MU-NLPC/Calc-aqua_rat huggingface dataset:
If d is the mean of x, y, and z, what is the mean of x + 5, y + 5, z + 5 ?
Choose the correct answer:
A) d
B) 3d
C) 15d
D) d + 5
E) d + 15

Solution: If we add or subtract a constant to each term in a set:   Mean will increase or decrease by the same constant.   SD will not change.   If we increase or decrease each term in a set by the same percent (multiply by a constant):   Mean will increase or decrease by the same percent.   SD will increase or decrease by the same percent.   So in our case mean will increase by 5 as we are adding 5 to each term in a set --> Mean =d + 5.   Answer: d + 5.
Answer: D
The remainder of the division of a number by 63 is 27. What will be the remainder when that number is divided by 8?
Please explain Choose the correct choice from the following answers.
A) 4	B) 5	C) 6	D) 2	E) 8

Solution: The easiest way to solve this question is by plugging in a number. Here are the steps I followed:   1) Choose a number X that when divided by 63 gives you 27 as a remainder. So I did x = 63 + 27= 
63 + 27 = 90
90. (90/63= 1R27)   2) Divide that number by 8. 90/8 = 11R2   Since the remainder is 2, the correct answer is choice 2.
Answer: D
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?	Choices:	A) 2.29	B) 2.88	C) 2.2	D) 2.12	E) 2.25

Solution: M = 6   S = 1.2   DS = 6 + 1.2= 
6 + 1.2 = 7.2
7.2   US= 6 - 1.2= 
6 - 1.2 = 4.8
4.8   x/7.2 + x/4.8= 1   x = 2.88   Answer: 2.88
Answer: B
The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability that exactly two visitors will buy a pack of candy?	Choose the correct choice from the following choices:
A) 0.343
B) 0.147
C) 0.189
D) 0.063
E) 0.027

Solution: 0.3*0.3*0.7 is equivalent to saying the the first person picks candy and second person picks candy and third person doesn't pick candy.   however this is a different case compared to   0.3*0.7*0.3 is equivalent to saying the the first person picks candy and second person doesn't pick candy and third person picks candy.   which in turn is a different case compared to   0.7*0.3*0.3 (I'll skip the verbose comments)   Hence the answer is   3*(0.3*0.3*0.7)= 
  3*(0.3*0.3*0.7) = 0.189
0.189   ANSWER 0.189
Answer: C
Which of the following is closest to the difference between sum R of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?	Choose the correct choice from the following.
A) 2.82	B) 2.72	C) 1.82	D) 1.72	E) 0.82

Solution: Sum R of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:   1/1 + 1/2 + 1/3 +.....+ 1/9   This is a harmonic progression. Harmonic progression is inverse of arithmetic progression.   Approximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)   Approximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)   The actual sum will be slightly more than the approximation.   Here we have 9 terms (odd).   Sum = 9 * 1/5   = 9/5   Product of all proper fractions in the form y/(y+1), where y is a positive digit:   1/2 * 2/3 * 3/4 *.....*9/10   We will be left with 1/10.   Required = 9/5 - 1/10   = 1.8 - 0.1= 
1.8 - 0.1 = 1.7
1.7   Closest is 1.72   Answer (1.72).
Answer: D
If a - b = 4 and a2 + b2 = 18, find the value of ab.
Pick: A) 9 B) 1 C) 2 D) 18 E) 19

Solution: 2ab = (a2 + b2) - (a - b)2   = 18 - 16= 
18 - 16 = 2
2   ab= 1.   Answer: 1
Answer: B
Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 60 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?  Select.
A) 1 hour B) 1 hour 10 minutes C) 2 hours 30 minutes D) 2 hours E) 2 hours 10 minutes

Solution: Both cars leave at the same time   Both cars travel at constant speed   Stealing a useful piece of information from Paragkan:   If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds   ratio of speed: (a/b) = sq. rt(b/a)   sq. rt(b/a)   sq. rt(90/60)   sq. rt(3/2)   So, for every three units of distance A travels, B travels two. Because we know the ratio of speed and the time it took B to travel the distance A hasn't yet covered, we can find the time it took A to cover the distance B did in 90 minutes.   90*(2/3)where represents the lesser amount of time it took A to travel the distance B did in 90 minutes.   = 60 minutes.   Therefore, A took 60 minutes to travel the first portion then 60 minutes to travel the distance B did in 90 minutes. A spent (60+60)= 
(60+60) = 120
120 minutes on the road.   D. 2 hours
Answer: D
The marked price of an article is 10% higher than the cost price. A discount of 10% is given on the marked price. In this kind of sale, the seller:  Choose the correct choice from the following answers:	A) bears no loss, no gain	B) gains 1%	C) loses 1%	D) None of these	E) Can't be determine

Solution: Let C.P.=Rs. 100. Then, marked price=Rs. 110.   S.P=90% of Rs. 110=Rs. 99. So, loss=1%   ANSWER:loses 1%
Answer: C
The sale price sarees listed for Rs.400 after successive discount is 30% and 20% is? Choose the correct choice from the following choices:
A) 297 B) 879 C) 342 D) 762 E) 224

Solution: 400*(70/100)*(80/100)= 
400*(70/100)*(80/100) = 224
224   Answer: 224
Answer: E
A shopkeeper sold an book offering a discount of 5% and earned a profit of 30%. What would have been the percentage of profit earned if no discount was offered?	Choose the correct choice from the following
A) 140	B) 120	C) 130	D) 136.8	E) 150

Solution: Let C.P. be $100.   Then, S.P. = $130   Let marked price be $x. Then, 95/100 x = 130   x = 13000/95 = $136.8   Now, S.P. = $136.8, C.P. = $100   Profit % = 136.8%.   136.8
Answer: D
How many digits 2^200 has?	Choose the correct choice.
A) 31
B) 61
C) 50
D) 99
E) 101

Solution: 2^10 = 1.024 * 10^3 => 2^100 = (1.024)^10 * 10^60   therefore 61 digits would be my best guess   61
Answer: B
Enzo is flying to Austria on vacation. He wants to bring several pairs of shoes with him. He knows each shoe's individual weight (x = weight as an integer). Choose an equation, that Enzo can use later in another equation, to find how many pairs of shoes he can take on his trip. So, this equation must result in an even number. What equation is true? Choose the most appropriate option:	A) 2x + 1 = even	B) (2x + 1)(2x + 1) = even	C) (1/2)(4x + 2) = even	D) (1/2)(4x + 2)(2x + 1) = even	E) (2x)(2x + 1) = even

Solution: Divisible by 2 (Parity Mathematics) states: an even number is an integer of the form n = 2k, where k is an integer; an odd number is an integer of the form n = 2k + 1.   A and C: 2x + 1 = odd   And from Multiplication Rule:   even x even = even   even x odd = even   odd x even = even   odd x odd = odd   So, B and D: odd x odd = odd, but   (2x)(2x + 1) = even: even x odd = even   Answer: (2x)(2x + 1) = even
Answer: E
Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 4H, which of the following represents the amount that Roberta paid?	Choose the correct choice:
A) D + 40
B) D + H – 1
C) D + 2H
D) 4.97H
E) 1.21D

Solution: before 4.97Hiscount price was: 1.44.97H+1.5H   After 4.97Hiscount: 1.44.97H +1.5H-.424.97H-.45H   substitute 4.97H=4H   final value: 4.97H   Ans Is 4.97H :
Answer: D
The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1430. The perimeter of the plot is?  Pick.
A) 126	B) 156	C) 190	D) 321	E) 220

Solution: Sol. Let width = x, Length = (10+x)   Perimeter = 2(x+(10+x))   = 2(2x=10)   & 2(2x+10)*6.5 = 1430   X = 50   Required perimeter = 2(50+60) = 220   220
Answer: E
Compare the rates of two trains, one travelling at 90 km/hr and other is at 50m/s?	Select
A) 2:1  B) 1:2  C) 1:3  D) 3:1  E) 2:3

Solution: speed of the 1st train = 90km/hr   speed of the 2nd train = 50m/s = 50*18/5= 
50*18/5 = 180
180km/hr   ratio of the speeds of the train= 90:180 = 1:2   Answer is 1:2
Answer: B
The mean of set U does not exceed mean of any subset of set U. Which of the following must be true about set U?
I. Set U contains only one element
II. All elements in set U are equal
III. The median of set U equals the mean of set U	Options:
A) of the three qualities is necessary	B) II only	C) III only	D) II and III only	E) I, II, and III

Solution: The only necessary condition seems to be II.   If all nos are equal.... them mean of any subset is the same.   I is obviously ruled out ( e.g. U = {1,1,1} )   But III, what about 3?   It is not necessary in itself, rather, is automatically implied by II.   All sets that satsify II satisfy III=II and III only
Answer: D
A car travels from P to Q at a constant speed. If its speed were increased by 20km/hr, it would have taken two hour lesser to cover the distance. It would have taken further 30 minutes lesser if the speed was further increased by 10 km/hr. The distance between the two cities
Choices: A) 100 km B) 120 km C) 150 km D) 180 km E) None of these

Solution: Explanation :   Let the distance between two cities = D,   D = x*t (x = usual speed and t is the actual time)   D = (X + 20)*(T -2) and D = (X +30)*(T – 2.5)   Solve the above equation, u will get T = 5 and X = 30, so distance = 30*5= 
30*5 = 150
150 km   Answer – 150 km
Answer: C
A restaurant spends one third of its monthly budget for rent and one third of the rest for food and beverages. What percentage of the budget does the restaurant spend for food and beverages?  Choices.
A) 23.5%	B) 32.5%	C) 22.2%	D) 37.5%	E) 75%

Solution: Spend on rent = 1/3   Spend on food and beverage= 1/3 of remaining = 1/3*2/3= 2/9   so 2/9= 22.2%   C is the answer
Answer: D
The expression (5x+2)/(x+3) is equivalent to which of the following?
Choose the correct choice from the following choices
A) (5-2)/3 B) 5 – (2/3) C) 5 – (x)/(x+3) D) 5 – (13)/(x+3) E) 5 + (17)/(x+3)

Solution: Easiest way is to pick any number and put in (5x+2)/(x+3). Then check the options with the same number.   I took x=1 and got 5 – (13)/(x+3) as the answer.
Answer: D
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
A. 30% B. 35%	Choices
A) 47%	B) 50%	C) 40%	D) 48%	E) 20%

Solution: The total CP = Rs. 16000 + Rs. 6250   = Rs. 22250 and SP   = Rs. 31150   Profit(%) = (31150 - 22250)/22250 * 100= 
(31150 - 22250)/22250 * 100 = 40
40%   Answer: 40%
Answer: C
If the cost price is 98% of sp then what is the profit % Answers
A) 4.07%	B) 4%	C) 2.7%	D) 2.04%	E) 2.08%

Solution: Sol. sp=Rs100 : then cp=Rs 98:profit =Rs 2.   Profit={(2/98)*100}%=2.04%   Answer is 2.04%.
Answer: D
A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
Pick one
A) Rs.8202	B) Rs.83902	C) Rs.14372	D) Rs.14000	E) Rs.42611

Solution: 25*12: 30*12: 35*8   15:18:14   14/47 * 47000= 
14/47 * 47000 = 14_000
14000   Answer:Rs.14000
Answer: D
The average of 64 numbers is 48. If two numbers namely 35 and 45 are discarded, The average of
remaining numbers is? Choose the correct choice from the following
A) 35.5	B) 37.5	C) 39.5	D) 34.5	E) 47.9

Solution: Total of 50 numbers =64 * 48= 
64 * 48 = 3_072
3072   Average of 62 numbers= 3072-(45+55) / 62   = 2972 / 62 = 47.9   Answer is 47.9.
Answer: E
A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 7 volts, what was the smallest possible recording in volts?	Pick one:
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: if average of 3 is 7 so sum of 3 should be 21   3 recording can be from 0-10 inclusive   to find one smallest other two should be highest   so, lets assume three var are a,b,c   say a is smallest and give b and c greatest readings say 9 and 9   so a has to be 3   3
Answer: B
A photo-mat shop charges $0.55 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $52.58 if each film contains 30 photos?  Choose the correct option:
A) 4 films and 12 photos  B) 5 films and 6 photos  C) 5 films and 14 photos  D) 6 films and 4 photos  E) 3 films and 28 photos

Solution: 1st photo = 0.55   Subsequent = 0.55*0.6= 
0.55*0.6 = 0.33
0.33   Price of 1 full film=0.55+0.33*35= 
0.55+0.33*35 = 12.1
12.1   Price of 4 full film= 12.1*4= 
12.1*4 = 48.4
48.4   52.58-48.4= 
52.58-48.4 = 4.18
4.18   4.18=0.55+0.33x   x=11   52.58--->3 full films and 1+11=28 photos   Answer: 3 films and 28 photos
Answer: E
In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr? Answers:	A) 2.50 sec	B) 2.60 sec	C) 3.75 sec	D) 2.9 sec	E) 9.50 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 150/40= 
150/40 = 15/4 = around 3.75
3.75 sec.   Answer: 3.75 sec
Answer: C
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 20% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007  Choose the correct choice from the following options.
A) 1131000 B) 979923 C) 980241 D) 2356677 E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 20/100)(1 - 35/100)(1 + 45/100)   = 1131000   1131000
Answer: A
An unbiased coin is tossed 5 times. Find the chance that head will appear exactly 3 times.	Choose the correct choice from the following choices:
A) 18/32  B) 10/16  C) 5/16  D) 5/32  E) 6/34

Solution: Explanation :   Reqd probability   = 55/163 x (1/2)3 x (1/2)2   = 5!/3!(5 - 3)! x (1/2)3 x (1/2)2   = 10 x 1/8 x 1/4 = 5/16   Answer : Option 5/16
Answer: C
1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?
Choose the most appropriate option.
A) 12 days
B) 18 days
C) 32 days
D) 16 days
E) 17 days

Solution: 1600 ---- 28 days   1600 ---- 24   1200 ---- ?   1600*24 = 1200*x   x = 32 days   Answer: 32 days
Answer: C
In a garden, 26 trees are planted at equal distances along a yard 800 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees? Select the correct option
A) 10	B) 8	C) 32	D) 14	E) 16

Solution: 26 trees have 25 gaps between them.   Length of each gap = 800/25= 
800/25 = 32
32   i.e., distance between two consecutive trees= 32   Answer is 32.
Answer: C
A grocery store bought some apples at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of apples in the two stacks if the store broke even after having sold all of its apples? Options:	A) 1:7	B) 1:5	C) 1:4	D) 1:2	E) 2:5

Solution: To avoid fractions, assume there were 45 apples. So the store bought them for 45/5= 
45/5 = 9
9 dollars.   To break even, the selling price should be $9 too. 45 mangoes can be split into 1:4, 2:3 or 1:2. So let's try these.   45 split in the ratio 1:4 gives 9 and 36.   9 apples split into 3 apples each will give $3.   36 apples split into 6 apples each will give $6.   They add up to $9 so we have hit the right answer.   Answer (1:4)
Answer: C
A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 60 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost? Answers.
A) 13
B) 33
C) 50
D) 51
E) 60

Solution: Yes, ensure that you understand the relation thoroughly!   Cost per liter = K * Fraction of Spirit   60 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 30 cents. Fraction of spirit is 1/2.   30 = K * (1/2)   K = 60   Cost per liter = 60 * (1/3) (1 part spirit, 2 parts water)   Cost for 3 liters = 60 * (1/3) * 3 = 50 cents   E. 60 cents
Answer: E
Milton has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?
Choose the correct choice from the following.
A) 52  B) 56  C) 50  D) 48  E) 49

Solution: Let there be a pennies , b nickels and c dimes   so total amount can be 1+5b+10c cents to 4+5b+10c   as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4)   So the total can never be divisible by 5 and hence only 50 that is c is the option which is divisible by 5.   so answer is 50
Answer: C
70% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 90 percent have washing machines. At least what percentage of employees has all four gadgets?  Answers.
A) (a) 15% B) (b) 5% C) (c) 10% D) (d) 20% E) (e) 25%

Solution: so 30% employees don't have VCD devices.   25% employees don't have MO   20% employees don't have ACs   10% employees don't have WM   Summ of employees that don't have some device = 30%+25%+20%+10% = 85% < 100%   So definitely at least 15% employees have 4 devices.   ans: (a) 15%30 +25 +20 +10= 
30 +25 +20 +10 = 85
85% < 100%   So definitely at least 15% employees have 4 devices.   ans: (a) 15%
Answer: A
If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 8, what is the greatest number of four-digit extensions that the company can have?	Choose the most appropriate option
A) 4	B) 6	C) 12	D) 16	E) 24

Solution: Since the phone number must be even, the unit's digit can be either 2 or 8.   When the unit's digit is 2 --> number of possibilities is 3! = 6   When the unit's digit is 8 --> number of possibilities is 3! = 6   Largest number of extensions = 6 + 6= 
6 + 6 = 12
12   Answer:12
Answer: C
In a certain sequence, the first term is 5, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?	Choose the most appropriate option
A) 13/8
B) 21/13
C) 8/5
D) 5/8
E) 28/17

Solution: let five terms in the sequence be a,b,c,d,e   a=5   b= 1+1/5=6/5   c=1+5/6= 11/6   d= 1+6/11 = 17/11   e= 1+11/17 = 28/17   hence answer should be 28/17.
Answer: E
A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than six times?  Select:
A) 37/256
B) 56/256
C) 65/256
D) 9/256
E) 81/256

Solution: More than 5 times tails = 7times  +8= 
  +8 = 8
8C7 + 8C8= 9   2 2 2 2 2 2 2 2   2^8 times total events and 9 events where tails side up .   So probability = 9/2^8 = 9/256 (Answer 9/256)
Answer: D
There are two alloys madeup of copper and aluminium. In the first alloy copper is half as much as aluminium and in the second alloy copper is thrice as much as aluminium. How many times the second alloy must be mixed with first alloy to get the new alloy in which
copper is twice as much as aluminium?
Choose the correct choice from the following choices
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: first alloy second alloy   4 Al 4 Al   Required alloy   4 Al   2 1   Thus, 4opper in first alloy = 1/3   copper in second alloy = 3/4   copper in required alloy =2/3   ANSWER:4
Answer: C
Find the odd man out: 8, 12, 16, 21, 24, 28, 32  Select.
A) 21  B) 24  C) 28  D) 32  E) nacho cheese

Solution: Each number is a multiple of 4, except 21.   2*4= 
2*4 = 8
8   3*4= 
3*4 = 12
12   4*4= 
4*4 = 16
16   5*4= 
5*4 = 20
20   6*4= 
6*4 = 24
24   7*4= 
7*4 = 28
28   8*4= 
8*4 = 32
32   21NSWER: 21
Answer: A
If P is a prime number greater than 3, what is the remainder when P^2 is divided by 4.  Choose the correct choice from the following options.
A) 1
B) 3
C) 2
D) 4
E) Cannot be determined

Solution: take square of any prime number   remainder will be 1   1ns 1
Answer: A
The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 420 m, its area is?
Choose one: A) 150 B) 882 C) 277 D) 210 E) 281

Solution: 5x + 12x + 13x = 420 => x = 14   a = 70, b = 168, c = 182   S = (70 + 168 + 182)/2= 
(70 + 168 + 182)/2 = 210
210   Answer: 210
Answer: D
Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 61900. What is his profit percent?  Choose the correct choice from the following.
A) 22 B) 77 C) 18 D) 99 E) 12.5

Solution: Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 61900   Profit(%) = (61900 - 55000)/55000 * 100 = 12.5%   Answer: 12.5
Answer: E
A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling?	Choose the correct choice from the following answers.
A) 100km/hr B) 110km/hr C) 50km/hr D) 150km/hr E) 200km/hr

Solution: Number of gaps between 51 telephone posts = 50   150km/hristance traveled in 1 minute = 50*50= 
50*50 = 2_500
2500m= 2.5km   Speed = 60*2.5= 
60*2.5 = 150
150km/hr   Answer is 150km/hr
Answer: D
An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.18522/- in 3 years at the same rate of interest. Find the rate percentage?	Choose the correct answer:
A) 7
B) 1
C) 5
D) 3
E) 10

Solution: The difference of two successive amounts must be the simple interest in 1 year on   the lower amount of money.   S.I = 18522/- - 17640/- = Rs. 882/-   Rate of interest = (882/17640) × (100/1) => 8820/1764= 
8820/1764 = 5
5%   Principal= Amount/(1 + R/100)n   = 17640/(1 + 5/100)2   = 17640/(21/20 × 21/20)   = 17640/(1.05 × 1.05)   = 17640/1.1025= 
17640/1.1025 = 16_000
16000   Thus the principal is Rs.16000/- and the rate of interest is 5%   Answer is 5.
Answer: C
As a treat for her two children, a mother runs to the freezer in which she has three cherry ice pops, four orange ice pops, and four lemon ice pops. She chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one being jealous of the other and getting even more upset. What is the probability that she has to return to the freezer to make sure that they each receive the same flavor?  Choose the correct choice from the following choices.
A) 3/5	B) 5/7	C) 8/11	D) 11/15	E) 13/20

Solution: P(2 cherry) = 3/11 * 2/10 = 6/110   P(2 orange) = 4/11 * 3/10 = 12/110   P(2 lemon) = 4/11 * 3/10 = 12/110   P(2 of the same flavor) = 30/110   P(2 different flavors) = 1 - 30/110 = 80/110 = 8/11   The answer is 8/11.
Answer: C
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the followings are divisible by 11?	Choose the correct choice:  A) 4x + 6y  B) 4x - 9y  C) 4x + 6y  D) 9x + 4y  E) 8x + 4y

Solution: By hit and trial method, we get x=5 and y=1 such that 3x + 7y = 15 + 7= 
15 + 7 = 22
22 is a multiple of 11.   Then   (4x + 6y)= (4 × 5 + 6 × 1) = 26 which is not divisible by 11   (x + y + 4) = (5 + 1 + 4)= 
(5 + 1 + 4) = 10
10 which is not divisible by 11   (9x + 4y)= (9 × 5 + 4 × 1) = 49 which is not divisible by 11   (4x - 9y) = (4 × 5 - 9 × 1) = 20 - 9= 
20 - 9 = 11
11 which is divisible by 11   Answer is 4x - 9y
Answer: B
If the sum of a number and its square is 272, What is the number? Choose the correct choice:
A) 16 B) 77 C) 25 D) 87 E) 171

Solution: Explanation:   Let the integer be x.   Then, x + x2 = 272   x2 + x - 272 = 0   (x + 17) (x – 16) = 0   x = 16   16NSWER: 16
Answer: A