Math DAT

A farmer redistributes his cows among three pastures. The first has 10 cows less than half of the total, the second has 8 cows less than one third the total, and the third has 6 less than one fourth the total. How many cows does he have? A. 58 B. 80 C. 166 D. 254 E. 288

288

If a series of 10 bits (each of which can be either 0 or 1) form a password, what is the total number of different passwords? A. 45 B. 100 C. 90 D. 1024 E. 512

2^n = 2^10 = 1024

Which of the following is the closest to the standard deviation of the following data set? {10, 13, 19, 14, 16} A. 0.03 B. 0.3 C. 3 D. 30 E. 300

3

Three dice are rolled. What is the probability of getting all even numbers? A. 1/216 B. 1/108 C. 1/72 D. 1/36 E. 1/8

(1/2)(1/2)(1/2) = 1/8

A die is rolled three times. What is the probability of getting, in order, an even number, a 6, and then a 5? A. 1/216 B. 1/72 C. 1/36 D. 1/9 E. 1/4

(1/2)(1/6)(1/6) = 1/72

. A standard deck of 52 cards contains 13 cards each from the four suits: spades, clubs, diamonds and hearts. If three cards are RANDOMLY picked WITHOUT replacement, what is the probability that they are ALL from the same suit?

(13/52)(12/51)(11/50)(4)

A bicyclist cycles 30 miles at 10 miles an hour, and cycles another 10 miles at 20 miles an hour. What is the bicyclist's approximate average speed for the whole trip? A. 10 miles per hour B. 11.4 miles per hour C. 14.3 miles per hour D. 17.2 miles per hour E. 20 miles per hour

(30/10) + (10/20) = 3.5 40/3.5 = B

Larry has 6 shirts and 4 pairs of jeans. How many different combinations of one shirt and one pair of jeans can Larry make? A. 2 B. 4 C. 6 D. 12 E. 24

(6)(4) = 24

In Gainesville, one in four people have blonde hair. What is the chance that if four people are chosen at random from Gainesville, at least one person has blonde hair? A. 1/256 B. 81/256 C. 175/256 D. 255/256 E. 1

1 - (3/4)(3/4)(3/4)

A soda bottle can be filled completely by a faucet in 10 seconds. The bottle also has a hole that can drain the full soda bottle to empty in 30 seconds. If the bottle is initially empty when the faucet is turned on, how long will it take for the bottle to be fully filled? A. 10 seconds B. 12 seconds C. 15 seconds D. 20 seconds E. 30 seconds

1/10 - 1/30 = 1/x 15

What is the probability of 5 consecutive heads or 5 consecutive tails in five tosses of a fair coin? A. 1/32 B. 1/16 C. 1/8 D. 1/4 E. 1/2

1/16

What is the probability of pulling two cards from the same suit in a row, with each card coming from a separate 52 card deck? A. 4/13 B. 1/4 C. 1/8 D. 1/16 E. 1/32

1/16 multiple by 4 because of the 4 diff suits

A runner will participate in two race events: a ten yard dash and a 50 yard dash. The runner is rated as having a 50 percent probability of winning the ten yard dash and a 30 percent probability of winning the 50 yard dash. If the runner completes both events, what is the probability he wins EXACTLY ONE of the races? A. 1/4 B. 5/16 C. 1/3 D. 1/2 E. 7/12

1/2 (1/2)(7/10) + (1/2)(3/10)

Three fair coins are tossed at once. What is the probability that two or more come up heads? A. 1/8 B. 1/4 C. 1/2 D. 3/4 E. 7/8

1/2 2 x 2 x 2 = 8 outcomes 4/8 = 1/2

Three dice are rolled. What is the probability that all three dice come up with the same number? A. 1/216 B. 1/108 C. 1/72 D. 1/36 E. 1/2

1/36

If four fair coins are tossed, what is the probability that one of them comes up with heads while the other three come up with tails? A. 1/16 B. 1/8 C. 1/4 D. 1/2 E. 3/4

1/4

The manager of a mechanic shop notices that Julio can change a tire in 5 minutes while his twin brother Jaden takes 10 minutes. How much time would it take both brothers working simultaneously to change one tire if Julio only works 2 minutes per tire? A. 4 minutes B. 6 minutes C. 8 1/2 minutes D. 12 2/5 minutes E. 34 minutes

1/5 = .2 tire 1/10 = .1 tire 2(.2 ) + 2(.1) = 6/10 (0.4tire) (10) = 4 4+2

What is the probability that the outcomes of a fair six-sided die, with the numbers 1 to 6, rolled twice will add up to 5? A. 1/6 B. 1/9 C. 1/36 D. 1/11 E. 1/12

1/9 4 outcomes 6 x 6 4/36 = 1/9

oanna must choose 3 friends from a group of 5 to play a game with. How many different groups of 3 friends can she make? A. 1 B. 5 C. 10 D. 20 E. 50

10

A filled grain silo has three cracks. One crack allows 1/5th of the total volume through per day. The second crack allows 1/4th of the total volume through per day, and the final crack allows 1/2 of the total volume through per day. How many hours will it take for the silo to completely empty? A. 23 B. 24 C. 25 D. 26 E. 27

100 units of grain in the silo at the start of the day: The first crack lets 1/5th of the volume spill every day, which will allow 20 unit add the grains per hour = 100 =26

36. Tim invests $1000 in an account that accrues 12% interest per year, compounded quarterly. After 15 months, how much interest has Tim earned? A. $50 B. $160 C. $405 D. $574 E. $762

1000(1+ 0.03)^5

How many groups of 3 puppies can be picked from a group of 10 puppies? A. 60 B. 100 C. 120 D. 150 E. 170

120

How many ways can you choose 7 people from a group of 10? A. 70 B. 120 C. 140 D. 240 E. 300

120 order doesnt matter? combination

John can mow a lawn in 2 hours, and Matt can mow the same lawn in 3 hours. How long will it take for John and Matt to mow the lawn working together, but John only works for 24 minutes? A. 80 minutes B. 120 minutes C. 144 minutes D. 164 minutes E. 180 minutes

144 mins

20 chess masters attend a tournament. Each player will play a game with every other player exactly once during the tournament. How many games are played during the tournament? A. 20 B. 40 C. 190 D. 300 E. 380

190

Which of the following best represents the standard deviation of the data set {10, 12, 13, 14, 16}? A. 2 B. 2.4 C. 2.8 D. 3 E. 3.2

2

The median of a set of 5 consecutive integers is 9. What is the variance of the set? A. 1 B. 1.5 C. 2 D. 2.67 E. 3.5

2 Variance = 2^2 + 1 + 0 + 1 + 2^2 / 5

Two normal dice are rolled. What is the probability of getting a sum of 7 or 11? A. 1/36 B. 1/9 C. 2/9 D. 1/2 E. 3/4

2/9

How many distinct ways can 2 people sit in 5 chairs? A. 10 B. 20 C. 50 D. 60 E. 80

20 5!/ (5-2)! order matters

5 people are applying for the positions of president and treasurer. How many different ways can the two positions be filled if each position can only be filled by one person? A. 10 B. 20 C. 40 D. 60 E. 100

20 5! / (5-2)!

Two regular ten-sided dice are labeled with the numbers 1 to 10. If one ten-sided die has its even numbers painted blue, and another has its perfect squares painted blue, what is the probability that both dice will roll a blue number? A. 1/100 B. 1/20 C. 3/20 D. 1/4 E. 7/20

3/20

six passengers get onto a train that has two cars. If each passenger is equally likely to board any of the two cars, irrespective of the others, what is the probability that the first car contains just one passenger? A. 1/6 B. 1/64 C. 3/32 D. 1/30 E. 7/64

3/32 1st person boards and the last dont board x6 =6(1/2)^6

What is the solution set to the following equation: A. {3, 4} B. {-3, -4} C. {3, -4} D. {-3, 4} E. {4}

4

Four dice are rolled. What is the probability of getting exactly three "4's" and one "2" in any order? A. 1/1296 B. 4/1296 C. 1/216 D. 1/396 E. 1/200

4/1296 (1/6)^4 x 4

A bag is filled with 20 pieces of candy A and 10 pieces of candy B. If you choose 2 pieces of candy at random without replacement, what is the probability of picking one piece of candy of each type? A. 2/9 B. 20/87 C. 40/87 D. 30/87 E. 1/3

40/ 87 (2)(20/30)(10/29)

There are seven bridges connected to an island. How many different ways can some one enter the island on one bridge and leave on a different bridge? A. 7 B. 14 C. 25 D. 42 E. 49

42

. How many distinct ways can a person choose 2 different cards from a standard deck of 52 playing cards without replacement? A. 155 B. 1024 C. 2652 D. 2704 E. 5304

52 x 51

Ernest must make up a password for his account. The password must contain two distinct letters of the English alphabet, followed by 2 distinct digits chosen from the numbers 0-9. In how many ways can Ernest choose a password? A. 70 B. 7,072 C. 58,500 D. 85,680 E. 100,100

58500 26 x 25 10 x 9

How many different ways (orders) can you arrange 6 different playing cards? A. 6 B. 36 C. 720 D. 1296 E. 46656

6 x 5 x 4 x 3 x 2 x1 720

There are seven bridges connected to an island. How many different ways can some one enter the island on one bridge and leave on a different bridge? A. 7 B. 14 C. 25 D. 42 E. 49

7 x 6

A triangle has side lengths of 10, 24, and 26. A second triangle has side lengths of 7, 24, and 25. What is the ratio of the area of the smaller triangle to the area of the larger triangle? A. 10 : 7 B. 7 : 10 C. 15 : 26 D. 26 : 15 E. 13 : 15

7:10 5,12,13 (.5)(7)(24)/ (.5)(10)(24)

How many different nontraditional words can be formed by rearranging the letters of the word "IDENTITY"? A. 8!/4 B. 8!/2 C. 8! D. 28 E. 82

8!/4 because of repeat words

There are 5 red jellybeans and 7 green jellybeans in a jar. How many additional red jellybeans must be added to the jar such that the chance of randomly picking a red jellybean from the jar is 2/3? A. 9 B. 16 C. 20 D. 25 E. 32

9

A drawer contains 6 black socks and 8 grey socks. If you pick a sock at random, then pick another sock at random without replacing the first one, what is the chance that both socks are grey? A. 4/13 B. 8/14 C. 15/91 D. 64/91 E. 1/2

A

Four dice are rolled. What is the probability of getting exactly three "4's" and one "2" in any order? A. 1/1296 B. 4/1296 C. 1/216 D. 1/396 E. 1/200

B

If you have two spheres, one with diameter 3, and the other with diameter 9, what is the ratio of the volumes of the largest sphere to the smallest sphere? A. 4 B. 9 C. 27 D. 81 E. 100

C (9)^3/(3)^3 (3)^6/(3)^3

A z score of -1.94 corresponds to a p value of 0.0262. In testing the null hypothesis that μ=16 at a significance level of 0.05, sample data yields a z score of 1.94. What is the difference between the test p value and the confidence level, and should the null hypothesis be rejected or does it fail to be rejected? A. .0238; fail to be rejected B. .0238; reject C. .0024; fail to be rejected D. .0024; reject E. .0052; fail to be rejected

C. .0024; fail to be rejected 2(P) - 0.05 p> 0.05 = fails to reject something to do with u is not equal to 16

Tank A is made up of a 50% solution of salt water. Tank B is made up of a 90% solution of salt water. Part of each tank is mixed together to make a 75% solution of salt water. If 4 liters were taken from tank A to make the solution, how much total solution was made? A. 16 liters B. 12 liters C. 32/3 liters D. 94/5 liters E. 18 liters

C. 32/3 liters (.5)(4) + (.9)(x) = (.75)(4+x) x + 4 = answer

A right prism has a height of 8 and a base shaped as an equilateral triangle. The equilateral triangle has a perimeter of 24. What is the volume of the prism? A. 124 B. 192 C. 64√3 D. 128√3 E. 216√2

D 128√3 equilateral triangle area = (s^2 (3)^1/2 ) / 4

If Mark has 200 Facebook friends, what is the probability that he shares the same birthday with AT LEAST ONE OF THEM? Ignore leap years, and assume that one year always has 365 days. A. 200/365 B. (1/365)^200 C. 1 - (1/365)^200 D. (364/365)^200 E. 1 - (364/365)^200

E. 1 - (364/365)^200

What is the standard deviation of the data set {6, 9, 12, 5}? A. 2.74 B. 3.29 C. 7.50 D. 4.18 E. 1.65

find avg find variance = 2^2 + 4^2 + 3^2 /4 sd = (variance) ^1/2

. A football player is running the length of a 100 yard long football field. For the first part of the field, he runs at a rate of 2 yards per second. He sprints the last part of the field at a rate of 4 yards per second. If the whole run takes 40 seconds, what is the fraction of the length of the field that the runner sprints? A. 1/2 B. 2/5 C. 1/3 D. 3/5 E. 2/3

x + y = 100 x/2 + y/4 = 40 solve for y =2/5