MU-NLPC/Calc-aqua_rat huggingface dataset:
Given a set of numbers {5,6,7,8,9,10}, what is the probability that is two numbers are selected randomly that their sum will be greater than 12?  Pick one:
A) 13/15
B) 9/12
C) 13/12
D) 13/11
E) 13/16

Solution: First problem is 6C2 = 12 .. Not 20..   Point 2, your sum should be greater than 12, so these are the following possibilities you have   ({5,8},{5,9},{5,10},{6,7},{6,8},{6,9},{6,10},{7,8},{7,9},{7,10},{8,9},{8,10},{9,10}) which leads to 13 pairs   So the probability is 13 on 12 or 13/12..   ANSWER:13/12
Answer: C
If x/y = 7/3, then (x + y)/(x - y) = ?	Select the correct option:  A) 5  B) 5/2  C) -1/6  D) -1/5  E) -5

Solution: Any x and y satisfying x/y = 7/3 should give the same value for (x + y)/(x - y).   Say x=7 and y=3, then (x + y)/(x - y) = (7 + 3)/(7-3) = 5/2.   Answer: 5/2.
Answer: B
If the sum of three consecutive even numbers is 50 more than the average of these numbers, then the largest of these numbers is?	Pick
A) 20	B) 24	C) 22	D) 26	E) 27

Solution: Explanation:   Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).   x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 50   3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 150   9x + 18 = 3x + 156   6x = 138   x = 23   Therefore, the largest number is 27.   ANSW27R 27
Answer: E
In one hour, a boat goes 7 km along the steram and 5 km against the stream. The speed of the boat in still waer (in km/hr) is:  Answers
A) 2	B) 4	C) 6	D) 12	E) 15

Solution: Sol.   Speed in still water = 1/2 (7+5) kmph = 6 kmph.   Answer 6
Answer: C
A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/10 that a person who randomly guesses the answer to each question will be a winner? Select:
A) 5	B) 10	C) 50	D) 100	E) 1000

Solution: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?   A.5   B.10   C.50   D.100   E.1000   Soln: ans is B   Probability that one question is answered right is 1/2.   Now for minimum number of questions needed to take probability less than 1/1000 is   => (1/2)^n < 1/1000   n = 10 satisfies this.   100
Answer: D
In a colony of 70 resident s, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony? Pick one.
A) 1:9	B) 1:6	C) 1:3	D) 1:1	E) 1ratio 3

Solution: Number of men in the colony = 4/7 (70) = 40   Number of women in the colony = 3/7 (70) = 30   Number of educated women in the colony = 1/5 (30) = 6   Number of uneducated women in the colony = 4/5 (30) = 24   Number of educated persons in the colony = 8/35 (70) = 16   As 6 females are educated, remaining 10 educated persons must be men.   Number of uneducated men in the colony = 40 - 10= 
40 - 10 = 30
30   Number of educated men and uneducated men are in the ratio 10:30=> 1:3   Answer: 1ratio 3
Answer: E
A card is drawn from a pack of 52 cards. The probability of not getting a face card? Choose the correct answer:
A) 9/13
B) 5/12
C) 3/13
D) 6/17
E) 1/13

Solution: Clearly in the 52 cards other than face cards = 52-16= 
52-16 = 36
36   probability of not getting a face card= 36/52 = 9/13   correct option is 9/13
Answer: A
How many 3-digit positive integers are there, where each digit is positive, and no 3 adjacent digits are same?  Choose the correct choice from the following answers
A) 1236	B) 504	C) 4096	D) 4608	E) 6561

Solution: First digit.. 9 posibilities   Second digit, 8 possibilities   third digit, 7 possibilities     9*8*7= 
  9*8*7 = 504
504.   504
Answer: B
Starting from his house one day, a student walk at a speed of 2 kmph and reaches his school 10 minutes late. Next he increased his speed by 1 kmph and reaches the school 10 minutes early. How far is the school from his house?	Choose the correct choice from the following answers:
A) 1km
B) 2km
C) 3km
D) 4km
E) 5km

Solution: Let the distance be x km   Difference in timings = 20 min = 20/60 = 1/3 hr   x/2-x/3 = 1/3   x = 2km   Answer is 2km
Answer: B
Calculate how many seconds it eill take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 2, 5, 8 and 11 seconds. ?
Choose the correct choice from the following options
A) 440 B) 420 C) 410 D) 442 E) 422

Solution: LCM of 2, 5, 8 and 11 is   440   LCM=440   440NSWER:440
Answer: A
When two dice are tossed, what is the probability that the total score is a prime number?  Answers:
A) 1/6	B) 3	C) 5/12	D) 7/12	E) 9/12

Solution: Total number of outcomes possible=36   probability of total score is a prime number=15   P(E) =15/36=5/12   ANSWER:5/12
Answer: C
The compound interest earned by Sunil on a certain amount at the end of two years at the rate of6% p.a. was Rs.370.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
Pick:	A) Rs.3360.80	B) Rs.3370.80	C) Rs.3320.70	D) Rs.3230.80	E) Rs.3130.80

Solution: Let the sum be Rs.P   P{ [ 1 + 6/100]2 - 1 } = 370.80   P(6/100)(2 +6/100) = 370.80 [a2 - b2 = (a - b) ( a + b)] P = 246 / (0.05)(2.05) = 3000. Amount =Rs.3370.80. Answer :Rs.3370.80
Answer: B
A team has to design a flag. The team has six blue strips of cloth and seven red strips of cloth that they must use as is to make the flag. How many different flags can the team design with the materials at hand?  Choose the correct choice:  A) 42  B) 120  C) 720  D) 1,716  E) 5,040

Solution: The # of permutations of total 6+7= 
6+7 = 13
13 strips where 6 are identical blue and 7 are identical red is 13!/(6!*7!)=1716 (note that they must use all the materials at hand, also I guess that the strips must be either only vertical or only horizontal).   Answer: 1,716.
Answer: D
The area of a rhombus is equal to the area of a rectangle whose length is 20cm and the breadth is 10cm. If one of the diagonals is 32cm what is the length of other diagonal?	Choose the correct choice from the following options.
A) 10	B) 12.5	C) 15	D) 16	E) 17.5

Solution: Area of rectangle=20x10=200cmÂ²   Let 'l' the length of other diagonal = 0.5x32xl = 200   which gives x=12.5cm   Answer: 12.5
Answer: B
An investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
Choose the correct option.
A) $480  B) $489.60  C) $634.64  D) $800.32  E) $240

Solution: 1.04*1.04*6000= 
1.04*1.04*6000 = 6_489.6
$6489.60   The answer is $489.60.
Answer: B
A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?
Answers
A) 160 km B) 180 km C) 200 km D) 220 km E) None

Solution: Solution   Speed Downstream	= (14 + 4) km/hr   = 18 km/hr.   Speed upstream	=(14 - 4) km/hr   = 10 km/hr..   Let the distance b/w A and B   be xkm.Then	=(x/18+ x/2 / 10)   = 19   = 19x / 180 = 19   x= 180.   Answer 180 km
Answer: B
The distance between two towns is 380 km. At the same moment, a passenger car and a truck start moving towards each other from different towns. They meet 4 hours later. If the car drives 5 km/hr faster than the truck, what are their speeds?	Choose the correct choice from the following answers:	A) 50 and 45	B) 45 and 50	C) 30 and 35	D) 35 and 30	E) 40 and 50

Solution: The main idea used in this kind of problems is that the distance equals speed multiplied by time S=V⋅t   V (km/hr) t (hr) S (km)   Car x + 5 4 4(x +5)   Truck X 4 4x   4(x+5)+4x=380   4x+4x=380−20   8x=360   x=3608   x=45   Therefore the truck's speed is 45 km/hr, and the car's speed is 50 km/hr.   So answer is 45 and 50.
Answer: B
Fred can fill K cans of water in 5 minutes. If there are T cans of water in one gallon, how many gallons can Fred fill in 35 minutes? Choose the correct choice from the following
A) 7K/T
B) 7KT
C) 7T/K
D) 35KT
E) 35T/K

Solution: Fred can fill this number of cans in 35 minutes:  (35/5)= 
 (35/5) = 7
7K.   One can is 1/T gallons.   Fred can fill 7K*(1/T)= 7K/T gallons of water in 35 minutes.   The answer is 7K/T.
Answer: A
The speeds of three asteroids were compared. Asteroids X-13 and Y-14 were observed for identical durations, while asteroid Z-15 was observed for 2 seconds longer. During its period of observation, asteroid Y-14 traveled three times the distance X-13 traveled, and therefore Y-14 was found to be faster than X-13 by 8000 kilometers per second. Asteroid Z-15 had an identical speed as that of X-13, but because Z-15 was observed for a longer period, it traveled five times the distance X-13 traveled during X-13's inspection. Asteroid X-13 traveled how many kilometers during its observation?  Choose the correct choice from the following: A) 500 B) 1,600/3 C) 1,000 D) 1,500 E) 2,000

Solution: X13: (t, d, s)   Y14: (t, 3d, s+8000mi/hour)   Z15: (t+2 seconds, s, 5d)   d=?   Distance = Speed*Time   x13: d = s*t   x14: 3d = (s+8000)*t ===> 3d = ts+8000t   z15: 5d = s*(t+2t) ===> 5d = st+2st ===> 5d - 2st = st   3d 5  - 2= 
5  - 2 = 3
st   3d= 5d - 2st + 8000t   -2d = -2st + 8000t   2d = 2st - 8000t   d = st -4000t   x13: d = s*t   st - 4000t = s*t   s - 4000 = s   -2000 = s   I got to this point and couldn't go any further. This seems like a problem where I can set up individual d=r*t formulas and solve but it appears that's not the case. For future reference how would I know not to waste my time setting up this problem in the aforementioned way? Thanks!!!   The distance of Z15 is equal to five times the distance of X13 (we established that x13 is the baseline and thus, it's measurements are d, s, t)   S(T+2) = 5(S*T)What clues would I have to know to set up the equation in this fashion? Is it because I am better off setting two identical distances together?   ST+2S = 5ST   T+2 = 5T   2=4T   t= 1/2   We are looking for distance (d=s*t) so we need to solve for speed now that we have time.   Speed y14 - speed x13   Speed = d/t   3d/t - d/t = 8000 (remember, t is the same because both asteroids were observed for the same amount of time)   2d = 8000   2 = 4000   d=s*t   d=4000*(1/2)= 
4000*(1/2) = 2_000
2000   ANSW2,000R: 2,000
Answer: E
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 7 seconds. Find the length of the faster train?	Choose the correct answer.
A) 70
B) 20
C) 30
D) 75
E) 15

Solution: Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 27 sec= 7 * 10= 
7 * 10 = 70
70 m.   The length of the faster train= 70 m.   70nswer: 70
Answer: A
A lady grows Cauliflower in her garden that is in the shape of a square. Each Cauliflower takes 1 square foot of area in her garden. This year, she has increased her output by 401 Cauliflower when compared to last year. The shape of the area used for growing the Cauliflower has remained a square in both these years. How many Cauliflowers did she produce this year? Choose the correct choice from the following choices:	A) 44001	B) 44000	C) 40400	D) 40401	E) Cannot be determined

Solution: Explanatory Answer   The shape of the area used for growing Cauliflower has remained a square in both the years.   Let the side of the square area used for growing Cauliflower this year be X ft.   Therefore, the area of the ground used for cultivation this year = X2 sq.ft.   Let the side of the square area used for growing Cauliflower last year be Y ft.   Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.   As the number of Cauliflower grown has increased by 401, the area would have increased by 401 sq ft because each Cauliflower takes 1 sq ft space.   Hence, X2 - Y2 = 401   (X + Y)(X - Y) = 401.   401 is a prime number and hence it will have only two factors. i.e., 401 and 1.   Therefore, 401 can be expressed as product of 2 numbers in only way = 401* 1   i.e., (X + Y)(X - Y) = 401 * 1   So, (X + Y) should be 401 and (X - Y) should be 1.   Solving the two equations we get X = 201 and Y = 200.   Therefore, number of Cauliflower produced this year = X2 = 2012 = 40401   Alternative Approach : Use answer choices   The area in both the years are squares of two numbers.   That rules out choice A,B and C . as 44001,44000 and 40400 are not the square of any number.   Check Choice D: If this year's produce is 40401, last year's produce would have been  40401- 401= 
 40401- 401 = 40_000
40000   40000 is the square of 200.   So, 40401 is the answer.   Choice 40401.
Answer: D
An workshop has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?  Choose the correct choice: A) 10 B) 12 C) 15 D) 24 E) 30

Solution: An workshop has 6 employees;for male 1C1 = 1 ........ 10   foe female = 5C2 = 10.........B   total = 10*1= 
10*1 = 10
10 - answer=10
Answer: A
haresh went to buy fruits.she bought 1 apple , 3 bananas , 5 oranges and paid 21 rupees.another person bought 7 apple ,5 bananas , 3 oranges and paid 51 rupees.if i want to buy 1 apple, 1 banana , 1 orange then how much i have to pay?  Answers.
A) 8 B) 9 C) 10 D) 11 E) 7

Solution: There can be multiple possible rates of apple, banana and orange to satisfy given conditions, But cost of 1 apple, 1 banana , 1 orange will be Rs 9.   1x+3y+5z = 21........(1)   7x+5y+3z = 51........(2)   Adding (1) and (2), we get   8x+8y+8z = 72   8*(x+y+z)=72   x+y+z=9   ANSWER:9
Answer: B
The speed of a boat in still water is 8km/hour. If it can travel 1 km upstream in 1 hourr, what time it would take to travel the same distance downstream?  Options
A) 2 minutes
B) 4 minutes
C) 6 minutes
D) 7 minutes
E) 8 minutes

Solution: Speed of the boat in still water = 8 km/hr   Speed upstream =11 = 1 km/hr   Speed of the stream = 8-1= 
8-1 = 7
7 km/hr   Speed downstream= (8+7)= 
(8+7) = 15
15 km/hr   Time taken to travel 1 km downstream=115 hr = 1×6015= 4 minutes   4 minutes
Answer: B
A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord, in feet? Pick
A) 30
B) 25
C) 15
D) 10
E) 5

Solution: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.   The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.   pi*r = 30. Round pi = 3, then r = 10.   Chord is about 10 feet long   ANSWER:10
Answer: D
X can finish a work in 21 days. Y can finish the same work in 15 days. Y worked for 5 days and left the job. how many days does X alone need to finish the remaining work?
Select the correct option:  A) 12  B) 13  C) 16  D) 14  E) 18

Solution: Work done by X in 1 day = 1/21   Work done by Y in 1 day = 1/15   Work done by Y in 5 days = 5/15 = 1/3   Remaining work = 1 – 1/3 = 2/3   Number of days in which X can finish the remaining work = (2/3) / (1/21)= 
(2/3) / (1/21) = 14
14   14
Answer: D
During the first two weeks of January, the total rainfall in Springdale was 30 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January? Select.
A) 5 inches
B) 6 inches
C) 9 inches
D) 10 inches
E) 18 inches

Solution: Total rainfall in 2 weeks = 18 inches.   Assume the rainfall in second week = 1.x   Rainfall in first week = x   Total rainfall = 2.5x = 18 inches   x = 12 and 1.5x = 18   Rainfall during second week = 18 inches   Option 18 inches
Answer: E
The least number which when divided by 4, 6, 7 and 8 leaves a remainder 6, but when divided by 9 leaves no remainder, is Choices:
A) 340
B) 342
C) 523
D) 363
E) None of these

Solution: Explanation:   L.C.M of 4, 6, 7, 8 = 168   therefore Required Number is of the form 168k+6.   Least value of k for which (168k+6) is divisible by 9 is k = 2   therefore Required Number = (168 x 2+6)=342. Answer: 342
Answer: B
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. Select the correct option
A) $ 165
B) $ 145
C) $ 175
D) $ 180
E) $ 170

Solution: Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 145.   So after completing the 1st week she will get $ (x+145).   Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.   = $ (x + 145 + 145)   = $ (x + 290)   So in this way end of every week her salary will increase by ($ 145)$ 145.
Answer: B
A fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is:
Pick
A) 8
B) 10
C) 11
D) 12
E) 13

Solution: Explanation:   Suppose he has 100 items. Let C.P. of each item be Re. 1.   Total cost = Rs. 100. Number of items left after theft = 80.   S.P. of each item = Rs. 1.10   Total sale = 1.10 * 80 = Rs. 88   Hence, loss % = 12/100 * 100= 
12/100 * 100 = 12
12%   Answer is 12
Answer: D
An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?	Pick one:
A) 3009  B) 3000  C) 3002  D) 3001  E) 3005

Solution: 4 --- 2000   5 --- ? => 3000   Answer: 3000
Answer: B
If the sides of a triangle are 91 cm, 84 cm and 35 cm, what is its area?	Choose the correct choice:	A) 120 cm2	B) 1470 cm2	C) 216 cm2	D) 197 cm2	E) 275 cm2

Solution: The triangle with sides 91 cm, 84 cm and 35 cm is right angled, where the hypotenuse is 91 cm.   Area of the triangle   = 1/2 * 84 * 35= 
1/2 * 84 * 35 = 1_470
1470 cm2   Answer: 1470 cm2
Answer: B
Little John had $10.50. He spent $2.25 on sweets and gave to his two friends $2.20 each. How much money was left?  Choose the correct choice from the following answers.
A) $1.85
B) $ 3.85
C) $4.85
D) $6.85
E) $5.85

Solution: John spent and gave to his two friends a total of   2.25 + 2.20 + 2.20= 
2.25 + 2.20 + 2.20 = 6.65
$6.65   Money left    10.50 - 6.65= 
 10.50 - 6.65 = 3.85
$3.85   correct answer is $ 3.85) $ 3.85
Answer: B
(√112+√567)/√175=?
Select.
A) 2√2	B) 13/5	C) 3√2	D) 3√3	E) √2

Solution: (√112+√567)/√175=(4√7+9√7)/5√7   =13/5   Hence, the correct answer is 13/5.
Answer: B
When a metallic ball bearing is placed inside a cylindrical container, of radius 2 cm, the height of the water, inside the container, increases by 0.6 cm. The radius, to the nearest tenth of a centimeter, of the ball bearing is	Choose the correct choice
A) 1 cm
B) 1.2 cm
C) 2 cm
D) 0.6 cm
E) None

Solution: Solution   When the ball was put in water, the volume of water increased by.   pi*22*0.6 = 2.4 pi cubic cm   The above volume is equal to the volume of the ball with radius r to find. Hence   (4/3)*pi*r3 = 2.4 pi   Solve the above for r   r = 1.2 cm   Answer 1.2 cm
Answer: B
What is the least number that should be added to 1054, so the sum of the number is divisible by 23? Pick one:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: (1054 / 23) gives a remainder 19 so we need to add 4.   The answer is 4.
Answer: D
The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (9,0) and (9,4). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?  Choose the correct choice from the following answers:  A) 1/5  B) 2/7  C) 3/8  D) 2/9  E) 1/4

Solution: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.   The center of the rectangle is the point (4.5,2).   The slope of line passing through points (1,1) and (4.5,2) = (2-1)/(4.5-1) = 1/3.5 = 2/7   The answer is 2/7.
Answer: B
A batsman makes a scores of 98 runs in his 19th inning and thus increases his average by 4. What is his average after 19th inning ?	Answers
A) 22	B) 24	C) 28	D) 26	E) None of the above

Solution: Let the average score of 19 innings be x.   Then, 18x+98/19=x+4   The average score after 20th innings   = x + 4 = 22 + 4= 
22 + 4 = 26
26   Answer 26
Answer: D
0.1+0.1^2+0.1^3 = Answers
A) 0.1  B) 0.111  C) 0.1221  D) 0.2341  E) 0.3

Solution: You have a mistake in your question. Choice B should be (.111) and not (.11).   The equation in the solution can be simplified to (.1 + .01 + .001).   Adding those together you get:   .100   .010   .001   ------   .111 - Which is answer choice (0.111)
Answer: B
Solve the equation for x : 14(-x + z) + 18 = -14(x - z) - 10  Choose one:
A) -2
B) -1
C) 0
D) 1
E) 2

Solution: 1   1   -14x + 14z + 18 = -14x + 14z - 10   -28x + 28 = 0   -28x -28  + 28= 
-28  + 28 = 0
0   -28x= -28   => x = 1
Answer: D
The average age of a husband and a wife is 25 years when they were married five years ago but now the average age of the husband, wife and child is 21 years(the child was born during the interval). What is the present age of the child? Choose the correct answer
A) 3 years B) 5 years C) 9 years D) 4 years E) 1 years

Solution: 30 * 2= 
30 * 2 = 60
60   21 * 3= 
21 * 3 = 63
63   -----------   3 years   3 yearsnswer:3 years
Answer: A
A cube is painted such that one pair of surfaces is painted brown and the other pair of surfaces is painted orange. The cube is cut in to 64 small cubes of equal size. Find how many cubes have both the color brown and orange?
Pick one: A) 22 B) 16 C) 11 D) 12 E) 10

Solution: There are 6 surfaces to the cube. In which opposite surfaces are painted brown and other 2 opposite surfaces are painted orange. Then 4 edges of the cube have both the colors. Since the big cube cut in to 64 smaller cubes, the 4 edges of the cube have both the colors. Since the big cube cut into 64 smaller cubes, the 4 edges of the big cube has 4×4=16 smaller cubes have both brown and orange colors. Answer = 16   Answer:16
Answer: B
At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 20 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?
Choose the correct choice from the following:	A) 3/25	B) 11/36	C) 5/12	D) 2/3	E) 25/36

Solution: Gas used = (5 hours)*(50 miles/hour)*(1 gallon/30 miles) = 8+1/3 gallons   Portion used = (8+1/3) / 20 = 5/12   Ans 5/12
Answer: C
If x > 0, x/50 + x/25 is what percent of x?
Choices.
A) 6%	B) 25%	C) 37 1/2%	D) 60%	E) 75 %

Solution: Just plug and chug. Since the question asks for percents, pick 100. (but any number will do.)   100/50 + 100/25= 2+4= 
2+4 = 6
6   6 is 6% of 100. 6%NSWER:6%
Answer: A
There is a ratio of 5 : 4 between two numbers. If forty percent of the first number is 12 then what would be the 50 percent of the second number? Choices:
A) 12 B) 24 C) 18 D) Data inadequate E) None of the above

Solution: a⁄b = 5⁄4, b = 4⁄5a Given (40% of a) = 2⁄5a = 12   a = 5 × 6 and b = 4⁄5 × 5 × 6 = 24   ∴ 50% of b = 24⁄2 = 12   12nswer 12
Answer: A
How many liters of water must be added to 18 liters of milk and water containing 10% water to make it 70% water?	Choose the correct answer:  A) 28  B) 32  C) 36  D) 40  E) 44

Solution: By rule of alligation:   70% - 10% = 60%   100% - 70% 70  - 10= 
70  - 10 = 60
60%   100% - 70% = 30%   Quantity of pure water : Quantity of the mixture  100  - 70= 
 100  - 70 = 30
30%   Quantity of pure water : Quantity of the mixture= 6 : 3   There are 18 liters of mixture, so we need to add 36 liters of pure water.   The answer is 36.
Answer: C