MU-NLPC/Calc-aqua_rat huggingface dataset:
P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is	Choose the correct choice from the following answers:	A) 40000	B) 50000	C) 60000	D) 70000	E) None of these

Solution: Explanation :   Let the amount invested by Q = q   40000 : q = 2 : 3   => 40000/q = 2/3   => q = 40000 * (3/2)= 
40000 * (3/2) = 60_000
60000. Answer : Option 60000
Answer: C
What is the largest 4 digit number exactly divisible by 50?
Pick one:
A) 4676
B) 4678
C) 9950
D) 9504
E) 9936

Solution: Largest 4 digit number = 9999   9999 ÷ 50 = 199, remainder = 49   Hence largest 4 digit number exactly divisible by 50   = 9999 - 49= 
9999 - 49 = 9_950
9950   answer :9950
Answer: C
2500÷10÷5=?
Select:
A) 43 B) 37 C) 50 D) 33 E) 32

Solution: 2500 ÷ 10 = 250   250 ÷ 5= 50   Answer is 50
Answer: C
A football field is 7200 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards? Choose the correct answer: A) 450 B) 600 C) 750 D) 2400 E) 3200

Solution: Answer A) 9600 yards need 1200 lbs   1 Yard will need 1200/7200 = 1/6 lbs   3600 Yards will need   1/6* 3600= 
  1/6* 3600 = 600
600lbs   600
Answer: B
Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?  Select:
A) 6/11 B) 5/11 C) 7/11 D) 8/11 E) 9/11

Solution: Explanation:   Solution 1   Part of the tank filled by pipe A in 1 minute =1/30   Part of the tank filled by pipe B in 1 minute=1/20   Part of the tank filled by pipe C in 1 minute =1/10   Here we have to find the proportion of the solution R.   Pipe C discharges chemical solution R.   Part of the tank filled by pipe C in 3 minutes =3 X 1/10 = 3/10   Part of the tank filled by pipe A,B,C together in 1 minute =1/30 + 1/20 +1/10=11/60   Part of the tank filled by pipe A,B,C together in 3 minute =3 X 11/60 =11/20   Required proportion =(3/10) / (11/20)=3 X 20 / 10 X 11 = 6 /11.   6/11NSWER IS 6/11
Answer: A
In a village of 100 households, 65 have at least one DVD player, 75 have at least one cell phone, and 35 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is:  Choose the correct choice from the following answers
A) 60 B) 55 C) 45 D) 35 E) 25

Solution: Am I missing something here??? it seems straightforward......   The obvious maximum that have all 3 is 35, because you are limited by the SMALLEST number.   The minimum is simply the sum of the max of each people who DONT have the product, so:    100-75= 
 100-75 = 25
25 don't have Cell    100-65= 
 100-65 = 35
35 don't have DVD   and  100-35= 
 100-35 = 65
65 don't have MP3   SO a total of   25+35+65= 
  25+35+65 = 125
125 combined who might NOT have SOME combination of the 3 products. So subtract that from 100, to give you the minimum of the people who COULD have all 3 and you get 100-125= -25.   35+25= 
35+25 = 60
60   60
Answer: A
P is three times as fast as Q and working together, they can complete a work in 8 days. In how many days can Q alone complete the work?
Choose the correct choice from the following answers:
A) 32 days
B) 16 days
C) 13 days
D) 15 days
E) 19 days

Solution: B   16 days   P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 8 days, which means Q can alone do the work in  4*8= 
 4*8 = 32
32 days.   32 daysnswer : 32 days
Answer: A
Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 13 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal	Options:
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: Since (ii) holds for every real number x, it will remain valid if we replace x with   -x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 13 = f(x)+f(1-x) = f(x)+3+f(-x)   so that f(x) + f(-x) = 13-3= 
13-3 = 10
10. (Observe that f(x)= 3x + 4 satisfies the conditions   in the problem.)   correct answer 10
Answer: C
Given that a “24-inch pizza” means circular pizza with a diameter of 12 inches, changing from an 12-inch pizza to a 24-inch pizza gives you approximately what percent increase in the total amount of pizza? Choose the correct choice:
A) 300 B) 500 C) 670 D) 800 E) 125

Solution: area of 12 inch pizza= 6*6*pi=36 pi   area of 24 inch pizza =12*12*pi=144 pi   108/36*100= 
108/36*100 = 300
300% increase   hence answer is 300
Answer: A
Which one of the following option is the closest in the meaning to the word given below..
MITIGATE  Choose the most appropriate option
A) Diminish  B) Divulge  C) Dedicate  D) Denote  E) Deno2S

Solution: Explanation:   Mitigate means to make something less severe. Divulge means reveal. Denote means indicate. Diminish means to make or to cause something to become less in size, importance etc.   Diminishnswer: Diminish
Answer: A
Sonika deposited Rs.6000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?	Choose the correct choice from the following answers:
A) 9660
B) 6560
C) 7560
D) 9560
E) 8560

Solution: (6000*3*2)/100= 
(6000*3*2)/100 = 360
360   9200   --------   9560   ANSWER:9560
Answer: D
A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers E are possible?
Choose the correct choice from the following options.
A) 2 B) 4 C) 6 D) 3 E) Not possible

Solution: Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2   Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total E of 6 possibilities.   6.
Answer: C
A car travels first 160 km at 75 km/hr and the next 160 km at 90 km/hr. What is the average speed for the first 320 km of the tour?  Choose the correct answer.
A) 71.11  B) 71.12  C) 71.1  D) 71.17  E) 81.81

Solution: Car travels first 160 km at 75 km/hr   Time taken to travel first 160 km = distancespeed=160/75   Car travels next160 km at 90 km/hr   Time taken to travel next 160 km = distancespeed=160/90   Total distance traveled = 160+160=2×160   Total time taken = 160/75+160/90   Average speed = Total distance traveled/Total time taken=320/(160/75+160/90)=81.81 km/hr   Answer:81.81
Answer: E
Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 20 grades are D's. What is the number of students in the course?
Choose the correct choice from the following answers.
A) 80  B) 110  C) 160  D) 200  E) 400

Solution: We start by creating a variable for the total number of students in the math course. We can say:   T = Total number of students in the math course   Next, we can use variable T in an equation that we translate from the given information. We are given that, of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 20 grades are D's. Since this represents all the grades in the class, it represents all the students in the class. Thus we know:   #A’s + #B’s + #C’s + #D’s = Total number of students in the class   1/5(T) + ¼(T) + ½(T) + 20 = T   We can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have:   4T + 5T + 10T + 400 = 20T   19T + 400 = 20T   400 = T   There are a total of 400 students in the math class.   Answer is 400.
Answer: E
Q' = 3Q - 3, what is the value of (4')' ?  Choose one:  A) 48  B) 57  C) 66  D) 72  E) 81

Solution: (4')'=(3*4-3)= 
(3*4-3) = 9
9'=9*9-9= 
9*9-9 = 72
72   Answer 72
Answer: D
A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Choose the most appropriate option:
A) 356
B) 352
C) 350
D) 359
E) 358

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 39 = 50/3   3(x + 300) = 1950 è x = 350m.   Answer: Option 350
Answer: C
A train 450 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
Choose the correct choice from the following:
A) 5 sec	B) 39 sec	C) 27 sec	D) 15 sec	E) 18 sec

Solution: Speed of the train relative to man = (68 - 8) kmph   = (60* 5/18) m/sec = (50/3)m/sec   Time taken by the train to cross the man   = Time taken by It to cover 450 m at 50/3 m / sec = 450 *3/ 50= 
450 *3/ 50 = 27
27 sec   Answer : 27 sec.
Answer: C
The greatest number of four digits which is divisible by 21, 35, 49 and 63	Pick one
A) 6612
B) 6615
C) 6610
D) 6611
E) 5671

Solution: Explanation:   The greatest four digit number is 9999   L.C.M of 21, 35, 49 and 63 is 6615.   On dividing 9999by 6615, the remainder is 3384   Required number is 9999 - 3384 is 6615   Answer: Option 6615
Answer: B
If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?  Choose one:
A) 5%	B) 10%	C) 12%	D) 15%	E) 17%

Solution: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%   10%
Answer: B
In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?	Choose the correct choice from the following options
A) 90%
B) 20%
C) 80%
D) 50%
E) 20%

Solution: Number of students passed = 60% of 140   = 60/100 * 140= 
60/100 * 140 = 84
84   Number of students failed= 140 - 84= 
140 - 84 = 56
56.   Required percentage= 28/56 * 100= 
28/56 * 100 = 50
50%.   Answer:50%
Answer: D
S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
Pick one.
A) 18	B) 16	C) 16	D) 17	E) 19

Solution: S:E = 1:3   E:M = 3:5   ------------   S:E:M = 3:9:15   3/27 * 162= 
3/27 * 162 = 18
18   18nswer: 18
Answer: A
There is enough provisions for 9600 women in an army camp for 400 days. If there were 4800 men less, how long will the provision last?
Options
A) 799  B) 800  C) 801  D) 802  E) 803

Solution: We have, M1D1 = M2D2   9600*400= 4800* D2   D2 = 9600*400/4800= 
9600*400/4800 = 800
800 days.   ANSWER:800
Answer: B
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is  Choose the correct choice from the following options:
A) 21 years
B) 22 years
C) 23 years
D) 24 years
E) 25 years

Solution: Explanation:   Let's Son age is x, then Father age is x+24.   => 2(x+2) = (x+24+2)   => 2x+4 = x+26   => x = 22 years   Answer: Option 22 years
Answer: B
Find the one which does not belong to that group ? Choices
A) 36 B) 71 C) 62 D) 12 E) 57

Solution: Explanation:   41, 43, 47 and 53 are prime numbers, but not 57.   Answer:57
Answer: E
The speed of a boat in still water is 18 kmph. What is the speed of the stream if the boat can cover 48 km downstream or 32 km upstream in the same time?	Select the correct option.
A) 4 kmph B) 5 kmph C) 6 kmph D) 7 kmph E) 8 kmph

Solution: X = the speed of the stream   (18 + X) / (18 - X) = 2/1   18+ X = 36 - 2X   3X = 18   X = 6 km/hour   If the speed of the stream is 6km/hour, then the 'downstream' speed of the boat is   18+6= 
  18+6 = 24
24km/hour and the 'upstream' speed of the boat is 18-6= 
18-6 = 12
12km/hour. In that way, if the boat traveled for 2 hours, it would travel 2x24= 48km downstream and 2x12 = 24km/hour upstream.   Answer : 6 kmph
Answer: C
What is the difference between the place value and the face value of 7 in the numeral 297832?
Choose the correct choice:	A) None of these	B) 5993	C) 994	D) 5994	E) 995

Solution: Explanation:   Place value of 6 = 7000   Face value of 6 = 7   Difference = 6000 - 7= 
6000 - 7 = 5_993
5993   Answer: 5993
Answer: B
When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 2, the speed of the leak is Vâ€™, When the height of the oil remaining is 10, what was the speed of the leak, in terms of Vâ€™?
Choose the correct choice: A) 2Vâ€™ B) 25Vâ€™ C) Vâ€™/2 D) Vâ€™/4 E) Vâ€™

Solution: When h=2 v=V'   So V' = k.4   Hence k = V'/4   Now when h=10   v=(V'/4).10^2   v=V'.100/4   v=25V'   Ans : 25Vâ€™
Answer: B
Subtracting 10% from X is the same as multiplying X by what number?	Choose the correct option:  A) 80%  B) 90%  C) 10%  D) 50%  E) 60%

Solution: Explanation:   X - (10/100) X = X * ?   ? = 90%   ANSWER IS 90%
Answer: B
A 10-by-9 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?	Choose the correct choice from the following choices
A) The volume of the cylinder with height 10 is 90/pi cubic inches greater than the volume of the cylinder with height 6. B) The volume of the cylinder with height 9 is 90/pi cubic inches greater than the volume of the cylinder with height 10. C) The volume of the cylinder with height 10 is 90pi cubic inches greater than the volume of the cylinder with height 6. D) The volume of the cylinder with height 9 is 90pi cubic inches greater than the volume of the cylinder with height 10. E) The volume of the cylinder with height 9 is 240/pi cubic inches greater than the volume of the cylinder with height 10.

Solution: Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 9 and 10 are the circumference of the base and not the radius. The volume of the cylinder with height 9 is 90/pi cubic inches greater than the volume of the cylinder with height 10. is the right answer.
Answer: B
Eric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 5250 Nis, how much more money does Nick contribute than Archi?	Choose the correct option.
A) 128 Nis
B) 212 Nis
C) 234 Nis
D) 250 Nis
E) 288 Nis

Solution: E:N:A 5:3:2.5   so total = 5x + 3x + 2.5 x = 10.5 x 5  + 3  + 2.5= 
5  + 3  + 2.5 = 10.5
10.5 x= 5250   so x = 500   Nick Contribution is 0.5 more than Archi so 0.5 x =0.5 * 500= 
0.5 * 500 = 250
250   So D. 250 Nis is the correct answer
Answer: D
The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
Choose one
A) 180
B) 282
C) 267
D) 287
E) 207

Solution: Let the five numbers be P, Q, R, S and T.   => P + Q + R + S + T = 655.   (P + Q)/2 = 85 and R = 125   P + Q = 170 and R = 125   P + Q + R = 295   S + T = 655 - (P + Q + R) = 360   180verage of the last two numbers   = (S + T)/2 = 180   180nswer:180
Answer: A
The average weight of a group of boys is 30 kg. After a boy of weight 45 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?  Options: A) 14 B) 15 C) 16 D) 17 E) 18

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 30x   After the boy weighing 45 kg joins the group, total weight of boys = 30x + 45   So 30x + 45 = 31(x + 1) = > x = 14.   14nswer: 14
Answer: A
In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is: Select.
A) 24
B) 26
C) 42
D) 46
E) none

Solution: Let the ten's digit be x.   Then, unit's digit = x + 2.   Number = 10x + (x + 2) = 11x + 2.   Sum of digits = x + (x + 2) = 2x + 2.   (11x + 2)(2x + 2) + (  + 2)= 
+ (  + 2) = 2
2x + 2.   (11x + 2)(2x + 2)= 144   22x2 + 26x - 140 = 0   11x2 + 13x - 70 = 0   (x - 2)(11x + 35) = 0   x = 2.   Hence, required number = 11x + 2 = 24   24nswer = 24
Answer: A
The ratio between the present ages of P and Q is 5:7 respectively.If the difference between Q’s present age and P’s age after 6 years is 2,what is the total of P’s and Q’s present ages ?	Choose the correct answer.
A) 48 years	B) 52 years	C) 56 years	D) Cannot be determined	E) None of these

Solution: Solution   Let the present ages of P and Q be 5x years and 7x years respectively.   Then,7x -(5x +6)=2 ⇔ 2x =8 ⇔ x=4.   ∴ Required sum =5x +7x =12x 5  +7= 
5  +7 = 12
12x=48 years. 48 yearsnswer 48 years
Answer: A
58, 52, 46, 40, 34, ... ?	Select.
A) 20
B) 22
C) 28
D) 27
E) 32

Solution: Each number is 6 less than the previous number.   58-6= 
58-6 = 52
52   52-6= 
52-6 = 46
46   46-6= 
46-6 = 40
40   40-6= 
40-6 = 34
34   34-6= 
34-6 = 28
28   ANSWER:28
Answer: C
Two years ago, John’s age was half of the age he will be in 8 years. How old is he now?  Choose the correct choice from the following answers
A) 14years  B) 15years  C) 16years  D) 12years  E) 18years

Solution: Let John=j,j-2=(j+8)/2,then j=12years   ANSWER:12years
Answer: D
If all the fractions 3/10, 1/16, 4/11, 2/9, 1/7, 5/14 and 5/24 arranged in descending order of their values, then which one will be the third?	Choose the correct choice from the following options.
A) 1/16
B) 2/9
C) 3/10
D) 4/11
E) None of these

Solution: 3/10= 
3/10 = 3/10 = around 0.3
0.3, 1/16= 0.0625, 4/11 = 0.36, 2/9 = 0.22, 1/7 = 0.14, 5/14 = 0.36 and 5/24 = 0.21   4/11 > 5/14 > 3/10 > 2/9 > 5/24 > 1/7 > 1/16   3/10 will be the third.   ANSWER:3/10
Answer: C
The captain of a cricket team of 11 players is 25 years old and the wicket-keeper is 3 years older. If the age of these two players are replaced by that of another two players, the average of the cricket team drops by 2 years. Find the average age of these two players.	Pick one:  A) 15 years  B) 15.5 years  C) 17 years  D) 16.5 years  E) None of the above

Solution: Let average of team = x years   Then, 25 + 28 + S9 = 11x … (i)   where S9 is the sum of ages of remaining players   Also, Np + S9 = 11(x – 2) ,…(ii)   where Np is the sum of ages of new players   (i) – (ii) ⇒ 53 – Np = 22   ⇒ Np = 31   ∴ Average age of new two players = 31⁄2 = 15.5 years   Answer 15.5 years
Answer: B
In the exam the average was found to be p mark. After deducting typographical error the average marks of 120 student reduced from 90 to 70 . Due to this the average came down by 12 marks. What was the number of students who took the exam? Choices.
A) 100 B) 120 C) 200 D) 130 E) 160

Solution: Explanation :   Number of student = (90-70) * 120/12= 
(90-70) * 120/12 = 200
200   Answer : 200
Answer: C
For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(106) – g(103)?	Choose the correct choice from the following options:
A) 100 B) 99 C) 98 D) 102 E) 104

Solution: g(106) = 1*3*5*7*9*...*99*101*103*105   g(103) = 1*3*5*7*9*...*99*101*103   g(106) - g(103) = 1*3*5*7*9*...*99*101*103*105 - 1*3*5*7*9*...*99*101*103 = 1*3*5*7*9*...*103*(105 - 1) = 1*3*5*7*9*...*99*101*103*104   hence:104
Answer: E
What is the area of square field whose side of length 14 m? Choose the correct option
A) 225  B) 196  C) 266  D) 288  E) 261

Solution: 14 * 14= 
14 * 14 = 196
196 sq m   Answer: 196
Answer: B
By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?  Select: A) 42 6/8% B) 42 8/7% C) 482 6/7% D) 42 6/7% E) 42 1/7%

Solution: SP = CP + g   50 SP = 50 CP + 15 SP   35 SP = 50 CP   35 --- 15 CP gain   100 --- ? => 42 6/7%   Answer:42 6/7%
Answer: D
A man swims downstream 60 km and upstream 100 km taking 10 hours each time, what is the speed of the man in still water?	Select the correct option.
A) 24	B) 42	C) 6	D) 8	E) 12

Solution: 60 --- 10 8S = 6   ? ---- 1   100 ----10 US = 10   ? ---- 1 M = ?   M = (10 + 6)/2= 
(10 + 6)/2 = 8
8   Answer:8
Answer: D
A positive integer is called "square-Free" if it has no factor that is the square of an integer greater than 1. If n is an even square-free integer, which of the following must also be square free? Choose the most appropriate option:	A) n/2	B) 2n	C) n+2	D) n^2	E) none of the above

Solution: Per definition a square-free integer has primes in power of 1. For example 5^3 is NOT square-free because it's a multiple of 5^2.   We are told that n=2k, since n itself is square-free, then k also must be square-free --> n/2=k.   Answer: A.   number for n. Say n=2, then among n/2, B, C, and D, only n/2 (n/2=1) will be square free.
Answer: A
A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Pick one:  A) 228  B) 278  C) 120  D) 998  E) 232

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.   Length of the train = 20 * 6= 
20 * 6 = 120
120 m.   Answer: 120
Answer: C
Cost of 16 mirror and 8 comb is Rs.368 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?
Select the correct option:
A) 10	B) 12	C) 20	D) 21	E) 22

Solution: Let the cost of each pen and pencil be 'p' and 'q' respectively.   16m + 8c = 368 --- (1)   4m + 4c = 96   8m + 8c = 192 --- (2)   (1) - (2) => 8p = 176   => m = 22   22
Answer: E
Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.	Select the correct option:
A) 127	B) 157	C) 147	D) 137	E) None of them

Solution: Required number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of 1651 and 2032   _______   1651 ) 2032 ( 1 1651   1651_______   381 ) 1651 ( 4   1524_________   127 ) 381 ( 3   381   0   Required number = 127.   127nswer is 127.
Answer: A
There are 5 people and 3 chairs. In how many different ways people can occupy the chairs? Choose the correct choice from the following
A) 60
B) 70
C) 80
D) 90
E) 100

Solution: number of ways = 5*4*3= 
5*4*3 = 60
60   60nswer is 60
Answer: A
A certain ski shop sells pairs of gloves in 13 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color? Select the correct option.
A) 1/144
B) 1/143
C) 1/25
D) 1/23
E) 1/12

Solution: there are 13 different colours sothere are 13 pairs of gloves dropped..   first can be any of 26..so 26/26..   second has to be its pair, which will be just one out of remaining 25.. 1/25..   overall prob=26/26*1/25= 1/25..   1/25
Answer: C
Of the eight participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?
Pick one:
A) 1
B) 4
C) 6
D) 9
E) 20

Solution: M under 18 - 2   F above 18 - 2   How many distinct groups can be formed now: 2c2 * 2c2 = 1   1nswer : 1
Answer: A
Mike weighs twice as much as Mary. Mike's weight is 50% of Michelle's weight. Alan weighs 40% of Charlie's weight. Charlie weighs 180% of Mary's weight. Which of these 5 people weighs the highest? Options:
A) Mary	B) Mike	C) Michelle	D) Alan	E) Charlie

Solution: Mary < Mike < Michelle   Alan < Charlie   Let x be Mary's weight.   Michelle's weight is 4x and Charlie's weight is 1.8x.   The answer is Michelle.
Answer: C
A certain stock exchange designates each stock with a two-letter or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes without using the letters A or Z?  Choose the correct choice from the following.
A) 13.8  B) 14,400  C) 15,000  D) 15,600  E) 16,200

Solution: The number of two-letter codes is  24*24= 
 24*24 = 576
576.   The number of three-letter codes is 24*24*24=13,824.   The total number of codes is 576+13,824=14,400.   The answer is 14,400.
Answer: B