MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 200 female managers in a certain company. Find the total number T of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
Choose the correct choice:
A) 300	B) T=400	C) T=500	D) 600	E) None of these

Solution: {Managers} = {Female Managers} + {Male Managers};   We are told that the total number of managers in the company is 2/5 of all the employees , thus {Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively.   Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200;   Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500.   Answer: T=500.
Answer: C
The ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings? Choose the correct answer
A) 2/9
B) 3/2
C) 3/8
D) 3/4
E) 3/1

Solution: Let the earnings of P and Q be 9x and 10x respectively.   New ratio = [9x + 1/4 (9x)]/[10x - 1/4 (10x)]   => 9*(1 + 1/4)/10*(1 - 1/4)   => 9/10 * (5/4)/(3/4) = 3/2   Answer:3/2
Answer: B
A parking space have 8 different slots. 8 cars has to arrange in 8 slots. But there are exactly 4 cars between 2 specified cars. In how many ways cars can be arranged?	Choose the most appropriate option.
A) 1210
B) 650
C) 1500
D) 1640
E) 1440

Solution: we arranged 2 specified cars in 2 slots = 2!   remaining 6 cars in 6 slots = 6!   number of ways = 2!*6! = 1440   correct option is 1440
Answer: E
Robex traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different.
Choose the correct answer
A) z=3x  B) x=3z  C) y=2x  D) x=2y  E) y=3x

Solution: Robex Travelled for x,y and for z min.   Total Time : x + y + z   Which is equal to : 3y   Equating both sides we get   x+y+z = 3y   => x+z =2y ........ Eqn 1   Looking out at options   D Says x =2y   Using it in Eqn 1   2y + z = 2y   => Z = 0 mins, Which I guess is not possible.   The Ans isx=2y
Answer: D
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
Choose the correct choice from the following
A) 275  B) 270  C) 279  D) 263  E) 271

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Smaller number = 270.   Answer is 270.
Answer: B
If 20% of a = b, then b% of 20 is the same as:  Choose the correct choice from the following:	A) 4% of a	B) 5% of a	C) 20% of a	D) 30% of a	E) None of these

Solution: Explanation:   20% of a = b =	(20/100)a=b.   b% of 20 =(b/100 x 20)=((20/100)a x 1/100 x 20)=(4/100)a=4% of a.   4% of aNSWER IS 4% of a
Answer: A
Calculate how long it will take a swimmer to swim a distance of 12km against the current of a river which flows at 1.2 km/hr, given that he can swim in still water at 5km/h  Choices:
A) 3.26
B) 3.16
C) 2.34
D) 3.98
E) 3.17

Solution: swim in still water at = 5   speed of river= 1.2   US = 5 - 1.2= 
5 - 1.2 = 3.8
3.8   Distance= 12   T = 12/3.8 = 3.16   Answer: 3.16
Answer: B
A train running at 1/6 of its own speed reached a place in 24 hours. How much time could be saved if the train would have run at its own speed?	Pick one.
A) 8hrs B) 20hrs C) 12hrs D) 15hrs E) 6hrs

Solution: time taken if run its own speed = 1/6*24= 
1/6*24 = 4
4 hrs   Time saved= 24 - 4= 
24 - 4 = 20
20 hrs   Answer : 20hrs
Answer: B
An article is bought for Rs.675 and sold for Rs.1000, find the gain percent? Choose the correct choice from the following choices
A) 34%  B) 44%  C) 48%  D) 32%  E) 46%

Solution: 675 ---- 325   100 ---- ? =>   =48%   Answer:48%
Answer: C
The salaries of A and B together amount to $6000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A's salary?  Choose one:  A) $1000  B) $1250  C) $2500  D) $4500  E) $5200

Solution: Let A's salary is x   B's salary = 6000-x   (100-95)% of x = (100-85)% of (6000-x)   x = $4500   Answer is $4500
Answer: D
There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs. 2288, then what was the price of the article initially?
Choose the correct choice from the following answers
A) Rs.2008 B) Rs.2022 C) Rs.2000 D) Rs.2029 E) Rs.2021

Solution: Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article = 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130 = 130 - 26 = Rs. 104.   In the 3rd year, price = 104 + 10% of 104 = 104 + 10.4 = Rs. 114.40.   But present price of the article is Rs. 2288   for 114.4 ---> 100 ; 2288 ---> ?   Required price = (2288 * 100)/114.4 = 20 * 100 = Rs.2000.   Answer:Rs.2000
Answer: C
On a weekend, 7 college friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? Pick.
A) $175 B) $210 C) $147 D) $560 E) $412

Solution: Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 7 for all answer choices.   175/7= 
175/7 = 25
25   210/7= 
210/7 = 30
30   147/7= 
147/7 = 21
21   560/7= 
560/7 = 80
80   412/7= 58.86   E is not an integer amount.   Answer:$412
Answer: E
which one is odd?
4377
3954
9861
8454
9831  Pick
A) 4377
B) 3954
C) 9861
D) 8454
E) None

Solution: 9861orrect Answer : 9861   sum of digit of all other number is 21, but sum of digit of 9861 is 24
Answer: C
The product of two natural numbers is 19. The sum of the reciprocal of its square is Choices:	A) 361/362	B) 362/361	C) 360/359	D) 359/360	E) None of these

Solution: Explanation:   Let the number be a and b. Then,   ab = 19 => a = 1, b = 19   So, 1/a2 + 1/b2 = (a2 + b2)/a2b2   = (12 + 192)/(1 x 19)2 = 362/361   Answer: Option 362/361
Answer: B
The crew of a rowing team of 8 members is to be chosen from 12 men (M1, M2, …., M12) and 8 women (W1, W2,…., W8), such that there are two rows, each row occupying one the two sides of the boat and that each side must have 4 members including at least one women. Further it is also known W1 and M7 must be selected for one of its sides while M2, M3 and M10 must be selected for other side. What is the number of ways in which rowing team can be arranged.	Choose the correct option
A) 2 B) 1 C) 5 D) 6 E) 4

Solution: We need two person for one side and 1 women for the another side. We select that women in 7 ways. Now that second side people can sit in 7x4! ways.   Now for the first side we need two people from the remaining 14. So this can be done in 14C214C2 ways and this side people can sit in 4C2×4!4C2×4! ways.   Again the first group may take any of the two sides. So total ways are 2×7×4!×14C2×4!   Answer:4
Answer: E
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 30 metres? Select
A) 22 seconds  B) 6 seconds  C) 7 seconds  D) 1 seconds  E) 2 seconds

Solution: Speed of the boat downstream   = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 60 m= 30/5= 
30/5 = 6
6 seconds.   Answer:6 seconds
Answer: B
A six-character password consists of three letter of the alphabet and three different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible? Choose the correct option:
A) 5,040
B) 2,228,720
C) 22,226,000
D) 22,237,440
E) 22,464,000

Solution: 4 character password: DLDLLD   First digit can be chosen in 10 ways.   The letter can be chosen in 26 ways.   Next digit can be chosen in 9 ways.   The letter can be chosen in 25 ways.   The letter can be chosen in 24 ways.   Next digit can be chosen in 8 ways.   This gives us 10*26*9*25*24*8 ways   Now, the letter can also be DDLLLD so there will be another 10*9*26*25*24*8 ways   Total = 10*26*9*25*24*8*2 = 22,464,000 ways   22,464,000
Answer: E
Find the odd man out. 23, 27, 36, 52, 77, 111, 162 Pick.
A) 111  B) 162  C) 52  D) 27  E) 36

Solution: 23 + 22 = 27   27 + 32 = 36   36 + 42 = 52   52 + 52 = 77   77 + 62 = 113   113 + 72 = 162   Hence, 113 should have come in place of 111111nswer is 111
Answer: A
Jaclyn buys $50 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter  Choose the correct answer:  A) 1187.5  B) 1234  C) 1289  D) 1345  E) None of these

Solution: Explanation:   I=(p x r x t)/100   1187.5nswer: 1187.5
Answer: A
If A = x% of y and B = y% of x, then which of the following is true?  Answers:  A) A is smaller than B.  B) Relationship between A and B cannot be determined  C) If x is smaller than y, then A is greater than B.  D) None of these  E) B is smaller than A

Solution: Explanation:   A = (x/100)y = (xy/100).................(Equation 1)   B = (y/100)x = (yx/100).................(Equation 2)   From these equations, it is clear that A = B   Answer: Option None of these
Answer: D
The number of arrangements that can be made with the letters of the word MEAUDOWS so that the vowels occupy the odd places?	Pick one.
A) A)522	B) B)534	C) C)576	D) D)656	E) E)476

Solution: Explanation:   The word MEAUDOWS has 8 letters of which 4 are vowels.   V-V-V-V-   As the vowels have to occupy odd places, they can be arranged in the 4 odd places in 4! i.e., 24 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.   Hence the total ways are  24 * 24= 
 24 * 24 = 576
576.   576)
Answer: C
A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among eight colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)	Pick:
A) 32 B) 33 C) 34 D) 35 E) 36

Solution: 8C2 = 28   The number of test subjects is  28 + 5= 
 28 + 5 = 33
33   The answer is 33.
Answer: B
A monk has a very specific ritual for climbing up the steps to the temple. First he climbs up to the middle step and meditates for 1 minute. Then he climbs up 8 steps and faces east until he hears a bird singing. Then he walks down 12 steps and picks up a pebble. He takes one step up and tosses the pebble over his left shoulder. Now, he walks up the remaining steps three at a time which only takes him 9 paces.
How many steps are there?  Choose the correct choice from the following answers
A) 50 steps B) 49 steps C) 44 steps D) 35 steps E) 49 steps

Solution: B   There are 49 steps.   He hears the bird singing on step 33. He picks up the pebble on the 21st step and tosses it on the 22nd step. The remaining 27 steps are taken three at a time which is 9 pac
Answer: B
Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Three years from today, the difference between the age of the boy and the combined ages of the girls will be Choose the correct choice from the following choices:	A) 1	B) 2	C) 3	D) –2	E) –1

Solution: girl1: g1, girl2: g2, boy:b, these are the symbols for their ages today.   g1+g2<b   (1 year from now): (g1+1)+(g2+1) = b+1 ; g1+g2 = b-1   The difference between the girls's age and the boy's age is one today:   Assume ages, g1:20, g2:25, b:46 (notice the difference is currently 1); in 3 years the ages will be g1:23, g2:28, b:49 ; 49-(23+28) = -2   The Answer should be –2.
Answer: D
The average score of a cricketer in 2 matches is 20 and in other 3 matches is 30. Then find the average score in all the 5 matches?
Answers
A) 26	B) 27	C) 30	D) 35	E) 42

Solution: 26verage in 5 matches = (2*20 + 3*30)/2+3 = 40+90 / 5 = 130/5= 
130/5 = 26
26   26nswer is 26
Answer: A
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey ?
Choose the correct option:  A) 1 kmph  B) 5 kmph  C) 6 kmph  D) 4 kmph  E) 7 kmph

Solution: Explanation:   Speed of Man = 4.5 kmph   Speed of stream = 1.5 kmph   Speed in DownStream = 6 kmph   Speed in UpStream = 3 kmph   Average Speed = (2 x 6 x 3)/9 = 4 kmph.   Answer: 4 kmph
Answer: D
A die is rolled twice. What is the probability of getting a sum equal to 9?
Choose the correct answer:  A) 2/3  B) 2/9  C) 1/3  D) 1/9  E) 1/7

Solution: Explanation :   Total number of outcomes possible when a die is rolled = 6 (âˆµ any one face out of the 6 faces)   Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 Ã— 6 = 36   E = Getting a sum of 9 when the two dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}   Hence, n(E) = 4   P(E) = n(E)/n(S)=4/36=1/9   ANSWER IS 1/9
Answer: D
Bob invested $2000 in fund A and $1000 in fund B. Over the next two years, the money in Fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after bob made these investments. Bob's investment in fund A was worth how much more than his investment in fund B?	Choose the correct choice from the following.
A) $500  B) $550  C) $600  D) $650  E) $700

Solution: Bob earned 2000*(1+0.12) in total by fund A and earned 1000*(1+0.3)^2 in total by fund B.   So 2000*(1.12) - 1000*(1.69)= 
2000*(1.12) - 1000*(1.69) = 550
550.   The answer is, therefore, ($550).
Answer: B
Four persons enter the lift of a seven storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor
Answers
A) 720  B) 1296  C) 1540  D) 1478  E) 360

Solution: Each person out of 4 has 6 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 6*6*6*6=6^4. Now, there is no need to actually calculate this value: 6^4 will have 6 as the units digit and there is only one option (1296)   Answer: 1296.
Answer: B
For any positive integer r, the sum of the first r positive integers equals r(r+1)/2 . If s and r are positive integers and s > r, what is the sum of all the integers between s and r, inclusive?	Choose the correct choice from the following
A) s(s+1)/2 + r(r+1)/2  B) s(s+1)/2 - r(r-1)/2  C) s(s+1)/2 - r(r+1)/2  D) s(s+1)/2 + r(r-1)/2  E) s(n+1)/2 - r(s-1)/2

Solution: The sum of all the integers between s and r,inclusiveis the sum of the first s positive integersminusthe sum of the first r-1 positive integers.   The sum of the first s positive integers is s(s+1)/2;   The sum of the first r-1 positive integers is (r-1)r/2;   Therefore the answer is s(s+1)/2 - (r-1)r/2.   Answer: s(s+1)/2 - r(r-1)/2.
Answer: B
24 machines can do a work in 10days. How many machines are needed to complete the work in 40days?
Choose the correct choice
A) 10  B) 6  C) 4  D) 7  E) 5

Solution: Required number of machines = 24*10/40= 
24*10/40 = 6
6   Answer is 6
Answer: B
Firm A's revenues are described by the equation Ra = 17.12x and its costs by Ca = 12.87x + 2400.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.
(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 2000 over the same period that B's volume increases from 2000 to 4000, the percent increase in profits for the firm with the biggest dollar increase in profits is	Select
A) 20% B) 30% C) 60% D) 50% E) 33%

Solution: Ok, I do not know whether it is exactly what you want to hear but I did it that way: first look at difference between revenue and variable cost => take the bigger one (b) which gives you: 4.5x-1500 just plug in 2000 and 3000. you get 7500 and 12000 (difference 4500). 4500> 0.5*7500 so 30%   30%
Answer: B
If X = 2 + 1/(1+1/(1-1/2))then the value of 5x+7/3?
Choose the correct answer.
A) 9 2/3
B) 10 1/3
C) 11
D) 11 2/3
E) 14

Solution: X = 2 + 1/(1+1/(1-1/2))   = 2 + 1/(1+2)   = 2 + 1/3   X = 7/3 ==> 5X + 7/3 => 5(7/3) + 7/3   ==> 35/3 + 7/3   ==> 42/3   ==> 14.   14)
Answer: E
Which of the following expressions CAN be equal to 0 when x^2 − x = 6 ?
Choose the correct choice:	A) x^2 − 3x +2	B) x^2 − 2x -4	C) x^2 − 5x +5	D) x^2 − 3x +1	E) x^2 − 4x +2

Solution: x^2 − x = 6   x^2 − x - 6= 0   x=3 or x=-2   Only one choice results in a possibility of 0 when you plug in 3 or -2 for x except rest of all   x^2 − 3x + 2   x^2 − 3x +2nswer is x^2 − 3x +2
Answer: A
How many ltrs of water must beadded to 16 ltrs of milk and water containing 10% water to make it 20% water in it?	Choose the correct option:
A) 1 liter
B) 2 liter
C) 3 liter
D) 4 liter
E) 4.5 liter

Solution: 2 litery rule of alligation,   % Concentration   of water in pure water (100) % Concentration   of water in the given mixture (10)   Mean % concentration   (20)   20 - 10= 
20 - 10 = 10
10 100 - 20= 80   => Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8   Here quantity of the mixture = 16 litres   => Quantity of water : 16 = 1 : 8   => Quantity of water =16×18=2 liter   2 liter
Answer: B
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 28 years now, the son's age five years back was:
Choose the correct choice.
A) 9 years  B) 4 years  C) 33 years  D) 8 years  E) 39 years

Solution: Let the son's present age be x years.   Then, (28 - x) = x   2x = 28 => x = 14   Son's age 5 years back = (14 - 5)= 
(14 - 5) = 9
9 years.   ANSWER:4 years
Answer: B
What Approximate Values should comein place of the question mark (?) in each of the following equations ?
85% of 225 + 56% of 450 + 32.98 x 5.001 = ? Choose the correct choice from the following choices:	A) 600	B) 625	C) 608	D) 605	E) 610

Solution: Explanation :   85x225/100+56x450/100+33x5 = 85 x 2.25 + 56 x 4.5 + 165 = 608   Answer : Option 608
Answer: C
Two concentric circles form a ring. The inner and outer circumferences of ring are (352/7) m and (518/7) m respectively. Find the width of the ring.	Answers:
A) 2 B) 4 C) 6 D) 8 E) None of them

Solution: Let the inner and outer radii be r and R meters.   Then 2(22/7)r = (352/7) = r =((352/7) X (7/22) X (1/2))=8m.   2(22/7)R=(528/7) = R=((528/7) X (7/22) X (1/2))= 12m.   Therefore, Width of the ring = (R - r) = (12 - 8)= 
(12 - 8) = 4
4 m.   Answer is 4.
Answer: B
In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 2 is
Pick one:
A) 1
B) 12
C) 16
D) 20
E) 24

Solution: I've never seen such kind of question in GMAT before.   OK there can be 4 cases:   |x+y| + |x-y| = 2   A. x+y+x-y = 2 --> x=1   B. x+y-x+y = 2 --> y=1   C. -x-y +x-y= 2 --> y=-1   D. -x-y-x+y=2 --> x=-1   The area bounded by 4 graphs x=1, x=-1, y=1, y=-1 will be square with the side of 4 so the area will be 1*1= 
1*1 = 1
1.   1nswer: 1
Answer: A
Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age? Choose the correct choice from the following choices.
A) 2 times B) 2 1/5 times C) 3 times D) 4 times E) 5 times

Solution: Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.   (4x + 8) = 5 (x + 8)   2   8x + 16 = 5x + 40   3x = 24   x = 8.   Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 
48/24 = 2
2.   2 times)
Answer: A
emblem is coded as 216;
crude is coded as 125
Cricket will be ? Choose one:
A) 243 B) 143 C) 343 D) 383 E) 393

Solution: coding follows (no. of letters)^3   emblem = 216 = 6^3   crude = 125 = 5^3   343ricket = 7^3 =343   ANSWER:343
Answer: C
The difference between the place values of 7 and 3 in the prime number 527435 is	Pick one:  A) 4  B) 5  C) 45  D) 6970  E) None

Solution: Solution   (place value of 7)-(place value of 3)   = (7000 - 30)= 
(7000 - 30) = 6_970
6970.   Answer 6970
Answer: D
What is the remainder when 25473 is divided by 5?
Select the correct option:	A) 3	B) 2	C) 4	D) 5	E) 0

Solution: If the digit in unit place is divisible by 5, then number will be divisible by 5.   3 is not divisible by 5,so the number is not divisible by 5.   The nearest multiple of 5 is 25470   25473-25470= 
25473-25470 = 3
3.   3nswer:3
Answer: A
The ages of 2 persons differ by 16 years. If 6 years ago the elder one be 3 times as old as the younger one, find the present age of younger person. Choose the correct option.
A) 10  B) 14  C) 20  D) 15  E) 32

Solution: age of the younger person = x   age of the elder person = x+16   3(x-6) = x+16-6   x= 14   Answer is 14
Answer: B
From the starting point in a boat race, one competitor started to sail north at a speed of 1.6 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours? Choose the correct answer:	A) 10.	B) 12.	C) 12.5.	D) 14.	E) 15.4.

Solution: Both competitors are sailing making angle of 90 degrees.   10.fter 5 hrs one competitor will cover a distance of = 1.6 *5= 
1.6 *5 = 8
8 KM   10.nd, other competitor will cover a distance of= 1.2*5= 
1.2*5 = 6
6KM   distance between them after 5 hrs= (8^2+ 6^2)^1/2= 10 KM   10. is the answer
Answer: A
What is the least number, which is perfect square but contains 2700 as its factor?	Choose the correct choice:
A) 8100 B) 10900 C) 54000 D) 2500 E) 2700

Solution: 900 * 3 * 3= 
900 * 3 * 3 = 8_100
8100   8100NSWER 8100
Answer: A
Machine A can finish a job in 4 hours, Machine В can finish the job in 2 hours, and Machine С can finish the job in 6 hours. How many hours will it take for A, B, and С together to finish the job?
Choose the correct choice:
A) 4/3  B) 6/5  C) 8/7  D) 10/9  E) 12/11

Solution: The combined rate is 1/4+1/2+1/6 = 11/12 of the job per hour.   The time to complete the job is 12/11 hours.   The answer is 12/11.
Answer: E
Three hoses work to fill a tub at at different rate. Hose Q and B, working together, can fill the tub in 6/5 of an hour. Hoses Q and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?
Edited for accurate solution Choose the correct choice from the following choices:
A) 3/10
B) 2/5
C) 1/2
D) 1
E) 6/5

Solution: Convert the given time to rate and you will be able to add it up.   Total Rate of Q and B = Rate of Q + Rate of B = 1/(6/5) = 5/6   Total Rate of Q and C = Rate of Q + Rate of C = 1/(3/2) = 2/3   Total Rate of B and C = Rate of B + Rate of C = 1/2   Adding all three,   2(Rate of Q + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2= 
5/6 + 2/3 + 1/2 = 2
2   Rate of Q + Rate of B + Rate of C= 1 tub/hour   Time taken by all three together to fill up the tub is 1 hour=1
Answer: D
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is: Choose the correct choice from the following:
A) 5% B) 8% C) 12% D) 15% E) 10%

Solution: S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.   S.I. for 5 years = Rs.	((2205/3)x 5)	= Rs. 3675   Principal = Rs. (9800 - 3675) = Rs. 6125.   Hence, rate =((100 x 3675)/(6125 x 5))%	= 12%   Answer :12%
Answer: C
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:  Pick:
A) 110 m
B) 120 m
C) 190 m
D) 150 m
E) 180 m

Solution: Answer: Option D   Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.
Answer: D
W and X start a business with Rs.5000 and Rs.20000 respectively. Hoe should they share their profits at the end of one year? Select the correct option.
A) 4:1  B) 1:3  C) 1:4  D) 1:5  E) 2:1

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by W and X =   5000 : 20000 => 1:4 .   Answer:1:4
Answer: C