MU-NLPC/Calc-aqua_rat huggingface dataset:
A train 600 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is:
Choose the correct choice from the following options:
A) 45 km/hr  B) 149 km/hr  C) 54 km/hr  D) 55 km/hr  E) 56 km/hr

Solution: Speed of the train relative to man = (600/15) m/sec = 40 m/sec. [40 * (18/5)] km/hr = 144 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 144 ==> x = 149 km/hr.   ANSWER: 149 km/hr
Answer: B
3/4th of a number exceeds its 2/3rd by 8. What is the number?
Pick one.
A) 96 B) 36 C) 72 D) 144 E) 146

Solution: Explanation:   Let the number be x.   3/4x = 2/3x + 8   Multiply by 12   9x = 8x + 96   x = 96   96NSWER :96
Answer: A
If p/q =4/5, then the value of 18/7 + {(2q - p) / (2q + p)} is ?	Choose the correct answer
A) 3 / 7	B) 34	C) 1	D) 2	E) 3

Solution: Answer   Given Exp. = 18 / 7 + {(2q - p) / (2q + p)}   Dividing numerator as well as denominator by q,   3xp = 18/7 + {2-p/q) / (2 + p/q)}   = 18/7 + {(2 - 4/5) / (2 + 4/5)}   = 18/7 + 6/14   = 18/7 + 3/7   =21/7= 
21/7 = 3
3   Correct Option: 3
Answer: E
The total age of A and B is 13 years more than the total age of B and C. C is how many years younger than A?	Choose the correct choice from the following
A) 13
B) 24
C) C is elder than A
D) Data inadequate
E) None

Solution: Solution   [(A+B) - (B+C)]	= 13   â€¹=â€ºA - C   = 13.   13nswer 13
Answer: A
A group consists of 7 men, 7 women and 6 children. In how many ways can 2 men , 1 woman and 2 child selected from the given group?  Pick one
A) 2210	B) 2205	C) 2215	D) 2230	E) 2245

Solution: Two men, one woman and two child can be selected in 7C2 * 7C1 * 6C2 ways     7*6/2*1*7*6*5/2*1= 
  7*6/2*1*7*6*5/2*1 = 2_205
2205 ways   Answer : 2205
Answer: B
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 45%?  Choose the correct choice from the following answers
A) 600  B) 887  C) 256  D) 654  E) 725

Solution: Cost price = Rs.500   profit = 45% of 500 = Rs.225   Selling price = Cost price + Profit   = 500 + 225= 
500 + 225 = 725
725   Answer: 725
Answer: E
Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3795. What is the difference between Rohan’s and Sudhir’s share in the profit?  Answers
A) s.345  B) s.350  C) s.352  D) s.362  E) s.368

Solution: Suresh : Rohan : Sudhir   Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8   = 6 : 3: 2   The difference between Rohan’s and Sudhir’s share = 1 share   :.i.e. = Rs. 3795 × 1/11 = Rs.345.   s.345
Answer: A
The average weight of a group of 30 friends increases by 3 kg when the weight of their 3 football coaches was added. If average weight of the group after including the weight of the 3 football coach is 33 kg, what is the average weight of their football coaches ? Choose the most appropriate option
A) 31 kg
B) 63 kg
C) 61 kg
D) 62 kg
E) 91 kg

Solution: let c=coach's avg. weight   original total weight=(30 friends)(30 kg avge)=900kg   (900+3c)/(30+3)=33 kg avg.   c=63 kg   Answer 63 kg
Answer: B
Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?	Choose the correct choice
A) 20 years  B) 22 years  C) 25 years  D) 27 years  E) 29 years

Solution: let varuns age =x   x+1=2(x-12)   der4 x=25..   ANSWER:25 years
Answer: C
Two members of a club are to be selected to represent the club at a national meeting. if there are 120 different possible selections of the 2 members, how many members does the club have?	Choose the correct choice from the following answers.
A) 20  B) 27  C) 16  D) 57  E) 95

Solution: I have done this problem by substituting numbers   We have n!/2!(n-2)! = 120   or n(n-1)/2 = 120 or n^2-n =240 or (n-16)(n+15)   n=16 satisfies the equation   16
Answer: C
In covering a distance of 15 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
Select the correct option:
A) 5 km/h  B) 8 km/h  C) 10 km/h  D) 15 km/h  E) 2.5 km/h

Solution: Let A's speed be X km/hr.   Then, 15/x - 15/2x = 3   7.5/x = 3   x = 2.5 km/hr.   Answer : 2.5 km/h
Answer: E
You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different Y ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter? Choose the correct choice:  A) 5  B) 6  C) 9  D) 12  E) 18

Solution: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:   XYZ   YZX   ZXY   And:   XYZ   ZXY   YZX   Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible Y is   2*6= 
  2*6 = 12
12.   Answer: 12.
Answer: D
Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long Q would it have taken for him to walk both ways. Pick
A) 8 h 45 min  B) 7 h 45 min  C) 6 h 45 min  D) 5 h 30 min  E) None of these

Solution: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes   2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.   3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.   4.Walking to to a viewpoint+Walking back Q=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.   8 h 45 minnswer: 8 h 45 min.
Answer: A
I. a2 + 11a + 30 = 0,
II. b2 + 6b + 5 = 0 to solve both the equations to find the values of a and b? Choose the correct choice from the following options:
A) If a < b B) If a ≤ b C) If the relationship between a and b cannot be established D) If a > b E) If a ≥ b

Solution: I. (a + 6)(a + 5) = 0   => a = -6, -5   II. (b + 5)(b + 1) = 0   => b = -5, -1 => a ≤ b   ANSWER:If a ≤ b
Answer: B
A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Choose the correct option: A) 2 B) 8 C) 9 D) 1 E) 6

Solution: 30 --- 3 DS = 10   ? ---- 1   18 ---- 3 US = 6   ? ---- 1 M = ?   M = (10 + 6)/2= 
(10 + 6)/2 = 8
8   Answer:8
Answer: B
What is the highest integer that is the sum of 2 distinct prime integers, each lesser than 60 ?
Choices:
A) 107
B) 112
C) 113
D) 129
E) 136

Solution: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. Here are the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.   Immediate two prime numbers before 60 are - 59 and 53   Sum = 59 + 53= 
59 + 53 = 112
112   Answer - 112
Answer: B
What is the angle between the minute and the hour hand of the clock which shows 12:24?  Choose the correct choice from the following answers:
A) 115
B) 120
C) 124
D) 130
E) 132

Solution: At 12:24   -minute hand will be at   24*6= 
  24*6 = 144
144 degrees from position of 12.   - Hour hand will move by 2*6= 
2*6 = 12
12 degree during the same time   So the difference between the two hands will be  144-12= 
 144-12 = 132
132 degrees. ANSW132R:132
Answer: E
In a certain game there are 10 steps, referred to as step 1, step 2, and so on with the final step being step 10. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Mary played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Andrea could have gotten?	Answers:  A) 25  B) 28  C) 24  D) 32  E) 30

Solution: There are two conditions:   1. Mary got at least one score of each of 1, 2, 3, 4, and 5.   2. She never got the same score in consecutive steps.   Taking that into account, the greatest possible score that Mary could have gotten is 5 + 1 + 5 + 2 + 5 + 3 + 5 + 4= 
5 + 1 + 5 + 2 + 5 + 3 + 5 + 4 = 30
30.   Answer: 30
Answer: E
The only items of clothing at Michelle’s Boutique are 4 shirts, 8 pairs of pants and 18 ties. What is the probability of randomly selecting 2 ties out of all the items in Michelle’s Boutique?	Select:
A) 51/145
B) 9/25
C) 3/5
D) 94/145
E) 5/6

Solution: We have 4 shirts, 8 pairs of pants and 18 ties. i.e 30 items   Total ways of picking two items out of all = 30C2 = 435   Total ways of picking two items out of all TIES = 18C2 = 153   Required Probability = 153/435 = 51/145   51/145nswer: Option 51/145
Answer: A
If 20 liters of chemical X are added to 80 liters of a mixture that is 15% chemical X and 85% chemical Y, then what percentage of the resulting mixture is chemical X?  Choose the correct answer:
A) 30%
B) 32%
C) 35%
D) 38%
E) 40%

Solution: The amount of chemical X in the solution is 20 +0.15(80) = 32 liters.   32 liters / 100 liters = 32%   The answer is 32%.
Answer: B
If d is the standard deviation a, b, and c, what is the standard deviation of a +2, b + 2, c + 2 ?
Choose the correct choice from the following choices.
A) 2d  B) d  C) 2d+2  D) 8d  E) 2d+4

Solution: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.   1) It depends on the separation between the successive terms of the set   2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant   e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}   3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number   e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}   When 2 is added in each term of set {a, b,c} then the new set {a+2, b+2, c+2} will remain same as the previous standard deviation i.e. d   Answer: d
Answer: B
Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 10 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?  Choose the correct answer
A) 10	B) 30	C) 50	D) 80	E) 100

Solution: Full time employee who have NOT worked for at least one year = a   Full time employee who have worked for at least one year = b   NON Full time employee who have worked for at least one year = c   NON Full time employee who have NOT worked for at least one year = d   a+b+c+d = 150   a+b = 80   i.e. c+d = 70   b+c = 100   i.e. a+d = 50   d = 20   i.e. c = 70-20= 
70-20 = 50
50   i.e. b= 100-50= 
100-50 = 50
50   i.e. a= 80-50= 
80-50 = 30
30   b= 10   10nswer: Option 10
Answer: A
Simplify
16âˆ’[2âˆ’(6+2(7âˆ’8âˆ’5Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯))] Choose the most appropriate option:
A) 23	B) 25	C) 28	D) 30	E) 32

Solution: Explanation:   =16âˆ’[2âˆ’(6+2(7âˆ’8+5))]   (Please check due to overline, sign has been changed)   =16âˆ’[2âˆ’(6+2Ã—4))]   =16âˆ’[âˆ’12]=16+12= 
16+12 = 28
28   Option 28
Answer: C
Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 2,000, how much money did investors B and C earn in total?
Choose the correct choice from the following answers.
A) $4,000 B) $6,000 C) $5,600 D) $9,500 E) $10,500

Solution: Let profit for A = 5x   profit for $6,000 = 7x   profit for C = 8x   Investor A earned = 2000   5x = 2000=>x=400   Total profit for $6,000 and C = 7x+ 8x = 15x   Therefore , 15x 7 + 8= 
7 + 8 = 15
15x   Therefore , 15x= 15*400= 6,000   Answer $6,000
Answer: B
Sandy walks around a circular field at the rate of one round per hour while Molly runs around it at the rate of seven rounds per hour. If they start in the same direction from the same point, how many minutes will it take until they meet again?
Choose one
A) 5	B) 8	C) 10	D) 12	E) 15

Solution: Since Sandy and Molly move in the same direction along the circle, they will first meet each other when there is a difference of one round between the two.   The relative speed of Sandy and Molly is   7 - 1= 
  7 - 1 = 6
6 rounds per hour.   The time required to complete one round at this speed is 1/6 hours= 10 minutes.   The answer is 10.
Answer: C
In each term of a sequence, 5 is added to get the next term. If the first term is 3, what is the seventy-first term?
Pick one:
A) 332
B) 353
C) 312
D) 360
E) 387

Solution: 1rst term + 70 terms = 3 + 5+5+5+5+5+5+5+...+5 (70 times)   3 + (5 x 70) = 3 + 350= 
3 + 350 = 353
353   Answer 353
Answer: B
If the positive integer x leaves a remainder of 2 when divided by 8, what will the remainder be when x + 9 is? Choose the most appropriate option:
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: x = 8q +2   x +9 =8q+2+9   8q+11 this can be furthur written as 8q +8 +3 = 8(q+1)+3   Remainder 3. Ans 3.
Answer: D
Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job.How long should it take both A and B, working together but independently, to do the same job?	Choose the correct choice from the following
A) 70 hours
B) 40/9 hours
C) 9 hours
D) 16 hours
E) 20 hours

Solution: A’s 1 hour's work = 1/8   B's 1 hour's work = 1/10   (A + B)'s 1 hour's work = (1/8) +(1/10)=9/40   Both A and B will finish the work in 40/9 days.   Option 40/9 hours is answer
Answer: B
David bought 4 pens with the average cost of $2. If David also buys the fifth pen with the price of $ 3, what is the average (arithmetic mean) price of those 5 pens?  Choices
A) $2.2 B) $2 C) $3.2 D) $4 E) $5.2

Solution: 4 pens -> Total cost = 4 * Avg cost = 4*2= 
4*2 = 8
8   Fifth pen cost= 3   Total cost for 5 pens= 8+3= 
8+3 = 11
11   AM= 11/5= 
11/5 = 11/5 = around 2.2
2.2   Hence $2
Answer: B
What is the true discount on a bill of Rs.2916 due in 3 years hence at 8% C.I.? Choose the most appropriate option
A) rs.600 B) rs.601 C) rs.602 D) rs.603 E) None of these

Solution: Explanation:   PW = Amount/(1+R100)T.   Answer: rs.602
Answer: C
The ratio between the speeds of two trains is 7: 8. If the second train runs 440 kms in 4 hours, then the speed of the first train is:  Choose the correct choice from the following answers:
A) 47.4 km/hr	B) 57.19 km/hr	C) 68.13 km/hr	D) 96.25 km/hr	E) 89.16 km/hr

Solution: Let the speed of two trains be 7x and 8x km/hr.   Then, 8x = (440/4)= 
(440/4) = 110
110   x= (110/8)= 
(110/8) = 55/4 = around 13.75
13.75   Hence, speed of first train= (7 x 13.75) km/hr = 96.25 km/hr.   Answer : 96.25 km/hr
Answer: D
If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 2 strokes ?  Select the correct option:	A) 3/4	B) 7/8	C) 1/4	D) 1/8	E) 1/16

Solution: Left 3/4fter 1st stroke = 1/2   Left 3/4fter 2nd stroke = 1/2 * 1/2 = 1/4   So removed = 1- 1/4 = 3/4
Answer: A
A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
Choices.
A) 126	B) 278	C) 281	D) 280	E) 219

Solution: 80* 7: x* 3 = 1:1 1/2   560: 3x = 2: 3   x = 280   Answer: 280
Answer: D
The speed of the boat in still water is 12km/hr. and the speed of the stream is 3km/hr. Find the distance travelled downstream in 12 minutes. Choose one:  A) 160 km  B) 180 km  C) 190 km  D) 170 km  E) 140 km

Solution: speed of the boat in downstream =speed of the water + speed of the boat   =12+3= 
12+3 = 15
15km/hr Distance travelled in 12 minutes=15 *12= 
15 *12 = 180
180km. Answer : 180 km
Answer: B
If 64(8^x) = 1 then x=	Choose one
A) 2	B) –1	C) 0	D) 1	E) -2

Solution: 8^x = 1/64   8^x = 1/8^2   8^x= 8^-2   x = -2   -2
Answer: E
What will be the cost of building a fence around a square plot with area equal to 64 sq ft, if the price per foot of building the fence is Rs. 58?
Choose the correct choice from the following options
A) 3944
B) 2882
C) 2999
D) 1856
E) 2121

Solution: Let the side of the square plot be a ft.   a2 = 64 => a = 8   Length of the fence = Perimeter of the plot = 4a = 32 ft.   Cost of building the fence = 32 * 58 = Rs. 1856.   Answer: 1856
Answer: D
John is filling out the office space for his employees. There are 8 people in his office, and he must assign 8 employees to the following positions: 2 next to his cabin, 2 near the gate, 2 in center, and 2 near coffee machine. Only 2 employees are secretary and can sit next to his cabin, and they cannot sit anywhere else. The other employees can sit anywhere they like. How many different groupings are possible?	Choose the most appropriate option:	A) 100	B) 90	C) 80	D) 70	E) 60

Solution: Secretary can sit in 2C2 ways = 1   Near the gate we can have 6C2 combinations (2 secretaries are already having a place)   In the center we can have 4 C2 employees as 4 already have a place   Near coffee machine we can have 2C2 employees as all other place are taken   Number of selection = 2C2 * 6C2 * 4C2 * 2C2 = 90   Ans: 90
Answer: B
What least number should be subtracted from 13605 such that the remainder is divisible by 87 ?	Options:
A) 27
B) 29
C) 28
D) 30
E) 33

Solution: 13605 ÷ 87 = 156, remainder = 33   Hence 33 is the least number which can be subtracted from 13605 such that the remainder   is divisible by 87   Answer is 33
Answer: E
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is	Choose the correct choice from the following.
A) 7/19	B) 7/11	C) 7/10	D) 7/21	E) 7/15

Solution: Explanation:   Drawing two balls of same color from seven green balls can be done in ways.   Similarly from eight white balls two can be drawn in ways.   P = 7C2/15C2 + 8C2/15C2 = 7/15   Answer:7/15
Answer: E
A 9% stock yields 25%. The market value of the stock is: Choose the most appropriate option:
A) Rs 45 B) Rs 25 C) Rs 40 D) Rs 39 E) Rs 36

Solution: Explanation:   For an income of Rs. 25, investment = Rs. 100.   For an income of Rs 9, investment =Rs.100/25 X9 =Rs36   Market value of Rs. 100 stock = Rs 36   Answer is Rs 36
Answer: E
The age of Amit is 3 times that of his son. 15 years ago, Amit was 9 times as old as his son, What will be the age of Amit after 15 years?  Choose the correct choice
A) 35 years
B) 60 years
C) 75 years
D) 65 years
E) None of these

Solution: Let the present age of Amit and his son be x and y respectively.   Then, x = 3y ...(i)   (x -15) = 9(y - 15)   or x - 15 = 9y -135 .   x - 9y = - 120 ...(ii)   Solving (i) and (ii),   we get y = 20 and x = 60   Thus Age of Amit after 15 years = 60 + 15= 
60 + 15 = 75
75 years   ANSWER:75 years
Answer: C
The second day of a month is Friday, What will be the last day of the next month which has 31 days?
Options.
A) Friday	B) Saturday	C) Wednesday	D) Data inadequate	E) None of these

Solution: Explanation :   We cannot find out the answer because the number of days of the current month is not given. Answer : Option Data inadequate
Answer: D
Find the odd man out. 0,3,7,15,24
Pick one:
A) 8  B) 10  C) 9  D) 6  E) 14

Solution: 1^2-1=0   2^2-1=3   3^2-1=8   4^2-1=15   5^2-1=24   Hence, it is clear that 8 should have come instead of 7   8nswer : Option 8
Answer: A
A regular hexagon is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of ∠OAB ? Choose the correct answer
A) 48 degrees B) 60 degrees C) 72 degrees D) 84 degrees E) 108 degrees

Solution: its a regular hexagon so divide the globe by 6.   = 360/6= 
360/6 = 60
60   72 would be the angle at O.   Angles at A and B are equivalent, so   60 + 2x= 180   2x = 120   x = 60   Angles OAB and OBA will be 60 degrees each.   60 degrees
Answer: B
A box measuring 49 inches long by 21 inches wide by 14 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?	Choose the correct option
A) 17	B) 42	C) 54	D) 108	E) 864

Solution: least number of cubes will be required when the cubes that could fit in are biggest.   7 is the biggest number that could divide all three, 49, 21 and 14.   Thus side of cube must be 7, and total number of cubes = 49/7 * 21/7*14/7= 
49/7 * 21/7*14/7 = 42
42   Ans 42 it is.
Answer: B
If 20% of a = b, then b% of 20 is the same as :	Select the correct option.
A) 4% of a  B) 6% of a  C) 8% of a  D) 10% of a  E) 15 of a

Solution: 20% of a = b -> 20/100 a = b   b% of 20 = b/100*20 = 4% of a   4% of aNSWER 4% of a
Answer: A
What is the total surface area in square meters of a rectangular solid whose length is 9 meters, width is 8 meters, and depth is 5 meters?  Choose one
A) 152 m2 B) 162 m2 C) 180 m2 D) 300 m2 E) 314 m2

Solution: Surface Area of a cuboid = 2(lb+bh+lh) = 2(9*8+8*5+9*5)=2(72+40+45)=2*157= 
2*157 = 314
314 m2   Answer : 314 m2
Answer: E
Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 15000 at the end of the year, what should be the share of Narendra? Choices.
A) A)Rs.7000	B) B)Rs.12000	C) C)Rs.8500	D) D)Rs.8600	E) E)Rs.8700

Solution: The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1.   :. Narendra’s share on profit of Rs.15000 = 15000 × 4/5 = Rs.12000.   Rs.12000)
Answer: B
In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?	Choose the correct answer:
A) 3 : 7
B) 5 : 7
C) 7 : 3
D) 7 : 5
E) 6 : 5

Solution: By the rule of alligation:   Cost of 1 kg pulses of 1st kind Rs. 15   Cost of 1 kg pulses of 2nd kind Rs. 20   Mean Price Rs. 16.50   Required rate = 3.50 : 1.50 = 7 : 3.   Answer:7 : 3
Answer: C
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 40 min, then the slower pipe alone will be able to fill the tank in?	Select:
A) 160 B) 787 C) 144 D) 128 E) 121

Solution: Let the slower pipe alone fill the tank in x min.   Then, faster pipe will fill it in x/3 min.   1/x + 3/x = 1/40   4/x = 1/40 => x = 160 min.   160nswer: 160
Answer: A
The fourth proportional to 6, 14 and 18 is?
Select
A) 21 B) 42 C) 77 D) 88 E) 99

Solution: (14*18)/6= 
(14*18)/6 = 42
42   Answer: 42
Answer: B
A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:2. The ratio of economy cars to sport utility vehicles is 4:2. What is the ratio of luxury cars to sport utility vehicles? Select the correct option:
A) 9:8  B) 8:9  C) 3:2  D) 8:6  E) 1:2

Solution: The ratio of economy to luxury cars is 3:2 --> E:L = 3:2 = 12:8.   The ratio of economy cars to sport utility vehicles is 4:2 --> E:S = 4:2 = 12:6.   Thus, L:S = 8:6.   Answer: 8:6.
Answer: D
It takes 1.5 hours for Tim to mow the lawn. Linda can mow the same lawn in 2 hours. How long will it take John and Linda, work together, to mow the lawn?  Choose the correct choice from the following answers:
A) 51.1 minutes	B) 51.3 minutes	C) 51.5 minutes	D) 51.7 minutes	E) 51.9 minutes

Solution: We first calculate the rate of work of John and Linda   John: 1 / 1.5 and Linda 1 / 2   Let t be the time for John and Linda to mow the Lawn. The work done by John alone is given by   t * (1 / 1.5)   The work done by Linda alone is given by   t * (1 / 2)   When the two work together, their work will be added. Hence   t * (1 / 1.5) + t * (1 / 2) = 1   Multiply all terms by 6   6 (t * (1 / 1.5) + t * (1 / 2) ) = 6   and simplify   4 t + 3 t = 6   Solve for t   t = 6 / 7 hours = 51.5 minutes.   Answer 51.5 minutes
Answer: C
find value for x from below equation? x + 1 = 3	Choose the correct answer:
A) -5 B) -4 C) 4 D) 3 E) 2

Solution: 1. Subtract 1 from both sides:   x + 1 - 1 = 3 - 1   2. Simplify both sides:   x = 2   2
Answer: E