MU-NLPC/Calc-aqua_rat huggingface dataset:
In an increasing sequence of 8 consecutive integers, the sum of the last 4 integers is 822. What is the sum of the first 4 integers in the sequence?
Choose the correct choice
A) 800	B) 808	C) 806	D) 802	E) 804

Solution: Solution:   In solving this problem we must first remember that when we have 8 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:   Integer 1: x   Integer 2: x + 1   Integer 3: x + 2   Integer 4: x + 3   Integer 5: x + 4   Integer 6: x + 5   Integer 7: x + 6   Integer 8: x + 7   We are given that the sum of the first 4 integers is 570. This means that:   x+7+ x+6 + x+5 + x+4 = 822   4x + 22 = 822   4x = 800   x = 200   The sum of the last 4 integers can be expressed and simplified as:   x+ x+1 + x+2+ x+3 = 4x + 6   Substituting 141 for x yields:   (4)(200) + 6 = 806   Answer: 806
Answer: C
A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 11/5 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups? Select:  A) (a) 7/16  B) (b) 7/15  C) (c) 10/21  D) (d) 22/37  E) (e) 1/2

Solution: A simpler way i guess would be to think that in total 5 cups were sold. Out of which 3 are small and 2 are large. Now let the small ones cost $5. so the large ones would cost $11.   So,   3*5= 
3*5 = 15
15 and   2*11= 
  2*11 = 22
22.   Total revenue was 15+22= 
15+22 = 37
37   and Large cup sales as found above is 22   Therefore answer is 22/37   (d) 22/37
Answer: D
Find the area of the quadrilateral of one of its diagonals is 40 cm and its off sets 11 cm and 9 cm?  Choose the correct choice from the following answers: A) 100 cm2 B) 150 cm2 C) 333 cm2 D) 400 cm2 E) 750 cm2

Solution: 1/2 * 40(11 + 9)   = 400 cm2   Answer: 400 cm2
Answer: D
The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is  Pick one.
A) 35.2
B) 36.1
C) 36.5
D) 39.1
E) None

Solution: Sol.   Therefore correct sum   = ( 36 × 50 + 48 – 23)   = 1825.   Therefore correct mean   = 1825 / 50   = 36.5.   Answer 36.5
Answer: C
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?  Choices: A) 76 m B) 17 m C) 88 m D) 55 m E) 44 m

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 867   3b2 = 867   b2 = 289 = 172 (b > 0)   b = 17 m.   Answer:17 m
Answer: B
In seven given numbers,the average of first four numbers is 4 and that of last four numbers is also 4. if the average of these seven numbers is 3, the fourth number is? Choose the correct answer:
A) 3 B) 4 C) 7 D) 11 E) 12

Solution: let 7 numbers are a,b,c,d,e,f,g.   given avg of first 4 nums are 4...i.e (a+b+c+d)/4=4   a+b+c+d=16   given avg of last 4 nums are also 4..i.e.(d+e+f+g)/4=4   d+e+f+g=16   e+f+g=16-d   given avg of 7 nums are 3....i.e (a+b+c+d+e+f+g)/7=3   a+b+c+d+e+f+g=21   16+16-d=21   d=32-21= 
32-21 = 11
11   ANSWER:11
Answer: D
Which of the following fractions R has a decimal equivalent that is a terminating decimal? Choose the correct choice from the following answers: A) 10/189 B) 15/196 C) 16/225 D) 25/144 E) 39/128

Solution: The fraction R will terminate if and only if the denominator has prime divisors only 2 and 5 or both.   A. 10/189 = 10/(3*3*3*7) Non-term.   B. 15/196 = 15/(2*2*7*7) Non-term.   C. 16/225 = 16/(5*5*3*3) Non-term.   D. 25/144 = 25/(2*2*2*7) Non-term.   E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.
Answer: E
A code is to be made by arranging 7 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?
Choose the most appropriate option:
A) 42
B) 210
C) 420
D) 840
E) 5,040

Solution: we have 7 letters out of which 3 are of one kind, 2 are of another kind..   so total ways = 7!/3!2!=420   ans 420
Answer: C
How many times are the hands of a clock at right angle in a day?  Pick one
A) 44
B) 21
C) 22
D) 41
E) 40

Solution: A   44   In 12 hours, they are at right angles 22 times.   In 24 hours, they are at right angles 44 times.
Answer: A
An amount of Rs.1638 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of A?
Options: A) 656 B) 456 C) 756 D) 745 E) 720

Solution: Let the shares of A, B and C be a, b and c respectively.   a : b : c = 1/2 : 1/3 : 1/4   Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.   a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.   Share of A = 6/13 * 1638 = Rs. 756   Answer: 756
Answer: C
Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct. Choose the correct choice from the following answers
A) 60000  B) 65000  C) 70000  D) 75000  E) None

Solution: Solution:   Out of 26 alphabets two distinct letters can be chosen in 26P2 ways.   Coming to numbers part, there are 10 ways (any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10 ways to choose the second digit.   Hence, there are totally  10 *10= 
 10 *10 = 100
100 ways.   Combined with letters there are,   26P2 *100= 65000 ways to choose vehicle numbers.   Answer: Option 65000
Answer: B
If a letter is picked randomly from the alphabet, what are the odds of it being in the first 10 letters or being a vowel (a, e, i, o, u, y)?
Choose the most appropriate option.
A) 6/13	B) 1/2	C) 15/26	D) 11/26	E) 8/13

Solution: P(10á´œV) = P(10) + P(V) - P(10âˆ©V), where 10 denotes the first ten letters, and V denotes a vowel.   P(10á´œV) = 10/26 + 6/26 - 3/26   = 1/2   Answer: 1/2
Answer: B
Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 31% ryegrass, what percent of the weight of the mixture is from mixture X?  Select the correct option
A) 20% B) 30% C) 40% D) 50% E) 60%

Solution: 31% is 6%-points above 25% and 9%-points below 40%.   Thus the ratio of mixture Y to mixture X is 3:2.   The percent of mixture X is 2/5 = 40%.   The answer is 40%.
Answer: C
A train covers a distance of 100km in 1 hour. If its speed is decreased by 30km/hr, the time taken by the car to cover the same distance will be?  Options:
A) 1hr
B) 1hr 25min
C) 50min
D) 1hr 30min
E) 1hr 45min

Solution: Speed = 100/1= 
100/1 = 100
100km/hr   New speed= 100-30= 
100-30 = 70
70 km/hr   Time taken= 100/70 = 1hr 25min   Answer is 1hr 25min
Answer: B
In a flower shop there were 5 flowers in each bouquet. If the seller has doubled the number of flowers in each bouquet then the new average of flowers in each bouque is
Choose the correct choice.
A) 12  B) 3  C) 8  D) 10  E) None of these

Solution: Answer   Now required average   = old average x Multiplicand   = 5 x 2 = 10   Correct Option: 10
Answer: D
(A% of B + B% of A) is equal to ? Select
A) A% of B
B) B% of A
C) 2% of AB
D) AB% of 3
E) None

Solution: Answer   A% of B + B% of A =AB/100 + AB/100   = 2AB/100 = 2% of AB   2% of ABorrect Option: 2% of AB
Answer: C
A train running at 50 km/hr takes 9 seconds to pass a platform. Next, it takes 6 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform. Choose the correct choice
A) a) 75m50m
B) b) 100m50m
C) c) 50m45m
D) d) 100/3 m200/3
E) e) none of these

Solution: A train running at 50 km/hr takes 9 seconds to pass a platform. Next, it takes 6 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.   Distance = Speed*time   It's probably best to convert to meters so we can find the length of the platform.   Distance = 50000 meters/h * 9 seconds*(1/60*60)   Distance =(50000*18 / [3600] ) = 125m   I'm not sure how we take the length of the train into account (if we do at all) to solve this problem. For example, If we were measuring by the time the very front of the train passed one end of the platform to the time the very front of the train passed the other end, the result would be different than if we counted when the very front of the train passed one end of the platform to the time the back side of the train passed the end.   As for the problem involving the man, the man is moving forward at a speed of 5km/h while the train is moving forward at a speed of 50km/h. Therefore, the train is moving past the man at a total speed of 45km/h.   distance = speed * time   distance = 45km/h * 12 seconds   distance (length of train) = 75 m   We know the length of the train is roughly 75m and the distance covered passing the platform was 125m. However, The platform isn't 125m long - it is 125m minus the length of the train long (or so I think) which is 125-75 or roughly 50m. Both of these answers are in A so I think that is the right answer. I am still having a bit of trouble conceptualizing why we have to subtract out the length of the train, however.   a) 75m50mNSWER: a) 75m50m) a) 75m50m
Answer: A
Ravi's salary was reduced by 25%. Percentage increase to be effected to bring salary to original level =	Choose the correct choice from the following answers:
A) 33.38 %
B) 33.33 %
C) 83.33 %
D) 33.35 %
E) 34.33 %

Solution: Explanation:   Let the Salary be 100.   Salary was reduced by 25%. So present salary = 75.   Percentage has to be increased in order to get Original level = 2575×1002575×100 = 33.33 %   Answer: 33.33 %
Answer: B
If p and q are positive integers, and 3 is not a factor of q, then q may be which of the following?	Answers:
A) (p−1)·p·(p+1)	B) (p−3)·(p−1)·(p+1)	C) (p−2)·p·(p+2)	D) (p−1)·p·(p+2)	E) (p−3)·(p+1)·(p+2)

Solution: Plugged in values :   let p=5   A. (p−1)·p·(p+1) --> divisible by 3   B. (p−3)·(p−1)·(p+1) --> divisible by 3   C. (p−2)·p·(p+2) --> divisible by 3   D. (p−1)·p·(p+2) --> not divisible. Hence the answer.
Answer: D
If 7 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
Choose the correct choice from the following choices.
A) 40:15:15 B) 40:25:18 C) 40:35:28 D) 40:25:24 E) 40:45:11

Solution: 7A = 8B = 10 40:35:28   A:B:40:35:28 = 1/7:1/8:1/10   = 40:35:28   Answer: 40:35:28
Answer: C
What least number must be added to 686, so that the sum is completely divisible by 5 ?	Choose the most appropriate option.
A) 2 B) 3 C) 5 D) 4 E) 6

Solution: If we divide 686 by 5 remainder is 1   5 - 1= 
5 - 1 = 4
4   Answer : 4
Answer: D
Dividing by 3⁄6 and then multiplying by 5⁄6 is the same as dividing by what number?	Answers.
A) 31⁄5
B) 16⁄5
C) 20⁄9
D) 9⁄20
E) 5⁄3

Solution: say X/3/6*5/6 = x*6/3*5/6 = x*5/3   5⁄3
Answer: E
If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled? Choose the correct choice from the following answers.
A) 25/216 B) 50/216 C) 25/72 D) 25/36 E) 5/6

Solution: Total ways in which a 6-sided die can be rolled three times = 6*6*6= 
6*6*6 = 216
216   To get exactly one 3, there are three ways:   A 3 on the first roll and non 3 on other two rolls. This can be done in 1*5*5= 
1*5*5 = 25
25 ways.   The 3 could be on the second or third roll too. So total favorable cases= 25*3= 
25*3 = 75
75   Required Probability= 75/216 = 25/72   Answer (25/72)
Answer: C
The cost to park a car in a certain parking garage is $9.00 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?
Options
A) $1.09	B) $1.67	C) $2.25	D) $2.36	E) $2.50

Solution: Total cost of parking for 9 hours = 9$ for the first 2 hours and then 1.75 for (9-2) hours = 9+7*1.75= 
9+7*1.75 = 21.25
21.25   Thus the AVERAGE parking price= 21.25/9 = 2.36 $   $2.36 is the correct answer.
Answer: D
A bag has 4 blue, 3 yellow and 2 green balls. The balls of the same color are identical. In how many ways can a child picks ball(s) out of the bag? He could even decide to pick ZERO balls. Pick one.
A) 60
B) 1260
C) 24
D) 120
E) 9

Solution: With the blue ball there are 5 scenarios-->   0 blue ball being selected   1 blue ball being selected   2 blue ball being selected   3 blue ball being selected   4 blue ball being selected   And for each of these cases there is only one possibilty as they are identical.   So there are 5 ways to select the blue ball   Same is the case with 3 yellow (for which we have 4 possibilties) and 2 green balls(we have 3 possibilties)   so in total 5*4*3= 
5*4*3 = 60
60 possibilties..   60NS:60
Answer: A
If it is true that x > -2 and x < 9, which of the following must be true?
Pick one
A) x > 2 B) x < -9 C) x < 2 D) -9 < x < 2 E) none of the above.

Solution: the range is -2 < x < 9   A. x > 2 - no because x can be between -2 < x < 2   B. x < -9 - no because the values of x are always >-9   C. x < 2 - no because x can be between 2 < x < 9   D. -9 < x < 2 - no because x can be between 2 < x < 9   E. none of the above.   Answer: none of the above.
Answer: E
Roshan is 5 years younger than Raj and they have an age ratio 3:4 respectively. How old is Roshan?  Select: A) 10 B) 15 C) 18 D) 24 E) 25

Solution: Let the age of Roshan be x.( x/x+5)=3/4   on cross multiplication and solving we get x=15   Answer: 15
Answer: B
If A, B and C together can finish a piece of work in 6 days. A alone in 12 days and B in 18 days, then C alone can do it in?	Choose the correct choice from the following choices.
A) 1 B) 7 C) 8 D) 9 E) 36

Solution: C = 1/6 - 1/12 – 1/18 = 1/36 => 36 days'   Answer: 36
Answer: E
An archer is shooting arrows from various distances. She shoots at a target from 50 yards, 60 yards, and 70 yards. The probability that she hits within the bullseye from 50 yards is 3/4, the probability that she hits within the bullseye from 60 yards is 2/3, and the probability that she hits within the bullseye from 70 yards is 3/5. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.	Choose the correct choice
A) 9/10	B) 14/15	C) 19/20	D) 29/30	E) 39/40

Solution: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)   The probability that she misses every shot = (prob that she misses from 50 yards)*(prob that she misses from 60 yards)*(prob that she misses from 70 yards)   Prob that she misses from 50 yards = 1 - 3/4 = 1/4; Prob that she misses from 60 yards = 1 - 2/3 = 1/3; Prob that she misses from 70 yards = 1 - 3/5 = 2/5   Thus the probability that she misses all shots = (1/4)*(1/3)*(2/5) = 1/30   Thus the probability that she makes at least one shot = 1 - (1/30) = 29/30   29/30
Answer: D
The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?	Choose the correct choice:
A) 2/25 B) 7/14 C) 9/3 D) 1/45 E) 18/35

Solution: Explanation:   If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 3/5 * 4/7 + 2/5 * 3/7   = 12/35 + 6/35 = 18/35   18/35
Answer: E
There are 10 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 10 points that contain the point A? Choose the correct choice from the following choices:
A) 36  B) 105  C) 182  D) 210  E) 455

Solution: Any 2 points out 9 points will create triangle with third point A, so the answer is 9C2=36.   36nswer: 36.
Answer: A
Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ? Choose the most appropriate option
A) 11/P + 6	B) 11/P + 7	C) 11/P + 2	D) 11/P + 1	E) 11/P + 8

Solution: Let Ben’s age now be B   Anita’s age now is A.   (11/P + 6 - 6) = P(B - 6)   But 11/P + 6 is 17 and therefore 11 = P(B - 6)   11/P = B-6   (11/P) + 6 = B   11/P + 6nswer: 11/P + 6
Answer: A
If I walk at 4 km/h, I miss the bus by 10 minutes. If I walk at 5 km/h, I reach 5 minutes before the arrival of the bus. How far I walk to reach the bus stand ?	Choose the correct answer
A) 5 km
B) 4.5 km
C) 5 1⁄4 km/h
D) Cannot be determined
E) None of these

Solution: d = product of speed difference of time /difference of speed   d = 4×5/60[10−(−5)/5−4]   [Here, –ve sign indicates before the schedule time]   ⇒ d = 5 km   5 kmnswer 5 km
Answer: A
If Yury has been writing programming code for 16 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written?
Choose one.
A) 126(10^2)	B) 126(10^3)	C) 144(10^2)	D) 1.26(10^7)	E) .126(10^9)

Solution: 5 LINES IN 20 SE144(10^2)ONDS   SO FOR 1 MINUTE ( 5 X 3 = 15 LINES )   I HOUR = 60 MINUTES   15 X 60 = 900 LINES IN AN HOUR   16 HOURS = 900 X 16 = 144(10^2)   ANSWER 144(10^2)
Answer: C
In your classes you counted 130 hands. How many students were at the class?  Choose the correct choice from the following.
A) 65 B) 61 C) 85 D) 86 E) 88

Solution: Total number of hands = 130   We have 2 hands.   To find how many students were at the class, divide the total number of hands by the number of hands we have.   We get, divide 130 by 2   130 ÷ 2 = 65   Therefore, there were 65 students at the class.   65NSWER IS 65
Answer: A
In how many ways can you sit 7 people on a bench if 3 of them must sit together?  Choices.
A) 720  B) 2,160  C) 2,400  D) 4,320  E) 40,320

Solution: In such questions, always tie the person that have to sit together. So we have effectively 4+1= 
4+1 = 5
5 persons to arrange.   They can be arranged in 5! ways.   Now the 3 persons can themselves be arranged in 3! ways.   Total ways: 5!*3!= 720.   720 is the answer.
Answer: A
A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability E that the 2 apples selected will include the spoiled one?
Choose the correct option:  A) a. 1/5  B) b. 3/10  C) c. 2/5  D) d. 1/2  E) e. 3/5

Solution: there can be two ways in which one can select a spoiled apple and a good apple.   1. you pick the spoiled one first and the good one later..   Prob of picking bad one = 1/5 (one bad apple)   Prob of picking a good one from the remaining 4 good apples (4/4 =1)   therefore the total prob for case 1 = i/5 * 1 = 1/5   Total prob E= porb1 + prob2 = 1/5+1/5 = 2/5.c. 2/5
Answer: C
The side of a square is increased by 25% then how much % does its area increases?
Select the correct option
A) 56.28
B) 56.25
C) 56.2
D) 56.24
E) 56.21

Solution: a = 100 a2 = 10000   a = 125 a2 = 15625   ----------------   10000 --------- 5625   100 -------? => 56.25 % Answer:56.25
Answer: B
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?	Choices:
A) 2/28
B) 2/25
C) 2/21
D) 2/08
E) 2/18

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = 32/212/152/212 = (3 * 2)/(15 * 14) = 1/35   Probability that both are yellow = 22/212/152/212 = (2 * 1)/(15 * 14) = 1/105   Probability that one blue and other is yellow = (32/211 * 22/211)/152/212 = (2 * 3 * 2)/(15 * 14) = 2/35   Required probability = 1/35 + 1/105 + 2/35   = 3/35 + 1/105 = 1/35(3 + 1/3)   = 10/(3 * 35) = 2/21   Answer:2/21
Answer: C
Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill cistern. How much time will be taken by A to fill the cistern separately?	Select.
A) 3  B) 5  C) 6  D) 8  E) 9

Solution: Let the cistern be filled by pipe A alone in x hours.   Then, pipe B will fill it in (x + 6) hours.   1/x + 1/(x + 6) = 1/4   x2 - 2x - 24 = 0   (x - 6)(x + 4) = 0 => x = 6.   Answer: 6
Answer: C
What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x  Choose the correct choice from the following answers: A) 1 B) 3 C) 5 D) 6 E) 8

Solution: 46080 /12= 
46080 /12 = 3_840
3840   3840 /10= 
3840 /10 = 384
384   384 /8= 
384 /8 = 48
48   48 /6= 
48 /6 = 8
8   8/4= 
8/4 = 2
2   2 /2= 
2 /2 = 1
1   1
Answer: A
power windows: 60%
anti-lock brakes: 25%
CD player: 60%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes? Pick.
A) 23 B) 18 C) 11 D) 3 E) 0

Solution: Answer:A   Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.   If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 60%, we can set up the following equation:   60=15+22+x   x=23, choice23.
Answer: A
A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 6 km in stationary water
Choose the correct choice from the following: A) 40 min B) 1hr C) 1hr 15 min D) 1hr 30 min E) 4 hr

Solution: rate down stream=(1/10*60)km/hr=6km/hr   rate up stream=2km/hr   speed still water =1/2(6+2)=4km/hr   required time =(6/4)=1 1/4=1hr 30 min   Answer(1hr 30 min)
Answer: D
The average age of 15 students of a class is 16 years. Out of these, the average age of 6 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?	Choose the correct answer:
A) 10years B) 11years C) 12years D) 13years E) 14years

Solution: Age of the 15th student   =[15 * 16 - (14 * 6 + 16 * 9)]   = (240 - 228)= 
(240 - 228) = 12
12 years.   Answer:12years
Answer: C
If p is the product of the integers from 1 to 35, inclusive, what is the greatest integer k for which 3^k is a factor of p? Select the correct option
A) 11  B) 13  C) 15  D) 17  E) 19

Solution: 35! has 3, 6, 9,....30, 33 as factors, which are 11 multiples of 3.   We need to add 4 more to these 11 because of 9, 18, and 27.   The greatest integer of k is 15.   The answer is 15.
Answer: C
A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?	Choose the most appropriate option:
A) 22 1/8 kmph
B) 24 3/2 kmph
C) 22 1/2 kmph
D) 22 1/5 kmph
E) 22 9/2 kmph

Solution: 100 --- 10 DS = 10   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (10 - 5)/2   = 2 2 1/2 kmph   Answer:22 1/2 kmph
Answer: C
The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? Choose the correct option
A) 2 kmph	B) 2 kmph	C) 8 kmph	D) 9 kmph	E) 1 kmph

Solution: Explanation:   S = 4   M = x   DS = x + 4   US = x - 4   6/(x + 4) + 6/(x - 4) = 2   x = 8   Answer: Option 8 kmph
Answer: C
A pipe can fill a cistern in 55 minutes. Find the time in which 1/11 part of the cistern will be filled? Options:	A) 5min	B) 2min	C) 3min	D) 1min	E) 10min

Solution: Full cistern filled in = 55 minutes   1/11 part filled in = 55*1/11= 
55*1/11 = 5
5minutes   5minnswer is 5min
Answer: A
Ravi, Ramu and Raja are three partners in business. If Ravi’s capital is equal to twice Ramu’s capital and Ramu’s capital is three times Raja’s capital, the ratio of the capitals of Ravi, Ramu, Raja is  Choose the correct choice from the following
A) 2:1:3
B) 1:2:6
C) 6:3:1
D) 1:3:6
E) None of these

Solution: Explanation:   Let Raja’s capital be Rs. X. Then,   Ramu’s capital = Rs 3x and A’s capital = Rs. 6x   Ravi : Ramu : Raja = 6x : 3x : x = 6 : 3 : 1   Answer: Option 6:3:1
Answer: C