MU-NLPC/Calc-aqua_rat huggingface dataset:
During a certain season, a team won 60 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?
Choose the correct answer:
A) 80 B) 70 C) 56 D) 50 E) 105

Solution: We are first given that a team won 60 percent of its first 100 games. This means the team won 0.6 x 100 = 60 games out of its first 100 games.   We are next given that the team won 50 percent of its remaining games. If we use variable T to represent the total number of games in the season, then we can say T – 100 equals the number of remaining games in the season. Thus we can say:   0.5(T – 100) = number of wins for remaining games   0.5T – 50 = number of wins for remaining games   Lastly, we are given that team won 70 percent of all games played in the season. That is, they won 0.7T games in the entire season. With this we can set up the equation:   Number of first 100 games won + Number of games won for remaining games = Total Number of games won in the entire season   60 + 0.5T – 50 = 0.7T   10 = 0.2T   100 = 2T   50 = T   Answer is 50.
Answer: D
Two trains A and B are 225 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
Choose the correct answer.
A) 10 s
B) 15 s
C) 4 s
D) 8 s
E) 12 s

Solution: DETAILED SOLUTION   Speed of A = 54∗1000/60∗60 = 15 m/s   Speed of B = 36∗1000/60∗60 = 10 m/s   Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s   The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25= 
150/25 = 6
6s.   What is the time taken for trains to completely cross each other? The length that needs to be crossed= 225 + 150= 
225 + 150 = 375
375 m. Time taken= 375/25= 
375/25 = 15
15 s.   CORRECT ANSWER 15 s.
Answer: B
What is the normal price of an article sold at $72 after two successive discounts of 10% and 20%?	Answers.
A) $92
B) $96
C) $100
D) $104
E) $108

Solution: 0.8*0.9*cost price = $72   cost price = $100   The answer is $100.
Answer: C
Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents V watch all of the shows?	Answers:
A) 150
B) 108
C) 42
D) 21
E) -21

Solution: OA is D.   100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula   100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.   The term between parantheses value 18% so the equation to resolve is   100=35+40+50-18-2ABC   therefore the value of ABC is 3.5% of 600,V is 21. 21 is the correct answer
Answer: D
Look at this series: 70, 71, 76, __, 81, 86, 70, 91, ... What number should fill the blank? Answers:
A) 70	B) 71	C) 80	D) 96	E) None

Solution: Explanation: In this series, 5 is added to the previous number; the number 70 is inserted as every third number.   70nswer: Option 70
Answer: A
We bought a total of 90 books at the store. Math books cost $4 and history books cost $5. The total price was $390. How many math books did we buy?	Choices:
A) 57 B) 60 C) 63 D) 66 E) 69

Solution: M + H = 90   H = 90 - M   4M + 5H = 390   4M + 5*(90 - M) = 390   M = 60   The answer is 60.
Answer: B
Thabo owns exactly 220 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?
Choose the correct option:
A) 10
B) 20
C) 30
D) 40
E) 50

Solution: I think we can use double-matrix method and solve using only one variable.   Our goal is to find the number of hardcover nonfiction books. Let that number be x. We are given that all 140 books are either paperback fiction, paperback nonfiction, or hardcover nonfiction. This implies that number of hardcover fiction books is 0.   40ouble-matrix: P = paperback; H = hardcover; F = fiction; NF = nonfiction   P H Total   F 2x+40 0   NF x+20 x   Total 3x+60 x 220   3x + 60 + x = 220   x = 40   Answer (40.)
Answer: D
In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :	Choices:  A) 35  B) 38  C) 40  D) 42  E) 44

Solution: Explanation:   Let the number of correct answers be X.   Number of incorrect answers = (60 – X).   4x – (60 – x) = 130   => 5x = 190   => x = 38   Answer: 38
Answer: B
The average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 154.4, what is the average of the other half?
Choose the correct choice from the following answers
A) 44.2 B) 47.8 C) 50.5 D) 53.6 E) 56.9

Solution: The average of this half is 154.4/4= 
154.4/4 = 38.6
38.6   This is 4.6 below the overall average, thus the average of the other half of the numbers must be 4.6 above the overall age, that is 43.2+4.6= 
43.2+4.6 = 47.8
47.8   The answer is 47.8.
Answer: B
Express a speed of 108 kmph in meters per second?
Pick one:
A) 10 mps B) 05 mps C) 09 mps D) 30 mps E) 11 mps

Solution: 30 mps   30 mps    108 * 5/18= 
 108 * 5/18 = 30
30 mps
Answer: D
A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m? Choose the correct choice from the following choices
A) 22377  B) 27782  C) 27891  D) 24000  E) 18771

Solution: 24 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x   24 = 1/100 * x => x = 24000   Answer: 24000
Answer: D
If 1 is added to the denominator of fraction, the fraction becomes 1/2. If 1 is added to the numerator, the fraction becomes 1. The fraction is ?
Choose the correct answer:
A) 4/7
B) 5/9
C) 2/3
D) 10/11
E) None

Solution: Answer   Let the required fraction be x/y   Then, x/(y + 1) = 1/2   ⇒ 2x - y = 1 ...(1)   (x + 1) / y = 1   ⇒ x - y = -1 ...(2)   Solving Eq. (1) and (2)   We get x = 2, y = 3   ∴ The fraction is 2/3   2/3orrect Option: 2/3
Answer: C
The ratio of length to width of a rectangular showroom window is 3.3 to 2. If the width of the window is 8 feet, what is the approximate length of the display in feet? Choose the correct choice:
A) 7  B) 11  C) 13  D) 16  E) 26

Solution: Explanation:   Letting L be the length of the window, the proportion for the ratio of the length to the width can be expressed in the following equation:   3.3/2=L/8   26.4=2L   13.2=L   Answer: Option 13
Answer: C
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.3982. What is the difference between Rohan’s and Sudhir’s share in the profit?
Choose the correct choice from the following:	A) 350	B) 360	C) 362	D) 375	E) 380

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. 3982 × 1/11 = Rs.362.   Option '362'
Answer: C
What is the greatest prime factor of 4^15 - 2^28?
Choices
A) 2	B) 3	C) 5	D) 7	E) 11

Solution: I'm happy to help with this.   We know 4 = 2^2, so 4^15 = (2^2)^15 = 2^(2*15) = 2^30   That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)   So, 4^15 - 2^28 = 2^30 - 2^28 = 2^(28 + 2) - 2^28 = (2^28)*(2*2) - 2^28 = (2^2 - 1) *(2^28)   = (4 - 1)*(2^28) = 3*(2^28)   The prime factors of 63 are 3, so the largest prime factor is 7, answer choice D.   Here's a blog you may find helpful.   http://magoosh.com/gmat/2012/gmat-math-factors/   Does all that make sense? Please let me know if you have any further questions.   Mike   Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.   3
Answer: B
A number of 44 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes? Choose the correct choice from the following choices:
A) 10	B) 14	C) 15	D) 16	E) 17

Solution: To maximize # of boxes we should minimize marbles per box: 13*3+1*5= 
13*3+1*5 = 44
44 --> 13+1=14.   Answer 14
Answer: B
A batsman makes a score of 82 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
Answers.
A) 25
B) 31
C) 27
D) 29
E) 34

Solution: Let the average after 17 innings = x   Total runs scored in 17 innings = 17x   Average after 16 innings = (x-3)   Total runs scored in 16 innings = 16(x-3)   Total runs scored in 16 innings + 82 = Total runs scored in 17 innings   => 16(x-3) + 82 = 17x   => 16x - 48 + 82 = 17x   => x = 34   Answer is 34.
Answer: E
Which of the following describes all values of x for which 1–x^2 >0?  Pick one:
A) x >= 1
B) x <= –1
C) 0 <= x <= 1
D) x <= –1 or x >= 1
E) –1 < x < 1

Solution: Which of the following describes all values of x for which 1–x^2 >= 0?   (A) x >= 1   Plugged in 2. 1–(2)^2 >= 0 -3>=0? NO. Wrong   (B) x <= –1   Plugged in -2. 1–(-2)^2 >= 0 -3>=0? NO. Wrong   (C) 0 <= x <= 1   Plugged in 0, 1, and 1/2. All of them work. But E is better because it describes all the values of x   (D) x <= –1 or x >= 1   A and B answer this. Wrong.   (E) –1 < x < 1   X is a positive or negative fraction.   x = -1/2 x = 1/2 x = 0   Plug all of them. They work.   Answer is –1 < x < 1.
Answer: E
The sum of ages of 5 children born 1.5 years different each is 50 years. What is the age of the Elder child?  Options
A) 8
B) 9
C) 10
D) 16
E) 13

Solution: Let the ages of children be x, (x + 1.5), (x + 3), (x + 4.5) and (x + 6) years.   Then, x + (x + 1.5) + (x + 3) + (x + 4.5) + (x + 6) = 50   5x = 35   x = 7.   x+6= 7+6= 
7+6 = 13
13   Answer : 13
Answer: E
Two wheels are connected via a conveyor belt. The larger wheel has a 48cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?
Choose the correct choice
A) 90r B) 75r C) 48r D) 24r E) (64π)/3

Solution: Interesting to note that the larger wheel has a diameter of 48 (8*6) while the smaller one has a diameter of 32 (8*4)...   If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 48pi and 32pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.5 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make   10*1.5= 
  10*1.5 = 15
15 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make   600*1.5= 
  600*1.5 = 900
900 revolutions per hour.   If r= 10, then the answer choice must be b.   A. 90r
Answer: A
A and B can do a piece of work in 18 and 9 days respectively. A does the work for a few days and left, then B continued for 6 days. How many days did A and B work together?
Pick one:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: A and B work together for 2days.   A 1day work 1/18   B 1day work 1/9   Let A work x days.   Then equation form is   (x/18) + ((x+6)/9) = 1   From this equation x value is 2.   ANSWER:2
Answer: B
Kate and David each have $10. Together they flip a coin 5 times. Every time the coin lands on heads, Kate gives David $1. Every time the coin lands on tails, David gives Kate $1. After the coin is flipped 5 times, what is the probability that Kate has more than $10 but less than $15?  Options:	A) 5 /16	B) 15/ 32	C) 1/ 2	D) 2/32	E) 11/ 16

Solution: After 5 tries Kate to have more than initial sum of 10$ and less than 15$ must win 3 or 4 times (if she wins 2 or less times she'll have less than 10$ and if she wins 5 times she'll have 15$).   So the question becomes "what is the probability of getting 3 or 4 tails in 5 tries?".   P(t=3 or t=4)=P(t=3)+P(t=4)=C35∗(12)5+C45∗(12)5=1532P(t=3 or t=4)=P(t=3)+P(t=4)=C53∗(12)5+C54∗(12)5=1532   Answer: 15/ 32.
Answer: B
I. a3 - 988 = 343,
II. b2 - 72 = 49 to solve both the equations to find the values of a and b?	Answers:
A) If a > b
B) If a ≥ b
C) If a < b
D) If a ≤ b
E) If a = b or the relationship between a and b cannot be established.

Solution: Explanation:   a3 = 1331 => a = 11   b2 = 121 => b = ± 11   a ≥ b   If a ≥ b)
Answer: B
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 6 boys when a boy gets any no. of prizes?  Choices.
A) 55 B) 230 C) 224 D) 216 E) 70

Solution: Ans.(D)   Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (6 x 6 x 6) ways = 63 ways = 216 ways Or nr ways = 63 ways = 216 ways
Answer: D
x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xyz is divisible by 6
2. (z-x)(y-x+1) = 4
3. xy is even
Options:
A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III

Solution: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1   Statement 1 would be true as at least one of the three numbers is divisible by 2 and one by 3 so xyz would be divisible by 6.   Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2= 
2*2 = 4
4 So, always true   Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence true.   So, I II and III are always true and hence answer is   I, II, and III.
Answer: E
Ranjeet purchased an item for Rs.3500 and sold it at the loss of 25%. From that amount he purchased another item and sold it at the gain of 20%. What is his overall gain/loss? Choose the correct choice from the following choices:
A) Loss of Rs.240	B) Gain of Rs.120	C) Loss of Rs.350	D) Neither gain nor loss	E) None of these

Solution: Explanation:   1st SP = Rs.3500 – 25% of 3500 = Rs.3500 – 875 = Rs.2625.   (24% = ¼)   2nd SP = Rs.2625 + 20% of 2625 = Rs.2625 + 525 = Rs.3150.   :. Overall loss = Rs.3500 – Rs.3150 = Rs.350.   Answer: Option Loss of Rs.350
Answer: C
Find the odd man out 3, 8, 38, 78, 158	Options:
A) 28  B) 8  C) 128  D) 18  E) 158

Solution: 3 x 2 + 2 = 8   8 x 2 + 2 =18   18 x 2 + 2 =38   38 x 2 + 2 =78   ANSWER:18
Answer: D
From the answers select the option that is near to √5?  Choose the correct option.
A) 2.2	B) 2.3	C) 3.0	D) 3.8	E) 1.9

Solution: 2.2 is nearly equal to the square root of 5.   2.2*2.2=4.4   2.3*2.3= 
2.3*2.3 = 5.29
5.29   Difference    5 - 4.4= 
 5 - 4.4 = 0.6
0.6   5 - 5.3=0.7   Since 0.6 is lesser among both, 2.2 is closer.   2.2nswer is 2.2
Answer: A
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg. What might be the weight of the new person?	Choose the correct choice from the following options:
A) 56 kg
B) 90 kg
C) 75 kg
D) Data inadequate
E) None of these

Solution: C   75 kg   Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (55 + 20)= 
(55 + 20) = 75
75 kg.
Answer: C
If x is divisible by 5, 20, and 125, which of the following must be the least multiple of x?	Pick one
A) 12500 B) 1250 C) 500 D) 100 E) 125

Solution: If x is divisible by 5, 20, and 125, then x must be a multiple of 5,4and 25.   Hence,the least multiple of x will be   5*4*25= 
  5*4*25 = 500
500.   ANSWER:500
Answer: C
Which of the following has 21^20 as a factor?
Choose the correct choice
A) 15^60	B) 30^20	C) 40^80	D) 42^20	E) 90^80

Solution: Here 21^20 = 3^20 * 7^20 Only Option D has both .   Smash 42^20
Answer: D
Mary and Mike enter into a partnership by investing $650 and $350 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $600 more than Mike did, what was the profit made by their business in that year? Pick:
A) $3000
B) $3200
C) $3300
D) $3400
E) $4000

Solution: Explanatory Answer   Let the profit made during the year be $3x   Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 6.5 : 3.5   i.e., 65% of 2x would go to Mary and 35% of 2x would go to Mike.   Hence, Mary would get (65 - 35)% of 2x more than Mike   Or30% of 2x = $600   i.e.,(30/100)*2x = 600   or 2x = 2000.   Hence, the profit made by the company during the year $3x = $3000.   $3000nswer : $3000
Answer: A
A can knit a pair of socks in 3 days. B can knit the same thing in 6 days. If they are knitting together, in how many days will they knit two pairs of socks?
Choose the correct answer:	A) 4 days	B) 2 days	C) 4 1⁄2 days	D) 3 days	E) None of these

Solution: ExplanationA’s one day’s work = 1⁄3 rd work.   B’s one day’s work = 1⁄6 rd work.   (A + B)’s one day’s work = 1⁄3 + 1⁄6 = 1⁄2 nd work.   ∴ A and B together can complete the work (knit a pair of socks) in 2 days.   ∴ They together knit two pair of socks in 4 days.   4 daysnswer 4 days
Answer: A
If 12 : 8 :: x : 16, then find the value of x  Select: A) 18 B) 24 C) 28 D) 16 E) 20

Solution: Explanation:Treat 12:8 as 12/8 and x:16 as x/16, treat :: as = So we get 12/8 = x/16=> 8x = 192=> x = 24 Option 24
Answer: B
It takes Kannan 10 minutes to walk to the car park and 110 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.? Pick: A) 8:50 a.m B) 5:50 a.m C) 7:50 a.m D) 6:50 a.m E) 7:00 a.m

Solution: The time it takes Kannan to get to work: time to walk to car park + time to drive     10 + 110= 
  10 + 110 = 120
120 minutes= 2 hours   Kannan needs to get out of the house 2 hours before 9:00 am at   9:00 - 2:00 = 7:00 a.m   correct answer 7:00 a.m
Answer: E
Reema can complete a piece of work in 12 days while Seema can the same work in 18 days. If they both work together, then how many days will be required to finish the work? Choices.
A) 6 days B) 7.2 days C) 9.5 days D) 12 days E) 13 days

Solution: EXPLANATION:   Hint:   A's one day work =	1/12   B's one day work =	1/18   (A + B)'s one day work =	1/12	+	1/18	=	(18 + 12)/(12 x 18)=	30/216=	1/7.2   Together, A & B will finish the work in 7.2 days.   ANSWER IS 7.2 days
Answer: B
Calculate the sum of first 39 natural numbers.	Pick
A) 780  B) 891  C) 812  D) 847  E) 890

Solution: Solution   We know that(1+2+3+.....+39)	= n(n+1)/2   Therefore (1+2+3+....+39)	=(39×40 / 2)   = 780.   780nswer 780
Answer: A
In a class of 50 students, 3/5 went away do painting, 1/5 went to play in the field. How many students are left in the classroom? Options
A) 20	B) 30	C) 5	D) 8	E) 10

Solution: 3/5 + 1/5 are the students who have left the classroom   3/5 + 1/5 = (3 + 1)/5 , since denominator is same for both fractions   = 4/5   Remaining students in the classroom = 1 - 4/5 = 5/5 - 4/5 = (5-4)/5 = 1/5   1/5 of 50 = 10   Ans: 10
Answer: E
Which is largest prime number? Choose the correct choice from the following choices
A) 653	B) 857	C) 859	D) 523	E) 461

Solution: Answer:859
Answer: C
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 42 kmph. Of how many minutes does the train stop per hour?	Options
A) 16	B) 4	C) 15	D) 18	E) 12

Solution: T = 3/45 * 60= 
3/45 * 60 = 4
4   Answer: 4
Answer: B
A sum of money is to be distributed among A, B, C, D in the proportion of 6 : 2 : 4 : 3. If C gets $500 more than D, what is D's share?
Choose the correct choice from the following choices:  A) $2000  B) $2500  C) $3000  D) $3600  E) $4200

Solution: Let the shares of A, B, C and D be 6x, 2x, 4x and 3x respectively.   Then, 4x - 3x = 500   x = $500   A's share = 6x = 6*$500 = $3000   The answer is $3000.6* 500= 
6* 500 = 3_000
$3000   The answer is $3000.
Answer: C
If A lends Rs.2000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?	Choose one:
A) 90 B) 122.5 C) 132.5 D) 114.5 E) 212.5

Solution: (2000*1.5*3)/100= 
(2000*1.5*3)/100 = 90
> 90   90NSWER:90
Answer: A
Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $6 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?  Pick.
A) 8n + 2  B) 8n + 4  C) 9n + 2  D) 9n + 5  E) 9n + 4

Solution: its C   n items for $8 each   total price $8n   postage and handling of $3 for 1st item and $1 for the rest   total postage and handling = $ [6+ (n-1)]   = $ n+5   total cost   8n+n+5 = 9n+5   9n + 5
Answer: D
Claire has a total of 92 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have?  Choose the correct choice from the following answers:
A) 39 B) 68 C) 54 D) 57 E) 60

Solution: G+H =92 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12= 
25*12 = 300
300   G=92-H OR 3(92-H) +4H =300 H = 300-276= 
300-276 = 24
24 THEN G= 92-24= 
92-24 = 68
68   68
Answer: B
A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 50km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is
Pick one.
A) 8.95km/hr
B) 26.7km/hr
C) 27.8km/hr
D) 28.5km/hr
E) 8.45km/hr

Solution: average speed = (2*50*20)/50+20 km/hr   =28.5 km/hr   Answer (28.5km/hr)
Answer: D
The mass of 1 cubic meter of a substance is 400 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)  Choose the correct option:
A) 1.5
B) 2.5
C) 3.5
D) 4.5
E) 5.5

Solution: 400 kg - 1 cubic meter;   400,000 g - 1 cubic meter;   400,000 g - 1,000,000 cubic centimeters;   1 g - 1,000,000/400,000 = 10/4= 
10/4 = 5/2 = around 2.5
2.5 cubic centimeters.   Answer: 2.5.
Answer: B
Manoj received Rs. 6000 as his share out of the total profit of Rs. 9000 which he and Ramesh earned at the end of one year. If Manoj invested Rs.120000 for 6 months, whereas Ramesh invested his amount for the whole year, what was the amount invested by Ramesh
Choose the correct choice from the following
A) Rs. 2000  B) Rs. 3000  C) Rs. 4000  D) Rs. 5000  E) None of these

Solution: Explanation:   Suppose Ramesh invested Rs. x. Then,   Manoj : Ramesh = 20000 * 6 : x * 12.   120000/12x : 6000/3000   => x = 120000/24= 
120000/24 = 5_000
5000   Option Rs. 5000
Answer: D
A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
Choose the correct choice from the following choices:
A) 87
B) 09
C) 40
D) 42
E) 76

Solution: 1/8 - 1/x   = 1/10   x = 40   Answer:40
Answer: C
Two trains 500 m and 750 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?	Pick:
A) 10.6
B) 45
C) 10.4
D) 10.8
E) 10.1

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 500 + 750= 
500 + 750 = 1_250
1250 m.   Required time= 1250 * 9/250= 
1250 * 9/250 = 45
45 sec.   Answer: 45
Answer: B