MU-NLPC/Calc-aqua_rat huggingface dataset:
Between 1800 and 1850 a population of a country increased from 12 million to 15 million. Between 1850 and 1900 its population increased from 15 million to 22 million. By what percent did the rate of population growth increase from the period 1800-1850 to the period 1850-1900?  Select the correct option:
A) 75%-100%
B) 101%-125%
C) 126%-150%
D) 151%-175%
E) 176%-200%

Solution: Solution:   This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.   We first set up the ratios of population growth to initial population for the two periods. The first ratio will be for the period 1800-1850, and the second ratio will be for the period 1850-1900. Because the populations are in millions, we do not have to express all the trailing zeros in our ratios.   1800-1850   growth/initial population = 3/12 = 1/4   1850-1900   growth/initial population = 7/15   Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percents.   1800-1850   growth/initial population = (1/4) x 60 = 15   1850-1900   growth/initial population = (7/15) x 60 = 28   We can plug 15 and 28 into our percent change formula:   (new – old)/old x 100   [(28 – 15)/15] x 100   13/15 x 100   At this point we can stop and consider the answer choices. 13/15 x 100 is greater than 75% but less than 100%.   75%-100%nswer 75%-100%.
Answer: A
Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6 Pick one
A) 3/18  B) 5/18  C) 18/7  D) 18/5  E) 7/18

Solution: Clearly n(S)=6*6= 
6*6 = 36
36   Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then   E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),   (6,6)}   n(E)=14.   Hence p(e)=n(e)/n(s)=14/36=7/18   Option: 7/18
Answer: E
Sam invested Rs. 8000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?  Choose the correct choice from the following answers.
A) 3200.0  B) 11520.0  C) 8820.0  D) 7354.0  E) 16537.11

Solution: P = Rs. 8000 ; R = 10% p.a. = 5% per half-year; T = 1 year   = 2 half-year   Amount = [8000 * (1 + 5/100)2]   = (8000 * 21/20 * 21/20)   = Rs.8820.00   Answer:8820.0
Answer: C
The value of x is to be randomly selected from the integers from 1 to 7, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative?
Select
A) 1/5
B) 2/7
C) 1/7
D) 3/7
E) 7/10

Solution: y will only be negative for x=2.   (We can check the values from 1 to 7 to be certain.)   P(y is negative) = 1/7   The answer is 1/7.
Answer: C
Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
Choose the correct choice from the following:
A) 333
B) 383
C) 402
D) 433
E) 483

Solution: Let say she pays $X per month.   interest for month 1 = 1000*10/100= 
1000*10/100 = 100
100   interest for month 2= (1000+100 -X)*10/100   = (1100 - X)*10/100   = 110 - X/10   interest for month 3 = (1100 -X + 110 - X/10 - X)*10/100   = 121 - 21/100 X   Total interest = 3X-1000   So 3X-1000 = 100 + 110 - X/10 + 121 - 21/100 X   =>331X = 133100   =>X = 402.11   ANSWER:402
Answer: C
In an xy-coordinate plane, a line is defined by y = kx + 1. If (2, b), (a, 4), and (a, b+1) are three points on the line, where a and b are unknown, then k = ? Choose the correct choice from the following choices
A) 1/2  B) 1  C) 3/2  D) 2  E) 5/2

Solution: b=2k+1...(1)   b+1=ak+1...(2)   4=ak+1...(3)   Taking (2) and (3)   4=b+1   b=3   Taking (1)   3=2k+1   k=1   Answer : 1
Answer: B
A person can row at 9 kmph and still water. He takes 3 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Choose the most appropriate option
A) 16 km B) 87 km C) 89 km D) 67 km E) 20 km

Solution: Let the distance between A and B be x km.   Total time = x/(9 + 1) + x/(9 - 1) = 3.5   => x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x   = 16 km.   16 kmnswer:16 km
Answer: A
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?  Select:
A) 45 B) 49 C) 20 D) 82 E) 13

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20   Answer:20
Answer: C
In a shop X number of kinds of fruits are there and 40 number of kinds of vegetables are there, then 1% of vegetable is equal to 20% of fruits then how many kinds of fruits are there Choose the correct choice from the following answers:	A) 20	B) 35	C) 70	D) 90	E) 1,40

Solution: 1/100(400) = 2/10(x)   X = 20..   Option 20.
Answer: A
The width of a rectangular hall is ½ of its length. If the area of the hall is 200 sq.m, what is the difference between its length and breadth?  Choose the correct choice from the following answers
A) 8m B) 10m C) 12m D) 15m E) 17m

Solution: Let the length of the hall be x m   10mreadth of the hall = 1x/2 m   Area of the hall = Length * 10mreadth   200 = x * 1x/2   x² = 400   x =20   Difference between the length and breadth of the hall = x - 1x/2 = x/2   =20/2= 
20/2 = 10
10m   ANSWER:10m
Answer: B
A chemical lab is scheduled to go through two air ventilation systems, a basic system and a more advanced system that takes forty minutes and 1.5 hours respectively to fully ventilate the room. If both ventilation systems were to operate at the same time with their respective constant rates, how many hours would it take to fully ventilate the chemical lab? Pick one: A) 2/7 B) 3/10 C) 5/11 D) 6/13 E) 7/15

Solution: The rate of the basic system is 1 room/ (2/3 of an hour) = 3/2 rooms per hour   The rate of the advanced system is 1/1.5 = 2/3 of a room per hour   The combined rate is 13/6 rooms per hour.   The time to ventilate one room is 6/13 of an hour.   The answer is 6/13.
Answer: D
If n is an integer and 102n^2 is less than or equal to 8100, what is the greatest possible value of n?
Choose the correct option.
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: 102 * n^2 <=8100   n^2 <=8100/102 which will be less than 81 since  8100/100= 
 8100/100 = 81
81 which is the square of 9   Next closest value of n where n^2<=81 is 8   Ans 8
Answer: B
A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 23 gallons of gasoline?	Options:
A) 190
B) 284.6
C) 300
D) 280
E) 312

Solution: so 12.2 * 23 = 280..   IMO option 280 is correct answer..
Answer: D
Vasya wrote down several consecutive integers. Which of the following could not be the percentage of even numbers among them?
Choose one:
A) 40
B) 45
C) 48
D) 50
E) 60

Solution: what you have to check is if the (answer given: 100-answer given) is either equal or two consecutive values..   reason for this is that there are only three possiblities of numbers of odd numbers in consecutive integers   1) equal to number of even numbers   2)one more than number of even numbers   3)one more than number of even numbers   (40) 40:60=2:3possible   (B) 45:55=9:11not possible   (C) 48:52=12:13possible   (D) 50:50=1:1possible   (E) 60:40=3:2possible   ans 40
Answer: A
Jar X is 1/4 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity? Pick one.
A) 2/5	B) 1/4	C) 1/3	D) 1/2	E) 2/3

Solution: Let P be the capacity of Jar X.   The amount of water in Jar Y is 1/2*P/2=P/4   Then the total amount in Jar X is P/4+P/4=P/2   The answer is 1/2.
Answer: D
Two goods trains each 2000 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	Choose the most appropriate option:
A) 228
B) 278
C) 192
D) 27
E) 21

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 2000 + 2000= 
2000 + 2000 = 4_000
4000 m.   Required time= 4000 * 6/125= 
4000 * 6/125 = 192
192 sec.   Answer:192
Answer: C
If r and t are positive integers, rt + r + t cannot be Choose the correct choice from the following answers
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: Let rt + t + r = x   Add 1 on both sides:   rt + t + r + 1 = x + 1   t(r + 1) + r + 1 = x + 1   (r + 1)(t + 1) = x + 1   Minimum value of (r + 1) = 2   Minimum value of (t + 1) = 2   Hence x + 1 cannot be prime   Substitute x from the given options:   6 + 1= 
  6 + 1 = 7
7 --> prime --> rt + t + r cannot be 6   Answer: 6
Answer: B
A certain ski shop sells pairs of gloves in 10 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?
Choose the correct choice from the following:
A) 1/144
B) 1/143
C) 1/24
D) 1/23
E) 1/19

Solution: there are 10 different colours sothere are 10 pairs of gloves dropped..   first can be any of 20..so 20/20..   second has to be its pair, which will be just one out of remaining 19.. 1/19..   overall prob=20/20*1/19= 1/19..   1/19
Answer: E
In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 3 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed? Choices.
A) 23,400 B) 60,840 C) 67,600 D) 608,400 E) 676,000

Solution: Two alphabets, 3 digits.   Ways of selecting 3 digits = 10X10X10 = 1000   Ways of selecting two alphabets = 26X26   In total total ways of selecting 5 vacancies = 676000   ANSW676,000R:676,000
Answer: E
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?  Choose the correct choice from the following answers:
A) 5760 lr B) 6000 lr C) 6500 lr D) 4000 lr E) 4500 lr

Solution: 1/x - 1/6 = -1/8   x = 24 hrs    24 * 60 * 4= 
 24 * 60 * 4 = 5_760
5760   5760 lrNSWER 5760 lr
Answer: A
A person walking at a constant rate of 6 miles per hour is passed by a cyclist traveling in the same direction along the same path at 10 miles per hour. the cyclist stops to wait for the person 10 minutes after passing her, while the person continues to walk at her constant rate, how many minutes must the cyclist wait until the person catches up?
Choose one:
A) 15min
B) 11min
C) 20min
D) 40min
E) 1hour

Solution: After passing the person the cyclist travels for 10 minutes at a rate of 10 miles/hour.   In those 10 mins the cyclist travels a distance of 5/3 miles.   In those 10 mins the person travels a distance of 1 miles.   So the person still has to cover 2/3 miles to meet the waiting cyclist.   The person will need 1/9 hours or 11 mins to cover the remaining 2/3 miles.   The answer is 11min
Answer: B
A focus group is currently made up of x men and y women. If 3 men and 7 women are added to the group, and if one person is selected at random from the larger focus group, then what is the probability that a man is selected?
Choose the correct choice from the following choices: A) x/(x + 7) B) x/(x + y) C) (y + 3)/(x + y + 7) D) (y + 4)/(x + y + 10) E) (x + 3)/(x + y + 10)

Solution: x men   y women   x+3+y+7 is the total   =x+y+10   x+3 is the number of men   so (x + 3)/(x + y + 10)   E. (x + 3)/(x + y + 10)
Answer: E
A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 35 grams of protein daily, how many grams of food X are in the mixture.	Choose the correct option: A) 100 B) 140 C) 150 D) 160 E) 200

Solution: Let x be the amount of food X.   0.1x + 0.15(300-x) = 35   0.05x = 10   x = 200   The answer is 200.
Answer: E
In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? Options
A) 80% B) 70% C) 60% D) 50% E) 40%

Solution: Explanation:   Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420   New C.P. = 125% of Rs. 100 = Rs. 125.   New S.P. = Rs. 420   Profit = 420 - 125 = Rs. 295   Required percentage = 295/420 * 100 = 1475/21 = 70%   Answer: 70%
Answer: B
Look at this series: 28, 25, 30, 27, 32, 29, ... What number should come next? Choose the correct choice from the following answers: A) 32 B) 34 C) 30 D) 31 E) 36

Solution: Explanation:   In this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on.   Answer: Option 34
Answer: B
If the area of a circle is 81pi square feet, find its circumference. Select.
A) 48  B) 38  C) 51  D) 92  E) 18

Solution: The area is given by pi   pi × r × r = 81 pi   r × r = 81 ; hence r = 81 feet   The circumference is given by   2 × pi × r = 2 × pi × 9 = 18 pi feet   correct answer is 18) 18
Answer: E
On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on october 1 than were in stock on January 1?  Answers
A) 8 B) 12 C) 20 D) 32 E) 36

Solution: Jan 1 = C   Feb 1 = C - 4   March 1 = C - 8   April 1 = C - 12   May 1 = C - 16   June 1 = C - 20   July 1 = C - 24   Aug 1 = C - 28   Sept 1 = C - 32   Oct 1 = C - 36   Difference between stock on October 1 than were in stock on January 1 will be -   C - ( C - 36 )= 36   Hence answer will be (36)
Answer: E
0.35 represents what percent of 7? Pick one.
A) 0.05%
B) 0.5%
C) 5%
D) 500%
E) 5000%

Solution: One more method   0.35 represents what percent of 7?   Divide by 7   0.05 represents what percent of 1?   Answer = 0.05*100= 
0.05*100 = 5
5%= 5%
Answer: C
How many integers between 5000 and 6000 that have distinct digits and increase from left to right ?  Choose the correct choice from the following choices
A) 10	B) 48	C) 60	D) 20	E) 600

Solution: Since the numbers must be distinct and increasing from left to right,   The only arrangements we could come-up with are:   545_ --> 4   546_ --> 3   547_ --> 2   548_ --> 1   556_ --> 3   557_ --> 2   558_ --> 1   567_ --> 2   568_ --> 1   578_ --> 1   Number of integers =20   20
Answer: D
3 and 9 are the first two terms in a geometric sequence. What is the arithmetic difference between the 7th term and the 5th term?
Pick
A) 3*3^2	B) 3* 3^13 - 5 * 3^11	C) 3^13	D) 8 * 3^6	E) 3^12 - 3^10

Solution: Common ratio = 9/3= 
9/3 = 3
3   7th term= 3*3^7   5th term = 3*3^5   Difference = 3 * (3^7 - 3^5) = 3 * 3^5 *(3^2 - 1)   = 3 * 3^5 * 8   = 8 * 3^6....   8 * 3^6
Answer: D
How many positive integers t less than 30 have no common prime factor with 30?
Choose one:
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: t=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.   This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.   Answer: 8.
Answer: D
An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.  Choose the correct choice from the following options.
A) 4 : 3 B) 8 : 7 C) 4 : 1 D) 6 : 5 E) None of these

Solution: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.   Let the dimensions of the carpet in the second case be 7y, 3y units respectively.   From the data,.   2(3x + 2x) = 2(7y + 3y)   => 5x = 10y   => x = 2y   Required ratio of the areas of the carpet in both the cases   = 3x * 2x : 7y : 3y   = 6x2 : 21y2   = 6 * (2y)2 : 21y2   = 6 * 4y2 : 21y2   = 8 : 7   ANSWER:8 : 7
Answer: B
There were totally 100 men.83 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married? Choose the correct choice from the following options:
A) 11 B) 12 C) 13 D) 14 E) 15

Solution: 100-(100-83)-(100-75)-(100-85)-(100-70)   = 100-17-25-15-30=100-87= 
100-87 = 13
13   ANSWER:13
Answer: C
There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field. If 2 rocks are to be chosen at random and without replacement, what is the probability that both rocks will be slate rocks?	Pick:
A) 1/3  B) 7/22  C) 1/9  D) 7/66  E) 2/45

Solution: Total No of Rocks = 45   Probability of choosing 1st Slate Rock = 15/45   Probability of choosing 2nd Slate Rock = 14/44 (Without replacement)   So combined probability = 15/45*14/44 = 7/66   So, ANSWER 7/66.
Answer: D
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?	Choose the correct choice
A) 350  B) 288  C) 277  D) 2912  E) 321

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x = 350 m.Answer: 288
Answer: B
A boy has six trousers and 9 shirts. In how many different ways can he select a trouser and a shirt?
Pick:
A) 186 ways	B) 78 ways	C) 56 ways	D) 54 ways	E) 189 ways

Solution: The boy can select one trouser in six ways.   The boy can select one shirt in 9 ways.   The number of ways in which he can select one trouser and one shirt is   6 * 9= 
  6 * 9 = 54
54 ways.   Answer:54 ways
Answer: D
A baseball player hit the following number of home runs in consecutive years: 35, 38, 39, 43, and 44. If the player had hit 3 additional home runs in the last year, which of the following statements best describes the change in the mean and the median of the home runs?
Choose the correct choice from the following answers:  A) The mean and the median will remain unchanged.  B) The mean will remain unchanged but the median will increase.  C) The mean will increase but the median will remain unchanged.  D) The mean and the median will increase by the same amount.  E) The mean and the median will increase by different amounts.

Solution: Old set = {35, 38, 39, 43, 44}.   New set = {35, 38, 39, 43, 47} --> the median (middle term) will remain the same and the mean will increase.   Answer: The mean will increase but the median will remain unchanged..
Answer: C
The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 76. Find their present ages.	Choose the correct choice from the following answers:
A) 20,35,45
B) 8,20,28
C) 16,28,36
D) 16,28,46
E) None of these

Solution: Let the present ages of three persons be 4K,7K and 9K respectively.   (4K - 8) + (7K - 8) + (9K - 8) = 76   20K = 100   K = 5   Therefore, then present ages are 20,35,45.   20,35,45NSWER:20,35,45
Answer: A
Bipin is 6 times old as Alok. Bipin's age will be twice of Chandan's age after 10 years. If Chandan's 7th birthday was celebrated 3 years ago, what is Alok's present age ?
Choose the correct choice from the following answers.
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: let the present ages of bipin, alok, chandan are b,a,c respectively   given conditions are   1)b=6a   2)(b+10)=2*(c+10)   3)chandans present age=c=10 years   therefore b=30   so a=5   ANSWER:5
Answer: D
At a school, three-fifths of the male students and two-thirds of the female students speak a foreign language. If the number of males is two-thirds the number of females, what fraction of the students speak a foreign language?  Choose the correct choice from the following answers
A) 11/25	B) 14/25	C) 16/25	D) 18/25	E) 21/25

Solution: Let x be the number of students in the school.   The number of males who speak a foreign language is (3/5)(2/5)x = (6/25)x   The number of females who speak a foreign language is (2/3)(3/5)x = (2/5)x   The total number of students who speak a foreign language is (6/25)x + (2/5)x = (16/25)x   The answer is 16/25.
Answer: C
The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?  Options:
A) 3
B) 7
C) 8
D) 6
E) 2

Solution: S = (1 + 2 + 3)/2= 
(1 + 2 + 3)/2 = 3
3   3nswer:3
Answer: A
The sum of the two numbers is 16 and their product is 35. What is the sum of the reciprocals of these numbers? Select the correct option.
A) 16/35  B) 1/35  C) 35/8  D) 7/32  E) None of these

Solution: Let the numbers be a and b. Then, a+b=16 and ab =35.   a+b/ab=16/35; (1/b+1/a)=16/35   Sum of reciprocals of given numbers=16/35.   Correct Option: 16/35
Answer: A
Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is?	Choose the most appropriate option.
A) 33
B) 76
C) 85
D) 22
E) 99

Solution: Since the numbers are co-prime, they contain only 1 as the common factor.   Also, the given two products have the middle number in common.   So, middle number = H.C.F of 551 and 1073 = 29;   First number = 551/29= 
551/29 = 19
19   Third number= 1073/29= 
1073/29 = 37
37.   Required sum= 19 + 29 + 37= 
19 + 29 + 37 = 85
85.   Answer:85
Answer: C
In a certain circle there are 10 points. What is the number of the triangles connecting 5 points of the 10 points?  Choose one:
A) 80
B) 96
C) 108
D) 120
E) 252

Solution: IMO : E   HERE we have to select 5 points out of 10 points. Order is not important   So the answer will be 10c5 = 252   Answer 252
Answer: E
In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 110?
Options:
A) 35
B) 77
C) 25
D) 18
E) 12

Solution: A scores 60 while B score 40 and C scores 30.   The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3= 
25 * 3 = 75
75.   In a game of 100 points, B gives (110 - 75)= 
(110 - 75) = 35
35 points to C.   35nswer:35
Answer: A
If the price of 23 balls is 276, then what will the price of 12 balls? Pick one.
A) 144
B) 148
C) 156
D) 186
E) None of these

Solution: Explanation :   Less balls, Less Price (Direct Proportion)   So, let the price be Rs. x   then,   23:12::276:x   =>x=276*12/23   =>x=144   So price of 12 balls will be Rs. 144   144nswer : 144
Answer: A
As a treat for her two children, a mother runs to the freezer in which she has three cherry ice pops, three 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
A) 2/5  B) 3/7  C) 7/12  D) 11/15  E) 17/25

Solution: P(2 cherry) = 3/10 * 2/9 = 6/90   P(2 orange) = 3/10 * 2/9 = 6/90   P(2 lemon) = 4/10 * 3/9 = 12/90   P(2 of the same flavor) = 24/90   P(2 different flavors) = 1 - 24/90 = 66/90 = 11/15   The answer is 11/15.
Answer: D
which one is odd?
4377
3954
9862
8454
9831	Choose the correct choice from the following choices:
A) 4377 B) 3954 C) 9862 D) 8454 E) None

Solution: 9862orrect Answer : 9862   sum of digit of all other number is 21, but sum of digit of 9862 is 25
Answer: C
In a box of 8 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?
Choose the correct choice from the following choices
A) 1/12	B) 5/14	C) 2/13	D) 2/15	E) 1/17

Solution: First, there are 6C3 ways you can select 3 good pencils from 4 good ones.   Second, there are 8C3 ways you select 3 pencils from 6 ones in the box.   Then, the probability that neither pen will be defective is: 6C3/8C3=20/56 = 5/14   Answer is 5/14
Answer: B