MU-NLPC/Calc-aqua_rat huggingface dataset:
The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 30 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours? Choose the correct choice from the following answers:
A) 81.25
B) 82.5
C) 83.75
D) 85.0
E) 87.5

Solution: Rate of flow of water in second hour = 30 gallons per hour   Rate of flow of water in first hour = 30/(3/2)= 
30/(3/2) = 20
20 gallons per hour   Rate of flow of water in third hour= (125/100)* 30 = (5/4) * 30= 
(5/4) * 30 = 75/2 = around 37.5
37.5 gallons per hour   Number of gallons of water that flowed through the pipe during the entire 3 hours= 20+30+37.5= 
20+30+37.5 = 87.5
87.5 gallons   Answer 87.5
Answer: E
John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance r before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.	Choose the correct choice from the following
A) 25% B) 50% C) 75% D) 100% E) 200%

Solution: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance r before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.   Lets say the distance of the trail is 100 miles. Lets also say that J rate = 10 miles/hour and K rate = 15 miles/hour.   If John stops at the 25% mark that means he travels 25 miles in 2.5 hours. It would take Karen t=d/r t=75/15= 
75/15 = 5
5 hours to reach john. If John had not stopped, their combined rate would 10+15= 
10+15 = 25
25 miles/hour meaning they would have met in 4 hours. Therefore, she ran one hour longer (25%) longer than she would have needed to if John ran for the entire time.   25%NSWER: 25%) 25%
Answer: A
A, B, C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?	Choose the most appropriate option
A) 45  B) 35  C) 55  D) 60  E) 66

Solution: Explanation :   A : B: C = 10*7 : 12*5 : 15*3 = 2*7 : 12*1 : 3*3 = 14 : 12 : 9   amount that C should pay = 175 * (9/35) = 5*9= 
5*9 = 45
45. 45nswer : Option 45
Answer: A
A coin is tossed live times. What is the probability that there is at the least one tail?  Choose the correct choice from the following choices
A) 31/32
B) 15/11
C) 14/15
D) 48/11
E) 99/18

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed five times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/32 ; P(T) = 1 - 1/32 = 31/32   31/32nswer: 31/32
Answer: A
If a fair die is rolled four time, what is the probability that a 3 occurs on at least one roll? Choose the correct choice from the following choices:  A) 25/36  B) 125/216  C) 91/216  D) 11/36  E) 248/479

Solution: Questions such as these that talk about at least or maximum or minimum in probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)   Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1-(5/6) (5/6)(5/6)(5/6) = 1-231/479 = 248/479.   5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.   248/479 is thus the correct answer.
Answer: E
The ages of two persons differ by 28 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively  Choose the correct choice:
A) 40,12
B) 20,10
C) 25,15
D) 30,10
E) None of these

Solution: Explanation:   Let their ages be x and (x + 28) years.   5 (x - 5) = (x + 28 - 5) or 4x = 48 or x = 12.   Their present ages are 40 years and 12 years   Option 40,12
Answer: A
At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other? Choices:
A) 51/11
B) 12 4/11
C) 13 4/11
D) 16 4/11
E) None

Solution: Explanation :   At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.   To be coincident, it must gain 15 min. spaces.55 min. are gained in 60 min.   15 min. are gained in   = (60/55 x 15)min   =16x4/11   The hands are coincident at 16x4/11 min past 3.   Answer : 16 4/11
Answer: D
Predict the next number
2,20,10,100,50  Choose the correct answer.
A) 200
B) 300
C) 400
D) 500
E) 600

Solution: Look upon the series carefully   2,20,10,100,50...   2 * 10= 
2 * 10 = 20
20   20/ 2= 
20/ 2 = 10
10   10 * 10= 
10 * 10 = 100
100   100/2= 
100/2 = 50
50   similarly   50 * 10= 
50 * 10 = 500
500   ANSWER:500
Answer: D
What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 30%? Select the correct option:
A) 70%  B) 69%  C) 80%  D) 82%  E) 55%

Solution: The question is very easy. My logic is the following:   A surface = 6*a^2   After 30% increase A surface = 6* ((1.3a)^2) = 6*1.69*a^2   The increase in the surface area = (6*1.69*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.69-1))/(6*a^2) = 1.69-1= 
1.69-1 = 0.69
0.69= 69%   Answer : 69%
Answer: B
Two numbers are in respectively 20% and 50% more than a third number. The ratio of the two numbers is?	Choose one
A) 2:5
B) 1:2
C) 4:5
D) 3:7
E) 5:6

Solution: Let the 3rd number be x   Then, first number = 120% of x = 120x/100 = 6x/5   second number = 150% of x = 150x/100 = 3x/2   Ratio of first two numbers = 6x/5 : 3x/2 = 12x:15x = 4:5   Answer is 4:5
Answer: C
A basket contains 6 blue, 6 red and 6 yellow marbles. If 6 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
Pick one.
A) 2/21  B) 3/25  C) 1/6  D) 9/34  E) 11/24

Solution: 18/18*12/17*6/16 = 9/34   the answer is (9/34)
Answer: D
A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone can do the whole work in
Choose the correct choice from the following.
A) 15days  B) 10days  C) 9days  D) 8days  E) 7days

Solution: Explanation:   Ratio of times taken by 15days and B = 1:3   Means B will take 3 times which 15days will do in 1 time   If difference of time is 2 days, B takes 3 days   If difference of time is 10 days, B takes (3/2) * 10= 
(3/2) * 10 = 15
15 days   Option 15days
Answer: A
If the figure 5286.142 is rounded off to the nearest thousand, hundred, ten and one and the result is represented using d,e,f,g respectively, which of the following statements would be accurate?	Choose one
A) f>e>g>d  B) e>f>g>d  C) g>f>e>d  D) e>d>g>f  E) e>g>f>d

Solution: 5286.142..   Nearest thousand 5000..d   Nearest hundred 5300..e   Nearest ten 5290..f   Nearest one 5286..g   e>f>g>d   The correct option is e>f>g>d
Answer: B
The product of two successive numbers is 462. Which is the smaller of the two numbers?  Pick
A) 21  B) 23  C) 26  D) 27  E) 29

Solution: 21   21   From the given alternatives,   21 × 22 = 462   ∴ Smaller number = 21
Answer: A
A boat can move upstream at 30 kmph and downstream at 15 kmph, then the speed of the current is? Pick one.
A) 5  B) 7.5  C) 32.5  D) 9.2  E) 5.8

Solution: US = 30   DS = 15   M = (30 - 15)/2= 
(30 - 15)/2 = 15/2 = around 7.5
7.5   Answer: 7.5
Answer: B
A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 25 paise per sq m is
Choose the correct answer
A) Rs. 186  B) Rs. 258  C) Rs. 486  D) Rs. 586  E) None of these

Solution: Explanation:   Rs. 186rea to be plastered = [2(l + b) Ã— h] + (l Ã— b)   = [2(25 + 12) Ã— 6] + (25 Ã— 12) = 744 sq m   Cost of plastering = 744 Ã— (25/100) = Rs.186 Rs. 186nswer: Rs. 186
Answer: A
If A = {17, 27, 31, 53, 61}, what is the sum of mean and median of the numbers in A?
Pick one:
A) 69 B) 75 C) 82 D) 91 E) 56

Solution: Mean = (17 + 27 +31 + 53 + 62 )/5= 
(17 + 27 +31 + 53 + 62 )/5 = 38
38   Median= 31   sum = 38+31= 
38+31 = 69
69   Option 69
Answer: A
A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?  Choose the correct answer.
A) 285 m  B) 240 m  C) 277 m  D) 765 m  E) 176 m

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/39 = 15 ==> x + 300 = 585 ==> x   = 285 m.   285 mnswer: 285 m
Answer: A
If the sum of the interior angles of a regular polygon is 1080 degrees, how many sides does the polygon have?	Choose one:	A) 4	B) 3	C) 6	D) 8	E) None of these

Solution: 8 sides...answer is 8
Answer: D
For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is	Options
A) 1/4 B) 1/5 C) 1/6 D) 1/7 E) 1/8

Solution: For all positive integers n and m,   A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,   note: i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 + 1/3^2)(1 + 1/5 + 1/5^2)…(1 + 1/p_n + 1/p_n^2)   B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.   A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}   A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)   The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/9 + 1/10 + 1/11 + 1/12 + 1/14 + ...   missing numbers are 1/8, 1/13, 1/16, ....   B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)   here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values   The largest reciprocal that present in B(25) but not in A(5) is 1/8   Answer 1/8
Answer: E
A focus group is currently made up of x men and y women. If 3 men and 7 women are added to the group, and if one person is selected at random from the larger focus group, then what is the probability that a woman is selected?
Select the correct option: A) x/(x + 7) B) y/(x + y) C) (y + 3)/(x + y + 7) D) (y + 7)/(x + y + 10) E) (x + 3)/(x + y + 10)

Solution: x men   y women   x+3+y+7 is the total   =x+y+10   y+7 is the number of men   so (y + 7)/(x + y + 10)   D. (y + 7)/(x + y + 10)
Answer: D
How many times in a day, are the hands of a clock in straight line but opposite in direction?
Choose the correct option.
A) 20
B) 22
C) 24
D) 48
E) 52

Solution: The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).   So, in a day, the hands point in the opposite directions 22 times.   Answer: Option 22
Answer: B
The dimensions of a room are 10m x 7m x 5m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1m x 3m. One window is of size 2m x 1.5m and the other 2 windows are of size 1m x 1.5m. The cost of painting the walls at Rs. 3 per sq m is?  Choose the correct choice from the following.
A) Rs.229	B) Rs.429	C) Rs.129	D) Rs.474	E) Rs.111

Solution: Area of 4 walls = 2(l+b)h   =2(10+7) x 5 = 170 sq m   Area of 2 doors and 3 windows = 2(1x3)+(2x1.5)+2(1x1.5) = 12 sq m   area to be planted = 170 -12= 
170 -12 = 158
158 sq m   Cost of painting= Rs. 158 x 3 = Rs. 474   Answer: Rs.474
Answer: D
I travel 20 miles towards north and then travel 25 miles eastward. I then travel 40 miles rightwards, then travel 30 miles towards left and then travels 12 miles to the left and finally 20 miles northwards. How far am i pproximately from my original destination and in what direction ?	Select the correct option:
A) 20 miles towards south
B) 13 miles towards south-west
C) 12 miles towards east
D) 13 miles towards north-east
E) None of these

Solution: Explanation:   Using pythagorus rule,   x2=(12)2+(5)2   x=13   ANSWER IS 13 miles towards south-west
Answer: B
A number is 101102103104...150. As 101 102 103 103.... 150. What is reminder when divided by 3? Choices:	A) 2	B) 5	C) 6	D) 7	E) 8

Solution: Divisibility rule for 3 also same as 9. so from the above discussion sum of the digits = 380 and remainder = 380/3 = 2.   2nswer:2
Answer: A
A bowl was half full of water. 4 cups of water were then added to the bowl, filling the bowl to 70% of its capacity. How many cups of water are now in the bowl?  Choose the correct choice from the following options:	A) 14	B) 15	C) 16	D) 17	E) 18

Solution: lets say total volume of the container = V   Initial water content is half of total volume = V/2   Then 4 cups of water were added.   Current water content = (V/2) + 4 cups = (70/100)V   => V = 20 cups   => current water content is equivalent to = V/2+ 4 cups = 20/2 + 4= 
20/2 + 4 = 14
14 cups; 14NSWER:14
Answer: A
There are eight boxes of chocolates, each box containing distinct number of chocolates from 1 to 8. In how many ways four of these boxes can be given to four persons (one boxes to each) such that the first person gets more chocolates than each of the three, the second person gets more chocolates than the third as well as the fourth persons and the third person gets more chocolates than fourth person?
Choose the correct choice from the following answers.
A) 35	B) 70	C) 105	D) 210	E) None

Solution: Solution:   All the boxes contain distinct number of chocolates.   For each combination of 4 out of 8 boxes, the box with the greatest number has to be given to the first person, the box with the second highest to the second person and so on.   The number of ways of giving 4 boxes to the 4 person is,   8C4 = 70.   Answer: Option 70
Answer: B
In right triangle ABC, AC is the hypotenuse. If AC is 20 and AB + BC = 50, what is the area of the triangle ABC?	Choose the correct choice.
A) 225 B) 525 C) 25√2 D) 200 E) 200√2

Solution: Square AB + BC = 50:   (AB)^2 + 2*AB*BC + (BC)^2 = 2500. Since (AC)^2 = (AB)^2 + (BC)^2 = 20^2 = 400, then (AB)^2 + 2*AB*BC + (BC)^2 = 400 + 2*AB*BC = 2500.   400 + 2*AB*BC = 2500.   AB*BC = 1050.   The area = 1/2*AB*BC = 525.   Answer: 525.
Answer: B
Michael completes a piece of work in 6 days, Madan completes the same work in 18 days. If both of them work together, then the number of days required to complete the work is?  Select:
A) 4.5 days	B) 8 days	C) 10 days	D) 12 days	E) 14 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 6 × 18/24 = 4.5 days   4.5 daysnswer : 4.5 days
Answer: A
Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/8 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?  Options:
A) 36  B) 60  C) 120  D) 144  E) 180

Solution: The number of ornaments = a   Ten more than 1/6 of the ornaments in her collection are handmade => Handmade = 10+a/6   1/2 of the handmade ornaments are antiques => Handmade ornaments = 1/2*(10+a/6) = 5 + a/12   1/8 of the ornaments in her collection are handmade antiques => Handmade ornaments = a/8   => 5 + a/12 = a/8 => a = 120   Ans: 120
Answer: C
A and B’s salaries together amount to Rs. 3,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is B’s salary?
Choose the correct choice:
A) 777
B) 750
C) 789
D) 776
E) 881

Solution: (5/100) A = (15/100) 750   A = 3750   A + 750 =3000   4750 = 3000 => 750 = 750   Answer 750
Answer: B
If n divided by 5 has a remainder of 4, what is the remainder when 3 times n is divided by 5?	Pick one
A) 1 B) 4 C) 3 D) 2 E) 0

Solution: As per question => N=5P+4 for some integer p   hence 3N => 15Q + 12   But again, 12 can be divided by 5 to get remainder 2 for some integer Q   hence 2
Answer: D
How many natural numbers that are less than 10,000 can be formed using the digits 0, 1, 2, 3, 4, 6, 78?	Choose the correct choice from the following answers
A) 5000	B) 4096	C) 6560	D) 4095	E) 8000

Solution: According to what i have read - it is always better to assume natural numbers beginning from 01 onward (for the gmat) unless otherwise stated. Assuming that to be the case we can sub divide the problem into :   A) Four digit Numbers : _ _ _ _ , The ones place - hundreds place can be filled by any one of the 8 numbers given (the problem speaks nothing about NOT REPEATING the numbers so we have to assume that they can be repeated) the thousands place can be filled by any number except0.. This gives us 7 x 8 x 8 x 8 = 3584   B) Three digit Numbers : _ _ _ , The ones place - tens Place can be filled by any one of the 8 numbers given ( the problem speaks nothing about NOT REPEATING the numbers so we have to assume that they can be repeated) , the hundreds place can be filled by only 7 of the given 8 numbers (If we use0we will end up with a two digit number ). This gives us 7 x 8 x 8 = 448   C) Two digit numbers : _ _ , The ones place can be filled up by any one of the 8 numbers given , and the tens place by any 7 of the 8 ... This gives us 7 x 8 = 56   D) Assuming that zero is not a natural number , we have seven different possibilities for the one digit numbers . 7   Add A + B + C + D , This gives us 3584 + 448 + 56 + 7= 
3584 + 448 + 56 + 7 = 4_095
4095 (D)   Now let us assume that ZERO is a NATURAL number (as some mathematicians do) ... A thru C is not effected by this assumption as the resultant would have meant that a four number digit with a zero at the beginning would have effectively made it a three digit no. , and a 0 to begin a three digit number would make it a two digit number etc ... The only difference including ZERO to be a natural number would have made for D , in that it would have given it 8 possibilities instead of 7 ... Which would have added 1 to our total making it 4096. Simply by looking at the answer choices we can determine that the test maker wanted natural numbers to begin from 1 and not from 0 ( as per the answer choices) ..
Answer: D
Efrida and Frazer who live 13 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?	Answers.
A) 6
B) 7
C) 8
D) 10
E) 11

Solution: It's a simple geometry problem. Look at the diagram below:   Answer: 11.
Answer: E
which of the following is odd, if r is even and t is odd? Select:
A) rt	B) 5rt	C) 6r + 5t	D) 5r + 6t	E) 6(r^2)t

Solution: Just checking options (In case you have difficulty then choose values of r=2 and t=1)   r = even   t= Odd   A. rt = Even*Odd = EvenINCORRECT   B. 5rt = Odd*Even*Odd = EvenINCORRECT   E. 6(r^2)t = 6*(Even^2)*Odd = EvenINCORRECT   D. 5r + 6t = 5*Even + 6*Odd = Even+Even = EvenINCORRECT   C. 6r + 5t = 6*Even + 5*Odd = Even+Odd = Odd6r + 5tORRE6r + 5tT   Answer: option 6r + 5t
Answer: C
In triangle PQR, the angle Q = 90 degree, PQ = 5 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ
Answers
A) 3.6 cm	B) 2.4 cm	C) 4.0 cm	D) 2.16 cm	E) 3.2 cm

Solution: Look at the diagram below:   Now, in case when QY is perpendicular to PR, two right triangles PQR and PQY are similar: QY:QP=QR:PR --> QY:5=8:10 --> QY=4.0.   Answer: 4.0 cm.
Answer: C
A football coach must choose 5 freshers from a team of 12players. How many different ways can the coach choose the freshers?
Choose the correct choice from the following answers.
A) 652
B) 634
C) 729
D) 850
E) 870

Solution: Choose 5 starters from a team of 12 players. Order is not important.   \inline {\color{Black} 12729_{5}}= 729   729
Answer: C
A salesperson receives a base salary of $1100 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 210 items for $150 each, what will her monthly salary be?	Choose the correct option:  A) $1,500  B) $1,800  C) $2,100  D) $2,500  E) $2,900

Solution: Ans : 1100+ 7.5 % * 150 * (210-50) = $ 2900   Answer $2,900
Answer: E
A year ago, the ratio of Betty's and Chi's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Betty?
Choose the correct option.
A) 34 years B) 29 yeras C) 25 years D) 30 years E) 40 years

Solution: (b-1)/(c-1)=6/7;   (b-1+4)/(c-1+4)=7/8;   by solving them we get   8b-7c=-3   7b-6c=1   then solving these eq we get   c7 -6= 
7 -6 = 1
1   then solving these eq we get   c=29   b=25   ANSWER:25 years
Answer: C
Randy can rebuild an automobile engine in b hours. Alvin can rebuild the same engine in a hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Alvin will have to complete?  Choose one.
A) b/(a+b)  B) (a-b)/(a+b)  C) b/(b-a)  D) ab/(a+b)  E) a/(a+b)

Solution: Randy can do the job in a hrs, Alvin can do the job in b hrs.   When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin.   Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b)   So Alvin does b/(a+b) of the work.   b/(a+b)nswer (b/(a+b)).
Answer: A
in 10 year, A willbe twice as old as B was 10 year ago. if A is now 9 year older then B, the present age of B is
Choose one:
A) 19 years
B) 29 years
C) 39 years
D) 49 years
E) None of these

Solution: Solution   Let B's present age = x years. then, A's present age = ( x + 9 ) years.   ∴ (x + 9) + 10 = 2 (x - 10) ⇔ x + 19 = 2 x - 20 ⇔ x = 39. Answer 39 years
Answer: C
20% of a number is added to 120, the result is the same number. Find the number? Select the correct option
A) 150
B) 288
C) 1687
D) 997
E) 121

Solution: (20/100) * X + 120 = X   2X = 300   X = 150   150nswer:150
Answer: A
What is the number of integers from 1 to 900 (inclusive) that are divisible by neither 11 nor by 35? Choose the correct choice from the following choices.
A) 884
B) 890
C) 892
D) 910
E) 945

Solution: Normally, I would use the method used by Bunuel. It's the most accurate. But if you are looking for a speedy solution, you can use another method which will sometimes give you an estimate. Looking at the options (most of them are spread out), I wont mind trying it. (Mind you, the method is accurate here since the numbers start from 1.)   In 1000 consecutive numbers, number of multiples of 11 = 1000/11 = 90 (Ignore decimals)   In 1000 consecutive numbers, number of multiples of 35 = 1000/35 = 28   Number of multiples of 11*35 i.e. 385 = 1000/385 = 2   Number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - (90 + 28 - 2) {Using the concept of sets here) = 892   Think: Why did I say the method is approximate in some cases?   Think what happens if the given range is 11 to 1010 both inclusive (again 1000 numbers)   What is the number of multiples in this case?   892
Answer: C
Shreyas bought an article and sold it for 140% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.29750/-?	Choose the correct choice: A) Rs.24600 B) Rs.21250 C) Rs.24250 D) Rs.23200 E) None of these

Solution: Explanation:   140% of CP = Rs.29750   :. CP = Rs.29750x100/140 = Rs.21250.   Answer: Option Rs.21250
Answer: B