MU-NLPC/Calc-aqua_rat huggingface dataset:
A man can row downstream at 20 kmph and upstream at 12 kmph. Find the speed of the man in still water and the speed of stream respectively?
Pick.
A) 13, 3	B) 12, 6	C) 16, 4	D) 14, 4	E) None of these

Solution: Explanation:   Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 20--- (1)   and x - y = 12 --- (2)   From (1) & (2) 2x = 32 => x = 16, y = 4.   Answer: Option 16, 4
Answer: C
A man said to his son, "I was two-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son?	Choose the correct choice from the following choices: A) 68.8 B) 28.7 C) 28.1 D) 28.8 E) 28.2

Solution: Present age of the son be P, he was born P years ago.   The age of the man was: (48 - P).   His age when the son was born should be equal to 2/3 of P.   (48 - P) = 2/3 P   5P = 144 => P = 28.8   Answer:28.8
Answer: D
If a certain number is divided by 2, the quotient, dividend, and divisor, added together, will amount to 62. What is the number?	Answers
A) 18  B) 28  C) 40  D) 38  E) 59

Solution: Let x = the number sought.   Then x/2 + x + 2 = 62.   x = 40.   40
Answer: C
A zinc-copper alloy with 2 kg of pure zinc would contain 90% of zinc. The alloy with 1 kg of 90% zinc alloy contains 84% of zinc. Calculate the weight and percentage of zinc in the zinc-copper alloy.	Choose the correct choice from the following choices:  A) 2.4 kg or 80%  B) 1.4 kg or 88%  C) 1.9 kg or 94.2%  D) 7.4 kg or 18%  E) 1.4 kg or 60%

Solution: Right Answer Explanation:   x : 2   y : 100   90   10 : 90 – y   (90-y)/2 = 10/x = ………..(1)   In the second case,   x 1   y 90   84   6 84-y   Therefore (84-y)/1 = 6/x ………..(2)   Dividing (1) and (2)   =   180 – 3y =840 – 10y   7y = 660   y = 94.2   x = 20/(90-80) = 20/10= 
20/10 = 2
2 kg   Quantity of zinc in x= 94.2% of x   = 0.942 2   =1.9 kg   Weight and percentage of zinc is 1.9 kg or 94.2%   1.9 kg or 94.2%
Answer: C
When viewed through a certain microscope objects appear 120 times larger. If a red blood cell appears to have a radius of 49.2 centimeters, what is the actual diameter, in millimeters of the cell? (1 millimeter = 0.1 centimeter)  Answers.
A) 0.82	B) 4.1	C) 8.2	D) 11.8	E) 82

Solution: 0.1 Centimetre = 1 millimetre   1 cm = 10 mm   49.2 cm = 49.2 * 10= 
49.2 * 10 = 492
492 mm   Objects are magnified by factor of 120.   Original radius= 492/120= 
492/120 = 41/10 = around 4.1
~4.1   Diameter= 4.1 * 2= 
4.1 * 2 = 8.2
8.2   Ans 8.2.
Answer: C
A man can hit a target once in 6 shots. If he fires 4 shots in succession, how many ways that he will hit his target?	Choose the correct choice from the following options
A) 71/234  B) 81/133  C) 81/343  D) 27/56  E) 91/324

Solution: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.   So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.   The event of not hitting the target even once is the complement of the event of hitting the target at least once.   The probability that he will not hit the target in any given shot = 1 - 1/6 = 5/6   Therefore, the probability that he will not hit the target in any of the four shots = 5/6^4 =27/56   27/56
Answer: D
The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is? Choose the correct option
A) 6
B) 9
C) 8
D) 3
E) 1

Solution: S = 1   M = x   DS = x + 1   US = x - 1   35/(x + 1) + 35/(x - 1) = 12   x = 6   6nswer: 6
Answer: A
P cando a work in 15 days and Q cando the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?  Select the correct option: A) 2/13 B) 3/17 C) 8/15 D) 9/21 E) 9/22

Solution: Amount of work P can do in 1 day = 1/15   Amount of work Q can do in 1 day = 1/20   Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60   Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15   Fraction of work left = 1 – 7/15= 8/15   8/15
Answer: C
In an examination a pupil's average marks were 63 per paper. If he had obtained 18 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?
Select the correct option:
A) 8	B) 9	C) 10	D) 11	E) 12

Solution: Let the number of papers be x. Then,   63x + 18 + 2 = 65x   = 2x = 20   = x = 10.   ANSWER:10
Answer: C
Patrick and Eric are on the two opposite banks of a river. They both have a rowing boat.
They both start at the same time towards the opposite bank. They pass each other at 180 meters from the bank where Patrick departed. When reaching the opposite bank, they both take a rest for the same amount of time before they return. On the way back, they pass each other at 100 meters from the bank from where Patrick returned.
Patrick and Eric both row with a constant speed, but Eric rows faster.
How wide is the river?  Pick
A) 350 m  B) 250 m  C) 443 m  D) 500 m  E) 440 m

Solution: E   440 meters   Call the requested width of the river r.   The first time that Patrick and Eric meet, the total distance that they have traveled together equals the width of the river, or r. The second time that Patrick and Eric meet, the total distance that they have traveled together equals twice the width of the river plus the width of the river, so 3 × r. Because Patrick and Eric row with a constant speed, it also holds that the distance that Patrick traveled in total at the second meeting, equals 3 times the distance that Patrick traveled in total at the first meeting.   The distance that Patrick traveled in total at the first meeting is 180. The distance that Patrick traveled in total at the second meeting is r + 100. When we combine the above, we get the following equation:   3 × 180 = r + 100.   When we solve this equation we find that r = 440.   Therefore, the river is 440 meters wide.
Answer: E
A certain series is defined by the following recursive rule: Sm=K(Sm-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, what is the 9th term?	Pick:	A) ROOT 2	B) ROOT 3	C) 64*ROOT 3	D) 64*3^1/3	E) 64*3^24

Solution: Ans...D   No need for any GP formula here   The rule is that mth term is K times the (m-1)th term.   1st = 64   2nd = k.64   3rd = k^2.64   .   .   .   9th term = k^8 *64   .   .   .   so 25th = k^24*64   Using this solve for k and substitute k in the equation for the 9th term
Answer: D
Each student at a certain business school is assigned a 7-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?
Pick one:
A) 9,000
B) 3,600
C) 2,700
D) 2,592
E) 3,600,000

Solution: The identification number is of the form _ _ _ _   1. First digit cannot be 0   2. Middle digits can be anything   3. Last digit has to be prime - 2, 3, 5, 7   We can have the following number of possibilities for each space   __ __ __ __   9 10 10 10 10 10 4   Total cases = 3,600,000   Answer : 3,600,000
Answer: E
A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle? Choose the most appropriate option
A) 16.665	B) 16.565	C) 15.465	D) 14.365	E) 14.378

Solution: Explanation :   Smaller triangle and original triangle will be similar to each other.   Ratio of area= (ratio of side)2   Area of smaller triangle = area of original triangle *(65/100)2   = 14.365.   Answer : 14.365
Answer: D
In a Company, there are certain number of team members and certain number of team leaders. If five team members are assigned to each team leader, then one member is left out without team leader. If six members are assigned to each team leader, then one team leader has no member at all. Find the number of team leaders in that company? Choose the most appropriate option.
A) 7	B) 36	C) 5	D) 8	E) 9

Solution: on the basis of question   x = 5y+1   x = 6(y-1)   on solving these 2 equations x 5 +1= 
5 +1 = 6
6(y-1)   on solving these 2 equations x= 36   ANSWER:36
Answer: B
At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 8 months? Select:
A) 2^3	B) 3^2	C) 2(3^10)	D) 3(2^8)	E) 3(10^2)

Solution: 3*2^n where n is the #of month --> 3*2^8 Answer (3(2^8))
Answer: D
In a queue that comprises of 7 students. Sam and Tom are in the queue, what is the probability that they will be standing next to each other in the queue?
Pick
A) 7%
B) 14%
C) 21%
D) 28%
E) 35%

Solution: Possible Sitting position is 7! = 120   Sam and Tom standing next to each other is 7 21%ombination 2   =7!/2!(7-2)!   =5040/2(120)   =5040/240= 
5040/240 = 21
21   Answer= 21%
Answer: C
A diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 47 grams of protein daily, how many grams of food X are in the mixture? Choices
A) 240 B) 260 C) 280 D) 300 E) 320

Solution: Let x be the number of grams of food X in the mixture.   0.1x + 0.15(400-x) = 47   0.05x = 13   x = 260   The answer is 260.
Answer: B
David works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 4 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?  Pick one:
A) 3/5
B) 2/5
C) 4/5
D) 1/5
E) 6/5

Solution: First notice the number of months for which he worked - March to Sept i.e. 7 months   Avg of monthly totals in tips for months other than August = x   Tips in August = 4x   Total tips for all months = 6*x + 4x = 10x   Tips for August/Total tips for all months = 4x/10x = 2/5   Answer : 2/5
Answer: B
If a certain number is divided by 12, the quotient, dividend, and divisor, added together, will amount to 64. What is the number?  Pick one.
A) 47
B) 48
C) 49
D) 50
E) None

Solution: Solution   Let x = the number sought.   Then x/12 + x + 12 = 64.   And x - 624/13 = 48.   Answer 48
Answer: B
Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?	Choose the correct choice:
A) 7 : 9 B) 7 : 6 C) 7 : 0 D) 7 : 2 E) 7 : 1

Solution: Let x be the investment of Ravi in 6% and y be in 7%   x(6)(n)/100 = y(7)(n)/100   => x/y = 7/6   x : y = 7 : 6   Answer:7 : 6
Answer: B
What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 5), (x, 5)?
Choices.
A) 60.	B) 85.	C) 125	D) 225	E) It cannot be determined from the information given

Solution: Irrespective of the values of x and y, we can find the length of one side of the square = distance between (20,20) and   (20,5) = 15.   Area = 15^2 = 225.   ANSWER:225
Answer: D
A person covered one-fourth of the total distance at 6 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?  Choices.
A) 10(5/7)kmph  B) 21(2/3) kmph  C) 13 (5/7)kmph  D) 15 (5/7)kmph  E) 13 (2/7)kmph

Solution: Let the total distance be x km   total time taken = (x/4)/6 + (3x/4)/24 = x/24 + x/32 = 7x/96   Average speed = x/(7x/96) = 96/7kmph = 13 (5/7)kmph.   ANSWER:13 (5/7)kmph
Answer: C
A no.when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
Select the correct option:
A) 2
B) 7
C) 9
D) 11
E) 15

Solution: 221 + 43= 
221 + 43 = 264
264/17= 9 (Remainder)   9
Answer: C
A, B and C can do a piece of work in 6 days, 12 days and 30 days respectively. How long will they taken, if all the three work together?  Pick:	A) 3 9/17	B) 4	C) 5	D) 67	E) 9

Solution: 1/6 + 1/12 + 1/30 = 17/60 => 60/17 => 3 9/17 days   3 9/17nswer:3 9/17
Answer: A
If Rs 1050 is divided into three parts, proportional to (1 / 3) : (3 / 4) : ( 4 / 6), then what is the first part? Select
A) 238  B) 2767  C) 200  D) 288  E) 171

Solution: Given:   1050 =	1	:	3	:	4   3	4	6   1) L.C.M. of 3, 4 and 6 is 12   Therefore, multiply numerator and denominator of (1/3) with 4, to obtain denominator 12. Similarly multiply (3/4) with 3 and (4/6) with 2   4	:	9	:	8	= 4 : 9 : 8   12	12	12   2) If a number a is divided in three ratios x : y : z,   First Part:	ax	------- (a is the number divided)   (x + y + z)   Therefore,   First Part:	(1050 x 4)	= 200   (4 + 9 + 8)   200orrect option :200
Answer: C
A man buys a cycle for Rs. 1800 and sells it at a loss of 10%. What is the selling price of the cycle? Choose the most appropriate option
A) 1410  B) 1620  C) 1430  D) 1440  E) 1540

Solution: S.P. = 90% of Rs. 1800 = 90/100 x1800= Rs. 1620   answer : 1620
Answer: B
The center of a circle lies on the origin of the coordinate plane. If a point (x, y) is randomly selected inside of the circle, what is the probability that y > 0 or y > x? Answers:  A) 5/8  B) 1/6  C) 3/8  D) 1/2  E) 3/4

Solution: The line y=x divides the circle into two equal areas.   All the points above the line y=x satisfy the condition that y > x.   All the points above the x-axis satisfy the condition that y > 0.   The union of these two areas is 5/8 of the circle.   The answer is 5/8.
Answer: A
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
A.	7
B.	8
C.	9
D.	10
Explanation: Choose the most appropriate option:
A) 5 B) 7 C) 9 D) 10 E) 11

Solution: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.   (2x + 2) + 2x + x = 27   5x = 25   x = 5.   Hence, B's age = 2x = 10 years.   Answer: Option 10
Answer: D
What is the largest 4 digit number exactly divisible by 88 Select the correct option.
A) 9900
B) 9999
C) 9988
D) 9944
E) None of these

Solution: Explanation:   Largest 4 digit number is 9999   After doing 9999 ÷ 88 we get remainder 55   Hence largest 4 digit number exactly divisible by 88 = 9999 - 55= 
9999 - 55 = 9_944
9944   Option 9944
Answer: D
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 4 m x 2 m x 25 cm?
Options
A) 5600 B) 6000 C) 1185 D) 7200 E) 8600

Solution: Number of bricks =Volume of the wall/Volume of 1 brick =	(400 x 200 x 25)/(25 x 11.25 x 6) = 1185.   Answer: Option 1185
Answer: C
The mean of 40 observations was 36. It was found later that an observation 34 was wrongly taken as 20. The corrected new mean is
Choose one:
A) 76.55
B) 36.35
C) 46.15
D) 16.05
E) 20

Solution: Explanation:   Correct Sum = (36 * 40 + 34 - 20)= 
(36 * 40 + 34 - 20) = 1_454
1454   Correct mean= = 1454/40= 
1454/40 = 727/20 = around 36.35
36.35   Answer: 36.35
Answer: B
The average of three numbers is 29. The average of two of these numbers is 38. What is the third number?	Choose the correct choice from the following answers:
A) 10  B) 14  C) 11  D) 17  E) 19

Solution: 11   11   3 numbers 29 x 3 = 87 total   2 numbers 38 x 2 = 76 total   The third number must therefore be   87 - 76= 
  87 - 76 = 11
11.
Answer: C
A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 3, 5, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following?	Choose the correct choice.
A) 1/9 B) 2/9 C) 1/6 D) 1/18 E) 5/36

Solution: There are 3*3= 
3*3 = 9
9 possibilities.   Bob has 2 chances so the probability is 2/9.   The answer is 2/9.
Answer: B
A bus traveled from its depot to its destination at an average speed of 60 kilometers per hour. On its return to the depot along the same route, the bus traveled at an average speed of only 40 kilometers per hour, making the trip 4 hours longer. What is the total distance of the round trip? Choose the correct choice from the following options
A) 360 kilometers  B) 400 kilometers  C) 600 kilometers  D) 800 kilometers  E) 960 kilometers

Solution: Let time for first trip be x hrs   For first trip distance travelled = 60x   For round trip distance travelled 40(x+4) = 40x+160   60x = 40x + 160   x = 8 hrs.   Total Round trip distance = 60*8*2= 
60*8*2 = 960
960 kilometers 960 kilometers
Answer: E
Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat? Answers
A) 3!  B) 8!  C) 7!  D) 9!  E) 11!

Solution: Ans.(B)   Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: B
A group of four mens and three womens have tickets for seven adjacent seats in one row of a theater. If the three womens will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?	Choices
A) 7! – 2!3!2! B) 7! – 4!3! C) 7 × 2!3!2! D) 7! – 6!3! E) None of these

Solution: There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like WWW.   Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question.   1. Total # of arrangements of 7 is 7!.   2. # of arrangements when 3 boys are seated together, like WWW;   Among themselves these 3 boys can sit in 3! # of ways,   Now consider these 3 boys as one unit like this {WWW}. We'll have total of 5 units: {WWW}{M}{M}{M}{M}. The # of arrangements of these 5 units is 5!.   Hence total # of arrangements when 3 men sit together is: 3!5!.   # of arrangements when 3 womens do not sit together would be: 7!-3!5!.   Answer: None of these).
Answer: E
If an integer n is to be selected at random from 1 to 900, inclusive, what is probability n(n+1) will be divisible by 9?
Choose the correct choice from the following answers:
A) 1/9 B) 1/3 C) 1/2 D) 2/9 E) 2/3

Solution: For n(n+1) to be a multiple of 9, either n or n+1 has to be a multiple of 9.   Thus n must be of the form 9k or 9k-1.   The probability is 2/9.   The answer is 2/9.
Answer: D
Aamir saves 32% of his monthly salary. If he spends Rs. 27200, then find his savings?  Select the correct option: A) 12890 B) 12890 C) 15800 D) 12800 E) 18800

Solution: Let the monthly salary of Aamir be Rs. x.   68% of x = 27200   => x = (27200 * 100)/68= 
(27200 * 100)/68 = 40_000
40000   His savings= 32/100 * 40000= 
32/100 * 40000 = 12_800
12800.   Answer:12800
Answer: D
Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Pick
A) 7 1/6 sec B) 7 3/2 sec C) 7 1/7 sec D) 7 1/2 sec E) 3 3/2 sec

Solution: 70 + 50= 
70 + 50 = 120
120 * 5/18= 100/3 mps   7 1/2 sec = 150 + 100= 
150 + 100 = 250
250 m   T= 250 * 3/100 = 15/2 = 7 1/2 sec   Answer:7 1/2 sec
Answer: D
A man walks at a speed of 3 km/hr and runs at a speed of 6 km/hr. How much time will the man require to cover a distance of 18 km, if he completes half of the distance, i.e., (9) km on foot and the other half by running?	Choose the correct choice from the following answers:
A) 6
B) 5
C) 3
D) 4
E) 4.5

Solution: Required time = (9)/3 + (9)/6= 
(9)/3 + (9)/6 = 9/2 = around 4.5
4.5 hours.   Answer:4.5
Answer: E
Evaluate: 45 - 12*3*2 = ?
Choose the correct choice:
A) 62	B) 52	C) 37	D) 12	E) 22

Solution: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right   12**2 = 4* 2= 
4* 2 = 8
8   Hence   45 - 12*3*2= 45 - 8= 
45 - 8 = 37
37   correct answer 37
Answer: C
In a race where 8 cars are running, the chance that car X will win is 1/2, that Y will win is 1/4 and that Z will win is 1/3. Assuming that a dead heat is impossible, find the chance that one of them will win. Select the correct option.
A) 1/140 B) 11/12 C) 14/8 D) 13/12 E) 57/120

Solution: Required probability = P(X) + P(Y) + P(Z) (all the events are mutually exclusive).   = 1/2 + 1/4 + 1/3   = 13/12   ANSWER:13/12
Answer: D
The diagonals of a rhombus are 15 cm and 20 cm. Find its area? Pick:
A) 987  B) 247  C) 150  D) 267  E) 121

Solution: 1/2 * 15 * 20= 
1/2 * 15 * 20 = 150
150   Answer:150
Answer: C
In the Land of Oz only one or two-letter words are used. The local language has 65 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?
Choose the correct option.
A) 65	B) 66	C) 67	D) 131	E) 130

Solution: The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...   The number of 1 letter words (X) that can be made from 65 letters is 65;   The number of 2 letter words (XX) that can be made from 65 letters is 65*65, since each X can take 65 values.   Total: 65+65*65.   Similarly:   The number of 1 letter words (X) that can be made from 64 letters is 64;   The number of 2 letter words (XX) that can be made from 64 letters is 64*64, since each X can take 64 values.   Total: 64+64*64.   The difference is (65+65*65)-(64+64*64)= 
(65+65*65)-(64+64*64) = 130
130.   Answer: 130.
Answer: E
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Choose the correct choice from the following
A) 76  B) 50  C) 88  D) 12  E) 81

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.Answer: 50
Answer: B
Marie earns $16 per hour for overtime hours. She worked 8 hours overtime last week
and 6 hours overtime this week. Which expression could be used to find Marie’s overtime pay for
the two-week period?  Choose the correct choice from the following.
A) $16 8 6 B) $16(8 6) C) 8(6) $16 D) 6($16 8) E) 8(6) 8($16)

Solution: You’re right if you chose (2) $16(8 6). In this expression, $16 (the overtime hourly wage) is   multiplied by the sum of 8 and 6 (the total overtime hours worked).   There is another way to work the problem. You could find the overtime pay for each week and   add: $16(8) $16(6). Both choice (2) and this expression yield the same result. Both are correct.   $16(8 6) $16(14) $224 $16(8) $16(6) $128 $96 $224   correct answer $16(8 6)
Answer: B
For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 3,675, what is the least possible value of k?
Choose the correct answer
A) 12
B) 14
C) 15
D) 21
E) 25

Solution: We basically need 5,5,3,7 and 7 in the number.   14!, has 3, 5, 7, 10, 14   now 10 = 2 x5   14 = 2x 7   cross check:   K! = 3675 * M (M is a positive integer)   K! = 3 * 5 * 5 * 7 * 7   14! has all the numbers above.. therefore 14..!   ANSWER:14
Answer: B
A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? Choose the correct choice from the following:
A) A)63kmph	B) B)63kmph	C) C)25kmph	D) D)62kmph	E) E)74kmph

Solution: Explanation:   M = 20   S = 5   DS = 20 + 5= 
20 + 5 = 25
25   Answer: Option 25kmph
Answer: C