MU-NLPC/Calc-aqua_rat huggingface dataset:
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?	Choose the correct choice from the following:	A) 1/126	B) 1/120	C) 1/24	D) 4/25	E) 1/2

Solution: Consider a case when all girls select black marbles...So Girl 1 will chose 1 black marble out of 10..and black marble will be chosen from 5 Black marbles   Girl 1 will have a probability of picking black marble 5/10   Girl 2 will have to pick a black marble out of 4 and total remaining no. of marbles 9=4/9   So we have Probability of all girls selecting black marbles as 5/10*4/9*3/8*2/7*1/6 =1/252   Since Girls can also select white marbles so we will have 2 cases so Probability of girls selecting all same colour marbles is 2*1/252 or 1/126   1/126ns is 1/126
Answer: A
The cost of 10 kg of mangos is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is $23. Find the total cost of 4 kg of mangos, 3 kg of rice and 5 kg of flour?	Pick
A) 347.4  B) 984.4  C) 877.4  D) 637.4  E) 667.4

Solution: Let the costs of each kg of mangos and each kg of rice be $a and $r respectively.   10a = 24r and 6 * 23 = 2r   a = 12/5 r and r = 69   a = 165.6   Required total cost = 4 * 165.6 + 3 * 69 + 5 * 23   = 662.4 + 207 + 115= 
662.4 + 207 + 115 = 984.4
$984.40   984.4
Answer: B
Which of the following is the lowest positive integer that is divisible by the first 6 positive integer multiples of 5?  Choose the correct answer.
A) 300	B) 600	C) 720	D) 950	E) 1500

Solution: The number must be divisible by 5, 2*5, 3*5, 2^2*5, 5^2, and 2*3*5.   The lowest such number is 2^2*3*5^2 = 300.   The answer is 300.
Answer: A
Each of the 59 members in Lourdes school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs? Choose the correct choice from the following choices.
A) 2	B) 5	C) 6	D) 8	E) 9

Solution: Each of the 59 members in Lourdes school class is required to sign up for a minimum of one and a maximum of three academic clubs.Total = G1 + G2 + G3 - (# In exactly 2) - 2*(# in 3 sets)   59 = 22+27+28 - (6) - 2x   so, # In 3 sets = 6=6
Answer: C
What annual installment will discharge a debt of Rs 2,360 due in four years at 12% p.a. simple interest?
Choose the most appropriate option
A) 400  B) 500  C) 300  D) 600  E) None

Solution: Explanation:   Installments paid at the end of 1st, 2nd, 3rd and 4th years earn a simple interest at 12% p.a. for 3, 2, 1 and 0 years respectively.   Hence the respective installments amount to, (100 + 3 x 12), (100 + 2 x 12), (100 + 1 x 12) and 100, when annual installment is Rs 100.   Hence amount paid is Rs. 136 + Rs 124 + Rs 112 + Rs 100 i.e., Rs 472, when the annual installment is Rs.100   For an amount of Rs 2,360, annual installment = 2,360×100/472=Rs500   Answer 500
Answer: B
Which is greatest in 16 ( 2/3) %, 2/5 and 0.17 ?	Choose the correct choice.
A) 2/3 B) 0.17 C) 3/2 D) 0.71 E) None of them

Solution: 16 (2/3)% =[ (50/3)* )1/100)] = 1/6 = 0.166, 2/15 = 0.133. Clearly, 0.17 is the greatest.   Answer is 0.17.
Answer: B
which of the following is the square of an prime number?  Choose the correct choice.
A) 144
B) 529
C) 576
D) 441
E) 256

Solution: A prime number is a number greater than 1, whose only two whole-number factors are 1 and itself.   here square root of 529 is 23 which is having only two factor, one and its self.   23 is a prime number   answer is 529
Answer: B
Xavier starts from P towards Q at a speed of 90 kmph and after every 12 mins increases his speed by 20 kmph. If the distance between P and Q is 61km, then how much time does he take to cover the distance? Choose the correct choice from the following answers.
A) 52  B) 48  C) 44  D) 40  E) 36

Solution: first 12min = 90 *12/60= 
90 *12/60 = 18
18km   2nd 12min= 110*12/60= 
110*12/60 = 22
22km   3rd 12 min= 130*12/60= 
130*12/60 = 26
26 km   TOTAL time 12.3=36 min   36
Answer: E
Last year the price per share of Stock N increased by p percent and the earnings per share of Stock N increased by q percent, where p is greater than q. By what percent did the ratio of price per share to earnings per share increase, in terms of p and q? Answers
A) (p-q)/(100+q) %	B) (100+q) %	C) 100*(p-q)/(100+q) %	D) 100*(p-q) %	E) p/q%

Solution: Let P = the old price per share; E = the old earning per share. Thus P/E is the price to earning ratio before the increases   After the increase the new price is: P*(1+p/100) and the new earning is: E*(1 +q/100)   The new P/E is: (1+p/100)P/(1+q/100)E   The Percent of P/E increase = (new P/E - P/E)/(P/E). Subsititute new P/E to the equation we have:   [(1+p/100)/(1+q/100)*P/E - P/E]/(P/E)*100%. Simplifly the expression and you should get the answer to be:   100*(p-q)/(100+q) %   Answer : 100*(p-q)/(100+q) %
Answer: C
In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey’s grade at the end of the first year is 48, what will be his grade at the end of the third year?	Pick one
A) 44
B) 89
C) 62
D) 75
E) 80

Solution: Cool question!   There's a lot of information given here, so let's eat slow here.   Joey scores a 48 at the end of his first year. That means that he's currently 24 years old (since given per instruction, after the first year one's grade is determined by doubling his/her age).   Now, come next year, or his second year at this psychology school, he's technically 25 years old. To find out the second year's grade, we want to double his age PLUS half of his previous grade.   Well, his second year is then going to be 25(2) + 24 = 74.   Now let's tackle the main question: what's his grade going to be the third year?   Well, he will be at an age of 26 on his third year at this school. Again, to find out his third year's grade, you're going to double his age (26x2), plus half of his previous year's grade (as calculated for his second year, his grade is 74; therefore, 74/2)   Having said that, the final answer would be 26(2) + 74/2 = 52 + 37= 
52 + 37 = 89
89 --> (89)
Answer: B
Find the odd one out:
125, 106, 88, 76, 65, 58, 53  Choose the correct answer:  A) 33  B) 88  C) 26  D) 18  E) 222

Solution: Explanation:   This sequence represents a series in which from the reverse order a prime number is added:   53+5= 
53+5 = 58
58   58+7= 
58+7 = 65
65   65+11= 
65+11 = 76
76   76+13= 
76+13 = 89
89   89+17= 
89+17 = 106
106   106+19= 
106+19 = 125
125   Hence 88 is the answer.   ANSWER: 88
Answer: B
Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/2 of the remaining paint. How many gallons of paint has Joe used?	Select
A) 18  B) 225  C) 175  D) 216  E) 250

Solution: Total paint initially = 360 gallons   Paint used in the first week = (1/4)*360= 
(1/4)*360 = 90
90 gallons.   Remaning paint= 270 gallons   Paint used in the second week = (1/2)*270= 
(1/2)*270 = 135
135 gallons   Total paint used= 225 gallons.   Option 225
Answer: B
There are 3 numbers A, B and C. If A:B = 5/4, B:C = 4/3,C:D = 3/6, then A:D will be? Select:
A) 5:6  B) 3 : 5  C) 5 : 7  D) 6 : 11  E) 5 : 3

Solution: Sol. A : B = 5 : 4, B : C = 4 : 3, C : D = 3 : 6   ∴A∶B∶C∶D= 5 : 4 : 3 : 6.   Thus, 5:6 : D = 5 : 6   5:6
Answer: A
The tax on a commodity is diminished by 20% but its consumption is increased by 20%. Find the decrease percent in the revenue derived from it? Pick one:
A) 20%
B) 18%
C) 4%
D) 12%
E) 14%

Solution: 100 * 100= 
100 * 100 = 10_000
10000   80 * 120= 
80 * 120 = 9_600
9600   10000------- 400   100 ------- ?= 4%   ANSWER:4%
Answer: C
The ratio of speed of A and B is 3:4.a definite distance covered by B in 24 minutes.
how much time A take to cover that distance?
Choose the most appropriate option:
A) 18 minute  B) 32 minute  C) 76/7 minute  D) 40 minute  E) 44/3 minute

Solution: ratio of time taken by A and B to cover a distance=1/3:1/4=4:3.   let time taken by A and B are 4x minute and 3x minute respectively.   3x=24;x=8.   hence,time taken by A=(4*8)= 
(4*8) = 32
32 minute   answer 32 minute
Answer: B
If the area of circle is 850 sq cm then its circumference? Choose the correct answer: A) 1719.96 m B) 1628.82 m C) 1925.23 m D) 1432.50 m E) 1893.45 m

Solution: 1719.96 mrea of Circle = ∏r2   = 22/7(r2) = 860   = r2 = (860)(7/22)   = r = 273.63   Circumference = 2∏r = (2)(22/7)(273.63)   = 1719.96 m   1719.96 mnswer: 1719.96 m
Answer: A
Whats the probability of getting 5 Sunday(my favorite day) in a 31 day month ?  Choices
A) 3/7  B) 4/7  C) 5/7  D) 6/7  E) 7/7

Solution: Solution:   3/7   Explanation:   If a 31day month starts on a Friday, Saturday or Sunday it will have five Sunday, if not it will have 4 Sunday   3/7nswer 3/7
Answer: A
A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely ?  Choose the correct answer
A) 3 hrs 15 min B) 3 hrs 45 min C) 4 hrs D) 4 hrs 15 min E) None

Solution: Solution   Time taken by one tap to fill half the tank = 3hrs.   Part filled by the four taps in 1 hour	= (4×1/6)   = 2/3.   Remaining part	= (1 - 1/2)   = 1/2.   Therefore,	‹=› 2/3 : 1/2 :: 1 : x   ‹=› (1/2×1×3/2)   ‹=› 3/ 4 hrs i.e 45 mins.   So, total time taken = 3 hrs 45 min.   Answer 3 hrs 45 min
Answer: B
If m = 9/25, c = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order?
Choose the correct choice.
A) c, m, w  B) c, w, m  C) m, w, c  D) w, c, m  E) w, m, c

Solution: Answer W - w, m, c   m ~ 1/3   c ~ 1/2   and m+w+c = 1 hence w ~ 1/6   Hence increasing order would be w -> m -> c   Answer w, m, c
Answer: E
A rectangle having length 100 cm and width 40 cm. If the length of the rectangle is increased by fifty percent then how much percent the breadth should be decreased so as to maintain the same area.
Answers
A) 25%
B) 33.33%
C) 40%
D) 75%
E) None of these

Solution: Explanation :   Solution: (50/(100+50) * 100)% = 33.33%   Answer : 33.33%
Answer: B
In the storage room of a certain bakery, the ratio of sugar to flour is 3 to 6, and the ratio of flour to baking soda is 5 to 1. If there were 30 more pounds of baking soda in the room, the ratio of flour to baking soda would be 4 to 1. How many pounds of sugar are stored in the room? Choose the correct choice from the following options:
A) 30
B) 50
C) 60
D) 45
E) 70

Solution: Sugar:Flour = 3:6 = 1:2 = 5:10   Flour:Soda = 5:1 = 10:2;   Thus we have that Sugar:Flour:Soda = 5x:10x:2x.   Also given that 10x/(2x+30) = 4/1 --> x=60 --> Sugar = 5x = 30.   30nswer: 30
Answer: A
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 60/r years. If Pat's parents invested $7,000 in a long-term bond that pays 6 percent interest, compounded annually, what will be the approximate total amount of the investment 20 years later, when Pat is ready for college?	Choices
A) $20000	B) $14000	C) $12000	D) $10000	E) $9000

Solution: Since investment doubles in 60/r years, then for r=6 it'll double in   60/6= 
  60/6 = 10
~10 years (we are not asked about the exact amount so such an approximation will do). Thus after 20 years investment will become $7,000*2=$14,000 .   Answer: $14000
Answer: B
A batsman scored 90 runs which included 4 boundaries and 6 sixes. What percent of his total score did he make by running between the wickets?  Pick one:
A) 45%
B) 500/11
C) 42.22%
D) 55%
E) 35%

Solution: Explanation :   Number of runs made by running,   =>90−(4×4+6×6).   =>90−52   =>38   Hence, the required percentage is:-   =>38/90 *100   =>42.22%   Answer : 42.22%
Answer: C
P alone can complete a piece of work in 13 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?	Choose the correct choice from the following answers
A) 6 (1/4) days B) 39/4 days C) 7 (3/4) days D) 8 (3/4) days E) 9 (3/4) days

Solution: Work done by P alone in one day = 1/13th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/13 of the total) = 1/39 of the total.   Work done by P and Q, working together in one day = 1/13 + 1/39 = 4/39 of the total   They would take 39/4 days to complete the work working together.   ANSWER:39/4 days
Answer: B
A merchant sells 30 metres of cloth and gains selling price of 10 metres. Find the gain percent.  Choose the correct choice from the following answers
A) 15 % B) 25 % C) 50 % D) 75% E) 70 %

Solution: Here, selling price of 10 m cloth is obtained as profit.   Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)   Selling price of 20 m cloth = Selling Price of 30 m of cloth   Let cost of each metre be Rs. 100.   Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000   Profit% =	10/20*100= 
10/20*100 = 50
50%   Profit of 50 % was made by the merchant.   ANSWER IS 50 %
Answer: C
Two kinds of Vodka are mixed in the ratio 1:5 and 5:1 and they are sold fetching the profit 10% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of	Choose one:	A) 21%	B) 20%	C) 21%18%	D) 23%	E) Cannot be determined

Solution: The profit on the first kind of vodka = x%;   The profit on the second kind of vodka = y%.   When they are mixed in the ratio 1:2 (total of 3 parts) the average profit is 10%: (x + 2y)/3 = 10.   When they are mixed in the ratio 2:1 (total of 3 parts) the average profit is 20%: (2x + y)/3 = 20.   Solving gives: x = 30% and y = 0%.   After the individual profit percent on them areincreased by 4/3 and 5/3 times respectively the profit becomes 40% and 0%,on the first and te second kinds of vodka, respectively.   If they are mixed in equal ratio (1:1), then the mixture will fetch the profit of  (40 + 0)/2= 
 (40 + 0)/2 = 20
20%.   Answer: 21%18%
Answer: C
Find the one which does not belong to that group ?
Answers.
A) 22	B) 83	C) 33	D) 49	E) 11

Solution: Explanation:   36 = 62, 49 = 72, 64 = 82, 81 = 92 and 100 = 102.   36, 64, 81 and 100 are squares of composite numbers, but not 49.   Answer: 83
Answer: B
A man can row 7 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place? Choose the correct answer
A) 3.3 B) 3.4 C) 3.5 D) 3.6 E) 3.7

Solution: M = 7   S = 1.2   DS = 7 + 1.2= 
7 + 1.2 = 8.2
8.2   US= 7 - 1.2= 
7 - 1.2 = 5.8
5.8   x/8.2 + x/5.8= 1   x = 3.40.Answer: 3.4
Answer: B
A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)?
Options.
A) 500
B) 200
C) 300
D) 250
E) 300

Solution: Let length of the tunnel = x meter   distance = (800 + x)meter   Time = 1 =1 minute = 60 seconds   Speed = 78 km/hr=78 Ã—5/18 =65/3 m/s   800+x =60 Ã— 65/3   800+ x=1300   x=500   500NSWER: 500
Answer: A
Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 40 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?	Choose the correct choice from the following options.
A) 16	B) 18	C) 20	D) 24	E) 30

Solution: Time taken = Total Distance / Relative Speed   Total Distance = 40 kms   Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4= 
6+ 4 = 10
10 kms/hr   Time taken= 40 / 10= 
40 / 10 = 4
4 hrs   Distance traveled by Brad= Brad's speed * time taken = 6 * 4= 
6 * 4 = 24
24 kms... Answer - 24
Answer: D
Find out the wrong term in the series 3, 6, 18, 108, 1944, 103432
Choose the correct choice:
A) 208646	B) 300458	C) 103432	D) 210546	E) 209952

Solution: Explanation:   Each number with in the series is the product of the two numbers that proceed it.   So, if (3 * 6 = 18) , then (108 * 1944 = 209952 ). 209952 should replace 103432.   Answer: 209952) 209952
Answer: E
There are 11 lines in plane. How many intersections (Maximum) can be made?
Choose the correct choice:
A) 55
B) 60
C) 65
D) 70
E) 75

Solution: First line will cut all other 10, similarly second will cut 9, and so on   total = 10+9+8+7+6+5+4+3+2+1= 
10+9+8+7+6+5+4+3+2+1 = 55
55   55NSWER:55
Answer: A
If in coded language
1 = 2
2 = 10
3 = 30
4 = 68
then
5 = ?  Choices:
A) 130
B) 140
C) 150
D) 160
E) 170

Solution: 1^3 + 1= 2   2^3 + 2= 10   3^3 + 3 = 30   4^3 + 4 = 68   5^3 + 5 = 130   130ns : 130   130NSWER:130
Answer: A
2 oranges, 3 bananas and 4 apples cost Rs.15. 3 oranges 2 bananas 1 apple costs Rs.10. what is the cost of 3 oranges, 3 bananas and 3 apples?	Choose the correct choice from the following options:
A) 30  B) 15  C) 10  D) 20  E) 40

Solution: 2or+3ba+4ap=15--->(1)   3or+2ba+1ap=10---->(2)   (1)+(2)   5or+5ba+5ap=15+10   5(or+ba+ap)5  +5  +5= 
5  +5  +5 = 15
15+10   5(or+ba+ap)=25   or+ba+ap=25/5   or+ba+ap=5   therefore 3or+3ba+3ap===>3(or+ba+ap);   3(5)=15;   ANSWER:15
Answer: B
In measuring the sides of a rectangle, one side is taken 6% in excess, and the other 5% in deficit. Find the error percent in the area calculated from these measurements.	Choose the correct choice from the following options
A) 0.11% B) 0.7% C) 0.4% D) 0.6% E) 0.8%

Solution: Let x and y be the sides of the rectangle. Then, Correct area = xy.   Calculated area = (53/50) x (19/20) y = (144/143)(xy)   Error In measurement = (144/143)xy- xy = (1/143)xy   Error percentage = [(1/143)xy (1/xy)100] % = (7/10)= 
(7/10) = 7/10 = around 0.7
0.7%.   Answer is 0.7%.
Answer: B
In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 8,000 have been vaccinated against both, how many have been vaccinated only against rubella?	Choose the correct choice from the following options: A) 2,5000 B) 7,500 C) 10,000 D) 15,000 E) 16,000

Solution: Use a single variable as far as possible.   Number vaccinated only against mumps = x   Number vaccinated against both = 2x = 8000 (so x = 4000)   Then, number vaccinated against mumps (including both) = x + 2x = 3x   Number vaccinated against rubella = 2*3= 
2*3 = 6
6x   Then, number vaccinated against only rubella= 6x - 2x = 4x 6  - 2= 
6  - 2 = 4
4x= 4*4000 = 16,000   Answer (16,000)
Answer: E
In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way? Answers.
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: T = 60/36 * 18/5= 
60/36 * 18/5 = 6
6 sec   Answer:6
Answer: D
In one hour, a boat goes 13 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is:
Choose the correct choice from the following answers
A) 2 B) 4 C) 9 D) 12 E) 15

Solution: Sol.   Speed in still water = 1/2 (13+5) kmph = 9 kmph.   Answer 9
Answer: C
During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 50 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?	Pick:	A) 8.5%	B) 50%	C) x/12%	D) 400/x%	E) 500/x%

Solution: Say x = 5 miles (so no remainder of the trip).   Time to cover x = 5 miles at 30 miles per hour = (time) = (distance)/(rate) = 5/30 = 1/6 hours = 10 minutes.   Time to cover x = 5 miles at 60 miles per hour = (time) = (distance)/(rate) = 5/50 = 1/10 hours = 5 minutes.   (Or simply, half rate will result in doubling the time.)   So, we can see that the time to cover x = 5 miles at 30 miles per hour (10 minutes) is 100% greater than the time to cover x = 5 miles at 60 miles per hour (5 minutes).   Now, plug x = 5 miles into the answer choices to see which one yields 100%. Only answer E works.   Answer: 400/x%.
Answer: D
A ratio between two numbers is 8:9 and their L.C.M. is 432. The first number is  Choose one.
A) 60	B) 45	C) 50	D) 48	E) None

Solution: Sol.   Let the required numbers be 8x and 9x. Then, their L.C.M. is 72x.   ∴ 72x = 432⇔ x = 6. Hence, the first number is 48.   Answer 48
Answer: D
If an object travels at seven feet per second, how many feet does it travel in one hour?  Answers:	A) 30	B) 300	C) 720	D) 25200	E) 18000

Solution: Speed = 7 feet per second.   1 Hour= 60X60 Seconds = 3600 Seconds.   Total no of feet traveled in 1 hour = 3600X7= 25200   Answer 25200
Answer: D
Mrs. Carolina. invested $9,000; part at 5%, and part at 8%. The total interest on the investment was $630. How much did she invest at each rate?	Choose the most appropriate option
A) x=$13,000, y =$26,000	B) x=$4,000, y =$8,000	C) x=$2,000, y =$4,000	D) x=$3,000, y =$6,000	E) x=$5,000, y =$10,000

Solution: I approached this question like a mixture problem.   I don't like the wordingpartat 5% andpartat 8% because we have variables x and y in the answer choices and I have no idea which one is x or y.   Anyway here's how I did it.   0.05(x) + 0.08(y) = 0.07(x+y)   0.01(y) = 0.02(x)   y = 2x   Note: 0.07(x+y) because $630 is 7% of 9,000   In which answer choice is y = 2(x)   Answer x=$3,000, y =$6,000
Answer: D
A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number E of ways this can be done is:  Choose the correct choice from the following
A) 122
B) 210
C) 216
D) 217
E) 225

Solution: We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.   We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.   For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.   Second step:   We have two set of numbers:   1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:   1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.   0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96   120+96= 
120+96 = 216
216=E   Answer: 216.
Answer: C
Calculate 42120 ÷ ? = 195 Pick
A) 212	B) 219	C) 217	D) 213	E) 216

Solution: Answer   Let 42120/X = 195   Then X = 42120/195= 
42120/195 = 216
216   Option: 216
Answer: E
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?	Select:  A) 11 seconds  B) 77 seconds  C) 76 seconds  D) 12 seconds  E) 17 seconds

Solution: Speed of the boat downstream = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 60 m= 60/5= 
60/5 = 12
12 seconds.   Answer:12 seconds
Answer: D