MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the probability that a leap year selected at random will not have 53 Sundays or Mondays. Choose the correct choice from the following answers
A) 6/7  B) 5/7  C) 4/7  D) 3/7  E) 2/7

Solution: There are 366 days in a leap year: 52 weeks and 2 more days. So, 52 Sundays, 52 Mondays and 2 days.   These 2 days can be: {Mon, Tue}, {Tue, Wed}, {Wed, Thu}, {Thu, Fri}, {Fri, Sat}, {Sat,Sun} and {Sun, Mon} (7 cases). In order to have 53 Sundays or 53 Mondays we should have either {Mon, Tue}   {Sat,Sun} or {Sun, Mon} case.   The probability of that is 3/7.   So probability of not having 53 Sundays or Mondays, probability is 1 - 3/7 = 4/7   Answer: 4/7.
Answer: C
There are 5 couples. If they will sit 10 chairs in a row such that each couple sits side by side, how many possible cases are there?  Answers:
A) 120  B) 240  C) 1,200  D) 2,460  E) 3,840

Solution: Tie the couples. Then we have 5 persons that have to be arranged in 5 places. 5! ways.   Now the couples can change position with each other. 2! ways.   5! * (2!)^2 = 120 *32= 
120 *32 = 3_840
3840   Answer is E.   5! * 2!= 240 ways.
Answer: E
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8.5 m x 6 m x 22.5 cm?
Choose the correct choice from the following options:
A) 6400
B) 6410
C) 6440
D) 6500
E) 6800

Solution: Number of bricks = Volume of Wall/Volume of Bricks   =850x600x22.5/25x11.25x6= = 6800   answer :6800
Answer: E
Positive integer x is 50 percent of 50 percent of positive integer y, and x percent of y equals 100. What is the value of y?
Choose the correct choice from the following answers
A) 50	B) 100	C) 400	D) 200	E) 2,000

Solution: x = 50% of 50% 0f y   = y/4   and   x/100 of y = 100   x /100 *4x =100   x = 50   and y= 200   Answer - 200
Answer: D
A train passes a station platform in 35 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 choice from the following choices.
A) 248 m  B) 225 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)/35 = 15 ==> x + 300 = 525 ==> x   = 225 m.   Answer: 225 m
Answer: B
The average of first four multiples of 4 is : Options:
A) 3	B) 9	C) 10	D) 15	E) 17

Solution: Solution   Average = 4(1+2+3+4)/4 =40/4= 
40/4 = 10
10 Answer 10
Answer: C
How many integers from 101 to 900, inclusive, remains the value unchanged when the digits were reversed?
Choose the correct answer:
A) 50  B) 60  C) 70  D) 80  E) 90

Solution: question is asking for palindrome   first digit possibilities - 1 through 8 = 8   9 is not possible here because it would result in a number greater than 9 (i.e 909 , 919..)   second digit possibilities - 0 though 9 = 10   third digit is same as first digit   =>total possible number meeting the given conditions = 8 *10= 
8 *10 = 80
80   Answer is 80.
Answer: D
Two numbers A and B are such that the sum of 8% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Choices.
A) 2 : 1	B) 1 : 2	C) 4 : 3	D) 1 : 3	E) 3 : 2

Solution: Explanation:   8% of A + 4% of B = 2/3(6% of A + 8% of B)   8A/100 + 4B/100 = 2/3(6A/100+8B/100)   ⇒8A + 4B = 2/3(6A + 8B)   ⇒24A + 12B = 12A + 16B   ⇒ 12A = 4B   ⇒ AB = 4/12   ⇒ A:B=1:3   Answer: Option 1 : 3
Answer: D
Three models (M, N, and O) of cars are distributed among three showrooms. The number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom. There are 19 cars of Model M, 17 cars of Model N, and 15 cars of Model O. What is the maximum number of cars of model M in any showroom ?  Choose the most appropriate option:	A) 17	B) 16	C) 15	D) 14	E) 13

Solution: The total number of cars is 51. So each showroom has 17 cars(since the number of cars in each showrooms should be equal   51/3= 
  51/3 = 17
17).   Moreover that the number of model M is maximum means that the numbers of model N and O should be minimum. Since each model must be represented by at least one car in every showroom that minimum number should be 1.   So Maximum number of model M is   17-2= 
  17-2 = 15
15.   The answer is (15)
Answer: C
If x is an integer and (x)(x^2)(x^3) is positive, which of the following could be negative?	Select.
A) x^4	B) (x)(x^3)	C) (x)(x)	D) x + x^3	E) 3x^2

Solution: Assuming) x is negative (makes it easier)   (-2)(-2^2)(-2^3)   (-2)^3.(-2)^3   The two negative numbers will remain negative, so they will both cancel out.   So we need an equation where x^n with n being odd.   a) not sufficient -> will always be positive   b) not sufficient -> equals x^4 which will always be positive   c) not sufficient -> equals x^2 which will always be positive   d) -2+-8 = -10!!!   e) 3*4=12 is positive (pemdas!)   Answer is x + x^3
Answer: D
A bat is bought for Rs.420 and sold at a gain of 20% find its selling price  Choose the correct choice:
A) s.430/-
B) s.480/-
C) s.400/-
D) s.504/-
E) s.600/-

Solution: 100 % ------> 420   120 % ------> 420*120/100   Selling price = Rs.504   s.504/-
Answer: D
The diagonals of a rhombus are 14 cm and 20 cm. Find its area?
Select:  A) 176  B) 140  C) 150  D) 179  E) 172

Solution: 1/2 * 14 * 20= 
1/2 * 14 * 20 = 140
140   Answer:140
Answer: B
A certain class of students is being divided into teams. The class can either be divided into 15 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
Choose the correct option:  A) 6  B) 36  C) 48  D) 60  E) 120

Solution: Let total no of students in the class be N   So, we are told that N is divisible by both 15 24   So, Lets find the least common multiple of 15 24 , ie 120   So our answer is (120) 120
Answer: E
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: Select the correct option.
A) 230	B) 240	C) 245	D) 250	E) 260

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.   Answer: Option 245
Answer: C
Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 15,6400, Deepak's share is:? Choose one
A) s.9520  B) s.8428  C) s.8400  D) s.8429  E) s.8420

Solution: Ratio of their shares   = 22500 : 35000   = 9:14   Deepak's share   = 15640 * 14/23   = Rs.9520.   s.9520nswer:s.9520
Answer: A
Which of the following numbers has neither 3 or 5 as a distinct prime factor? Choose the correct choice from the following answers.
A) 77	B) 80	C) 125	D) 132	E) 210

Solution: 77=7*11   80=2^4*5   125=5^3   132=2^2*3*11   210=2*3*5*7   77 has distinct prime factors of 7 and 11.   77nswer 77
Answer: A
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.2090.What was his original salary?  Choose the correct choice from the following choices:
A) 2277
B) 2999
C) 1000
D) 2651
E) 2000

Solution: X * (110/100) * (95/100) = 2090   X * (11/10) * (1/100) = 22   X = 2000   Answer: 2000
Answer: E
A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?  Choose the most appropriate option:
A) 5/5
B) 5/1
C) 5/9
D) 5/2
E) 5/7

Solution: Two balls can be picked from nine balls in 9C2 ways.   We select one white ball and one red ball from five white balls and four red balls. This can be done 5C1 . 4C1 ways.   The required probability   = (5 * 4)/95/92   = 20/36   = 5/9   Answer:5/9
Answer: C
The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers? Choose the correct choice from the following answers:
A) 2
B) 3
C) 9
D) 7
E) 1

Solution: Explanation:   Let the ten's digit be x and units digit by y.   Then,   (10x + y) - (10y + x) = 63   9(x - y) = 63   x - y = 7   Thus, none of the numbers can be determined.   Answer: 7
Answer: D
By walking at 3/4th of his usual speed, a man reaches office 5 minutes later than usual. What is his usual time?  Choices:
A) 15min B) 50min C) 65min D) 60min E) 70min

Solution: let T be the usual time.   time spent=4T/3   therefore, 4T/3=T+5   4T=3T+15...therefor T=15min   15minNSWER:15min
Answer: A
A hostel had provisions for 250 men for 44 days. If 50 men left the hostel, how long will the food last at the same rate?	Choose the correct choice.
A) 55
B) 40
C) 50
D) 60
E) 65

Solution: A hostel had provisions for 250 men for 44 days   If 50 men leaves the hostel, remaining men = 250 - 50= 
250 - 50 = 200
200   We need to find out how long the food will last for these 200 men.   Let the required number of days= x days   More men, Less days (Indirect Proportion)   (men) 250 : 200 :: x : 44   250×44=200x   5×44=4x   x=5×11=55   55NSWER 55
Answer: A
I live X floors above the ground floor of a high-rise building. It takes me 30 s per floor to walk down the steps and 2 s per floor to ride the lift. What is X, if the time taken to walk down the steps to the ground floor is the same as to wait for the lift for 7 min and then ride down?  Choose one.
A) 4	B) 7	C) 14	D) 15	E) 17

Solution: Explanation :   Since I live X floors above the ground floor and it takes me 30 s per floor to walk and 2 s per floor to ride, it takes 30X s to walk down and 2X s to ride down after waiting 420 s   => 30X = 2X + 420   => X = 15.   Answer : 15
Answer: D
Tough and Tricky questions: Remainders.
1^1 + 2^2 + 3^3 + ... + 7^7 is divided by 7. What is the remainder?  Answers:  A) 0  B) 1  C) 2  D) 3  E) 4

Solution: a number is divisible by 5, if its last digit is divisible by 5   let's look into the sum of last digits of each term of the given expression   1^1=1   2^2=4   3^3=7   4^4=6   5^5=5   6^6=6   7^7=3   adding all these numbers we get 32 which gives a remainder of4 when divided by 7. so answer must be 4.   bunuel, can you please confirm the answer of this question.   Yes, the OA is C. Clicked the wrong button when posting. Edited. Thank you.   4
Answer: E
What is the next number: 2, 17, 257, __ Choose the correct answer:
A) 2977 B) 3837 C) 4097 D) 4847 E) 5387

Solution: 4^0 + 1 = 2   4^2 + 1 = 17   4^4 + 1 = 257   4^6 + 1 = 4097   The answer is 4097.
Answer: C
Square X is inscribed in circle Y. If the perimeter of X is 64, what is the circumference of Y?  Choose the correct choice from the following options:  A) 16√ 2π  B) 8√ 2π  C) 22√ 2π  D) 12√ 2π  E) 9

Solution: square forms two right angled triangles.   Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter.   hypotenuse here = diagonal of the square = 16 sqrt(2) = diameter   => radius = 8 sqrt(2)   Circumference of the circle = 2pi r = 16 pi sqrt(2)   16√ 2πnswer is 16√ 2π.
Answer: A
The sum of three integers A, B and C is 300. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?
Choose the correct option.
A) 175
B) 180
C) 185
D) 190
E) 195

Solution: A is one third of the sum of B and C..   or A=1/3(B+C)...   But A+B+C=300   so 1/3(B+C)+B+C=300   4(B+C)/3= 300   B+C =300*3/4= 
300*3/4 = 225
225   A=300-225= 
300-225 = 75
75   2)B is one fifth of the sum of A and C   or B=1/5(A+C)...   But 175+B+C=300   so 1/5(175+C)+175+C=300   175+C=300*5/6= 
300*5/6 = 250
250   but 175=75, so C=250-75= 
250-75 = 175
175   175nswer : 175
Answer: A
For every $20 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $8 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as  Answers:  A) 1 : 8 : 800  B) 1 : 4 : 100  C) 20 : 4 : 1  D) 100 : 4 : 1  E) 400 : 4 : 1

Solution: B.........M........Y   20.....0,20......Y   B.........8........1   What I did first was to turn 0.20 to 2 (by multiplying by 10), so that it is easy to find the LCM. This led me to this:   B.........M........Y   200.....2.........Y   B........80......10   Then I multiplied every row by 80 (the LCM of 2 and 80), which led me to this:   B.........M........Y   8000...80.......10   Then I got rid of the extra zero, and in the correct order this is Y:M:B=1:8:800   1 : 8 : 800NS 1 : 8 : 800
Answer: A
Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of X to Y is 5:4?	Pick
A) 6:1  B) 5:4  C) 20:7  D) 10:9  E) 14:11

Solution: I got C but with a different, yet slightly longer approach, which I constantly use for proportion problems such as this one. Usually, this approach is very efficient when used with slightly difficult questions, but this problem is quite hard so I had to slightly tweak it. I will show you how I usually use the approach and later show you how to use it with this specific problem.   Example.   1 Liter of Solution A contains 45% alcohol, while 1 Liter of Solution B contains 20% alcohol. In what ratio must the two solutions be used to get a solution with 30% alcohol   Solution:   1.	45/100*[A/(A+B)]+20/100*[B/(A+B)] = 30/100   2.	Multiply 100 to both sides to arrive at 45A/(A+B) + 20B/(A+B) = 30   3.	Multiply (A+B) to both sides to arrive at 45A + 20B = 30A + 30B   4.	Distribute to arrive at 15A = 10B   5.	Thus the ratio is A/B = 10/15 = 2/3   Now using this same approach, we tackle Gopu106’s question. It is important to first think of X in the mixture as the alcohol in the problem above; hence, a mixture of X and Y in the ratio of 3:2 translates to X is 3/5 of the solution. Applying this concept to all three equations, we write:   1.	3/5*[A/(A+B)]+3/7*[B/(A+B)] = 5/9   2.	Now here is the tweak that must be made to continue with this approach. You must find the common denominator for all three numbers and organize the fractions accordingly. By finding the common denominator of 5,7,9 (or 315) we re-write the equations as follows   3.	189/315*[A/(A+B)]+135/315*[B/(A+B)] = 175/315   4.	Multiply 315 to both sides to arrive at 189A/(A+B) + 135B/(A+B) = 175   5.	Multiply (A+B) to both sides to arrive at 189A + 135B = 175A + 175B   6.	Distribute to arrive at 14A = 40B   7.	Thus the ratio is A/B = 40/14 = 20/7 or answer 20:7
Answer: C
In assembling a Bluetooth device, a factory uses one of two kinds of modules. One module costs $10 and the other one, that is cheaper, costs $2.5. The factory holds a $62.50 worth stock of 22 modules. How many of the modules in the stock are of the cheaper kind?
Answers.
A) 31
B) 35
C) 21
D) 40
E) 45

Solution: So the number of $2.50 modules must be 21 so that the leftover 1 modules are of $10 which will give a total value $62.50. 21*2.50+1*10 = 52.50+10= 
52.50+10 = 62.5
62.50   Answer : 21
Answer: C
A train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?
Select.
A) 3:5
B) 3:3
C) 3:1
D) 3:4
E) 3:2

Solution: :   Since S # 1/t   S1 : S2 = 1/t1 : 1/t2 =1/8 :1/6   =3:4   Answer:3:4
Answer: D
A series S1 of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series S2, the nth term defined as the difference between the (n+1) term and the nth term of series S1, is an arithmetic progression with a common difference of 30.
First term of S1 is Choose the correct choice from the following choices:
A) 80
B) 90
C) 100
D) 120
E) 130

Solution: Explanation :   According to the question,   S1:- 2a, b, a, c, 2a + 20   And,   S2:- b - 2a, a - b, c - a, 2a + 20 - c   Also,   => b - 2a + 30 = a - b i.e. 3a - 2b = 30 .   => a - b + 30 = c - a   => c - a + 30 = 2a + 20 - c i.e. 3a - 2c = 10   Solving them, we get a = 50, b = 60, c = 70   So series S1: 100, 60, 50, 70, 120 and series S2: -40, -10, 20.   Answer : 100
Answer: C
How many sides does the polygon have if the total angles measures up to 900 degrees?
Choose one:
A) 3	B) 7	C) 4	D) 6	E) None of these

Solution: 7 sides...answer is 7
Answer: B
Average weight of 15 boys in a class is 48 kgs. The average weight of the class of 25 students is 45 kgs. What is the average weight of the 15 girls in the class?
Choose the correct choice from the following answers
A) 45
B) 47.3
C) 39.8
D) 45.5
E) 40.5

Solution: total weight of boys in class 15 X 48=720kg   total weight of all student in the class room 25 X45=1125kg   total no of girls in the class 1125-720= 
1125-720 = 405
405kg   average weight of girls   405/10= 
  405/10 = 81/2 = around 40.5
40.5kg   correct ans is 40.5
Answer: E
A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 670 m?  Select the correct option
A) 120 sec  B) 91 sec  C) 89 sec  D) 80 sec  E) 85 sec

Solution: Explanation:   v = 240/24 (where v is the speed of the train) = 10 m/s   t = (240+670)/10= 
(240+670)/10 = 91
91 seconds   Answer: Option 91 sec
Answer: B
A train passes a man standing on the platform. If the train is 245 meters long and its speed is 126 kmph, how much time it took in doing so? Choices
A) 2 sec  B) 67 sec  C) 5 sec  D) 9 sec  E) 7 sec

Solution: D = 245   S = 126 * 5/18= 
126 * 5/18 = 35
35 mps   T= 245/35= 
245/35 = 7
7 sec   Answer:7 sec
Answer: E
The age of man is three times the sum of the ages of his two sons.Nine years hence,his age will be double of the sum of the ages of his sons.The fatherâ€™s present age is :	Choose the most appropriate option.
A) 40 years
B) 45 years
C) 50 years
D) 55 years
E) 81 years

Solution: Solution   Let the sum of present ages of the two sons be x years.   Then,father's present age = 3x years.   âˆ´ (3x + 9)=2 (x +18) â‡” 3x + 9 = 2x + 36 â‡” x =27   Hence,father's present age = 81 years. Answer 81 years
Answer: E
If a radio is purchased for Rs 490 and sold for Rs 465.50 Find the loss%? Select the correct option:
A) 3% B) 4% C) 5% D) 6% E) None of these

Solution: Explanation :   Loss = 490 – 465.5 = 24.5 loss in % = 24.5/ 490 x 100 = 5%.   Answer : 5%
Answer: C
A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings?
Select the correct option:
A) 12	B) 13	C) 46	D) 37	E) 26

Solution: 16x + 85 = 17(x + 3)   x = 34 + 3= 
34 + 3 = 37
37   Answer: 37
Answer: D
if page of chemistry book is 30 more than page of physics book.if ratio of pages is
5:3.a child torn 15 pages of chemistry book.calculate new ratio.  Choose the correct choice from the following options:	A) 1:1	B) 2:1	C) 5:4	D) 4:3	E) 2:3

Solution: chemistry page=5x, physics page=3x   5x-3x=30,2x=30,x=15   chemistry page=75, physics page=45   after torn 15 page of chemistry=60   ratio become 60/45=4:3   answer 4:3
Answer: D
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?  Choose the correct choice from the following answers.
A) 12
B) 77
C) 48
D) 99
E) 11

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.9= 
1.10 + 0.9 = 2
2 km= 2000 m.   Required time = 2000 * 3/125= 
2000 * 3/125 = 48
48 sec.   Answer: 48
Answer: C
In the equation 2x â€“ cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 4 ? Choose the correct choice from the following answers.
A) âˆ’9/2  B) -4  C) 3  D) 4  E) 9/2

Solution: 2x - cy = 18   x=6, y=2;   12-2c=18   c=-3   2x-cy=18   when y=4, c=-3, x=   x=3   ANSWER:3
Answer: C
0.0203 x 2.92/0.0073 x 14.5 x 0.7 = ?  Options
A) 0.7	B) 0	C) 0.8	D) 8	E) 7

Solution: = 0.0203 x 2.92/0.0073 x 14.5 x 0.7   = 203 x 292/73 x 145 x 7   = 4/5= 
4/5 = 4/5 = around 0.8
0.8   Answer is 0.8.
Answer: C
If two sides of a triangle have lengths 3 and 8, which of the following could be the perimeter of the triangle? I. 9 II. 15 III. 19
Options.
A) None B) I only C) II only D) III only E) I, II, and III

Solution: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   Therefore:   (8-3) < {third side} < (8+3).   5 < {third side} < 11.   Perimeter = {third side} + 8 + 3 = {third side} + 11.   16 < {perimeter} < 22.   answer III only
Answer: D
A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?	Choose the correct choice from the following answers.
A) 20
B) 24
C) 25
D) 26
E) 30

Solution: Ans.(A)   Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
Answer: A
A is the average (arithmetic mean) of the first 7 positive multiples of 5 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n?	Choose the correct choice from the following answers: A) 5 B) 6 C) 10 D) 15 E) 20

Solution: If A^2 - B^2 = 0, then let's assume that A = B.   A must equal the 4th positive multiple of 4, thus A = 20, which also equals B.   B is the second positive multiple of n, thus n = 20/2= 
20/2 = 10
10.   The answer is 10.
Answer: C
A school give scholarship of a total of $940,000 to students, the scholarship consist of 3 types $95,000, $35,000, and $10,000. What is the smallest possible number of students who take the scholarship? Options:	A) 13	B) 14	C) 15	D) 16	E) 17

Solution: The number of first-place students=f   The number of second-place students=s   The number of third-place students=t   Then, an equation 95,000f+35,000s+10,000t=940,000 is derived.   In order for f+s+t to be minimum, f should be maximum followed by s and t.   Then, f=9, s=1, t=5 are derived and f+s+t=9+1+5= 
9+1+5 = 15
15.   ANSWER:15
Answer: C
How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 25%?  Choose one
A) 100 ml  B) 60 ml  C) 125 ml  D) 130 ml  E) 150 ml

Solution: we can also go by answer choices   Tke 100 ml for eg   400 (old)+100 (new concentr)ml     500*25/100= 
  500*25/100 = 125
125 ml (25ml is de old concentration +100 ml (newly added)   Answer 125 ml
Answer: C
At garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 9th highest price and the 35th lowest price among the prices of the items sold, how many items were sold at the garage sale?
Select:
A) 43	B) 28	C) 44	D) 49	E) 46

Solution: 8+34+1= 
8+34+1 = 43
43   43nswer: 43
Answer: A
Find the one which does not belong to that group ?
Choose the correct choice from the following choices.
A) 3 B) 4 C) 5 D) 9 E) 7

Solution: Explanation:   3, 5, 9 and 7 are odd numbers, but not 4.   ANSWER IS 4
Answer: B
If log 32 x= 0.8, then x is equal to  Answers:  A) 25.6  B) 16  C) 10  D) 12.8  E) None

Solution: Solution   log32 x	=0.8.   x=(32)0.8   ‹=›(25)4/5   ‹=›24   ‹=› 16.   Answer 16
Answer: B
When running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 42 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile? Choose one:	A) 5 minutes, 17.6 seconds	B) 5 minutes, 21.8 seconds	C) 5 minutes, 43.56 seconds	D) 5 minutes, 44.44 seconds	E) 6 minutes, 10.4 seconds

Solution: One approach:   The watch starts to work after Nuria began his running. It means the time should be greater than credited 5 minutes, 42 seconds. The only number is 6 minutes, 10.4 seconds.   Another approach:   11/25 close to 30 second when added to the 5 minutes, 44 seconds, it means it passes 6 minute.   Answer: 6 minutes, 10.4 seconds
Answer: E