to find the percentage of females in employed people.   Total employed people 64%, out of which 38 are employed males,hence 26% are employed females.   (employed females)/(total employed people)=26/64=40%   Answer: 40%.
Answer: D
A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?	Answers
A) 1/3  B) 2/3  C) 2/5  D) 3/7  E) 3/11

Solution: Let b stand for boy and g for girl. The sample space of the experiment is   S = {(g, g), (g, b), (b, g), (b, b)}   Let E and F denote the following events :   E : ‘both the children are girls’   F : ‘at least one of the child is a girl’   Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}   Now E n F = {(g,g)}   Thus P(F) = 3/4   and P (E n F )= 1/4   Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3   1/3
Answer: A
The speed of a boat in upstream is 70 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?  Select:
A) 10 kmph
B) 67 kmph
C) 5 kmph
D) 88 kmph
E) 12 kmph

Solution: Speed of the boat in still water   = (70+80)/2= 
(70+80)/2 = 75
75 kmph. Speed of the stream= (80-70)/2= 
(80-70)/2 = 5
5 kmph.   Answer:5 kmph
Answer: C
While driving from A-ville to B-town, Harriet drove at a constant speed of 100 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 150 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?  Choose the correct choice from the following options.
A) 138
B) 148
C) 150
D) 162
E) 180

Solution: 5hr = 300min.   If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.   Now let plug in ans. D or E and verify which one give same distance on each leg.   E. t= 180min   * leg A-B ---> d = 100.180/60 = 18000/60   * leg B-A ----> d = 150*120/60 = 18000/60   so the correct ans. is180
Answer: E
If x, y, and z are positive integers, and 2x = 5y = 6z, then the least possible value of x + y + z is
Answers:
A) 15 B) 26 C) 37 D) 42 E) 60

Solution: Take LCM of 2,5 and 6 = 30   Now 2x = 30 => x =15   5y = 30 => y = 6   6z = 30 => z =5   15+6+5= 
15+6+5 = 26
26.   Option 26.
Answer: B
Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 36 kmph respectively. In what time will they be clear of each other from the moment they meet?	Choices:  A) 18.4 sec  B) 77 sec  C) 76 sec  D) 20 sec  E) 66 sec

Solution: Relative speed = (42 + 36) * 5/18 = 21.7 mps.   Distance covered in passing each other = 120 + 280= 
120 + 280 = 400
400 m.   The time required= d/s = 400/21.7 = 18.4 sec.   18.4 secnswer:18.4 sec
Answer: A
P,Q and R enter into a partnership in the ratio 7/2 : 4/3 : 6/5. After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs.21600, then B’s share in the profit is:	Choose the correct choice from the following answers.
A) Rs.2100 B) Rs 2400 C) Rs.3600 D) Rs.4000 E) Rs.3000

Solution: Ratio of initial investments = 105 : 40 : 36.   Let the initial investments be 105x, 40x & 36x.   Therefore, P : Q : R = 105x * 4 + 150/100 x 105x * 8 : 40x * 12 : 36x * 12   = 1680x : 480x : 432x = 35 : 10 : 9.   Therefore, Q’s share = Rs. 21600 * 10/54   = Rs.4000.   ANSWER:Rs.4000
Answer: D
What will be the remainder when 8-3 + 3^5 + 2^10 is divided by 4?	Answers
A) 12	B) 3	C) 16	D) 0	E) 9

Solution: The multiplication(e.g. 2^10) is done first and then the sum(e.g. 15+20) and   subtraction (e.g. 8-3), and after all this expression it should be divided by 4 and the answer is 0, option 0.
Answer: D
A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? Answers.
A) 9:7 B) 9:8 C) 9:1 D) 9:2 E) 9:9

Solution: (3*6 + 6*6): (4*12)   54:48 => 9:8   Answer:9:8
Answer: B
Find the numbers which are in the ratio 3:2:4 such that the sum of the first and the second added to the difference of the third and the second is 28?
Select:	A) 4,3,22	B) 4,4,22	C) 12,6,16	D) 9,6,12	E) 9,2,23

Solution: Let the numbers be a, b and c.   a:b:c = 3:2:4   Given, (a + b) + (c - b) = 21   => a + c = 28   => 3x + 4x = 28 => x = 4   a, b, c are 3x, 2x, 4x   a, b, c are 12, 8, 16.   Answer:12,6,16
Answer: C
In a city the doors of buildings where numbered from 1 to 100. How many 3’s are there as the door number?  Choose the correct answer:
A) 10
B) 20
C) 30
D) 40
E) 50

Solution: We will have the 3’s as follows 3,13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93.   In 33 we have 2 3’s. So we get 20 3’s from 1 to 100.   Note: for any numbers from 1 to 9 we’ll get 20 as answer.   Answer 20
Answer: B
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: Choose the correct answer:
A) 200 m B) 225 m C) 245 m D) 250 m E) 300 m

Solution: Explanation:   Speed =45 X 5/18 m/sec =25/2 m/sec   Time = 30 sec.   Let the length of bridge be x metres.   Then,	130 + x	/30=25/2   2(130 + x) = 750   x = 245 m.   ANSWER IS 245 m
Answer: C
If 0.75: x :: 5:8, then x is equal to:
Choose the correct option.
A) 1.12 B) 1.16 C) 1.20 D) 1.3 E) None of these

Solution: Explanation:   (x * 5) = (0.75 *8)= 
(0.75 *8) = 6
6/5= 
6/5 = 6/5 = around 1.2
1.20   Answer: 1.20
Answer: C
If y = x^2 + ux + v, y is minimum when x is:  Select the correct option
A) u/u B) -u/u C) -u/2 D) -v/2 E) v/u

Solution: We're given the equation Y = X^2 + uX + v.   IF.. we use a simple Classic Quadratic....   u = 2   v = 1   Y = X^2 + 2X + 1   We can then go about finding the answer that yields the MINIMUM result when X = ...   Answer A: u/v = 2/1= 
2/1 = 2
2 --> 4+4+1= +9   Answer B: -u/v = -2/1 = -2 --> 4-4+1 = +1   Answer -u/2: -u/2 = -2/2 = -1 --> 1-2+1 = 0   Answer D: -v/2 = -1/2 -->(1/4)-1+1 = +1/4   Answer E: v/u = 1/2 --> (1/4)+1+1 = +2 1/4   From these results, we can see the minimum result:   -u/2
Answer: C
164 pencils are distributed to children with the same number. What can’t be the range including the number of children?  Pick one.
A) 1~10 B) 10~20 C) 50~60 D) 20~30 E) 70~80

Solution: In 164=1*164=2*82=4*41=6*24, you can come up with 4 cases. Amongst these cases, what is not included is C. 50~60. Therefore, the answer is 50~60.
Answer: C
How many three digit even numbers M can be formed that are divisible by 9 such that both M and M^2 have the same units digits?	Choose the correct choice from the following answers.
A) 20
B) 21
C) 22
D) 23
E) 24

Solution: For an even number to have the same units digit as its square, it must have the units digit of 0 (0^2 = 0) or 6 (6^2 = 6). Thus the units digit of M must be 0 or 6.   For a number to be divisible by 9, the sum of its digit must be divisible by 9.   If the units digit of M is 0, then M could be:   900;   810, 180;   720, 270;   630, 360;   540, 450;   990.   10 numbers.   If the units digit of M is 0, then M could be:   306;   216, 126;   936, 396;   846, 486;   756, 576;   666.   10 numbers.   Total = 10 + 10= 
10 + 10 = 20
20.   20nswer: 20.
Answer: A
There are seven pairs of black shoes and 5 pairs of white shoes .Tey all are put into a box and shoes are drawn at a time.To ensure that at leat one pair of black shoes are taken out,What is the minimum number of shoes required to be drawn out so as to get at leat 1 pair of correct shoes.
Choose the correct choice
A) 13 B) 14 C) 15 D) 16 E) 17

Solution: All the one sided (assume only left) white shoes, total draws required: 5   All the one sided (assume only left) black shoes, total draws required: 7   So, total draws are: 5+7= 
5+7 = 12
12   Next draw or 13th draw will contain any color right footed shoe, i.e. making at least one correct pair.   So, minimum number of shoes required to be drawn out is: 13   13NSWER:13
Answer: A
The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?  Choose the most appropriate option:
A) Rs.4529  B) Rs.4586  C) Rs.4597  D) Rs.4530  E) Rs.4528

Solution: Area of the four walls = 2h(l + b)   Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.   Total cost = 906 * 5   =Rs.4530   Answer: Rs.4530
Answer: D
If a 1 mm thick paper is folded so that the area is halved at every fold, then what would be the thickness of the pile after 50 folds ?	Choose the correct choice from the following answers
A) 100 km	B) 1000 km	C) 1 million km	D) 1 billion km	E) None

Solution: after 1 hold, thickness will be 2mm   After 2 hold, thich ness will be 4mm   after 50th hold thick ness will be 2^50 mm..converting to km....gives 1 billion km   ANSWER:1 billion km
Answer: D