Quantitative Reasoning

If x>0 what is the value of the expression ((abs -x) + (abs 2x)) / (abs -3x)

Answer 1

y+8 is what percent of y^3 - 4 when y=4? a. 20 b. 25 c. 33 1/3 d. 300 e. 500

Answer 20 Plug 4 into the two equations.

a/2 is what percent of a^2/3 when a =3? a. 25 b. 33.33 c. 50 d. 60/66 e. 75

Answer 50 3/2 = 3 1/2 x 3 = 3

If a > 1, which of the following is equal to (2a + 6) / (a^2 + 2a - 3)

Answer: 2/ a-1 Factor out the 2 on top 2(a +3) / (a+3) (a-1) or you can plug and chug

A car loses half its value every 3 years. If 6 years after it was made it is worth $12,000 less than its original value, how many dollars will be worth 9 years after it was made? a. 1000 b. 2000 c. 3000 d. 4000 e. 6000

Answer: 2000 At the beginning you know the car is worth x, after 3 years its worth x/2, after 6 its worth x/4, and after 9 its worth x/8. x-12000 = x/4 = 3x=48000 --> x = 16000 x 1/8 = 2000 (1200 less than original value)

What is the distance between (-6,7) and (4,31)? a. 10 b. 18 c. 24 d. 26 e. 37

Answer: 26 The formula for the distance d between two points (x1, y1) and (x2,y2) is d=squareroot ((x2-x1)^2 + (y2-y1)^2)

Sherry invests money in stock. Her initial investment is 3000 and after one month the stock's value increases by 20%. After another month, her investment's value increases again, this time by 10% of the previous month's value. How much is her investment worth now? a. 3300 b. 3840 c. 3960 d. 4000 e. 4150

Answer: 3960

If 2x - 9y = 11 and x + 12y = 8 what is the value of x + y?

X + Y = 1 2x - 9y =11 +(x+12Y =-8) 3X + 3Y = 3 X + Y = 1

For all x, 2^x, 2^x, 2^x, 2^x, 2^x =

2^x+2 2^x 2^x 2^x 2^x = 4(2^x) = 2^2(2^x) = 2^x + 2

If a bicyclist in motion increases his speed by 30 percent and then increases this speed by 10 percent what percent of the original speed is the total increase in speed?

43%

If r and s are positive integers and 4r + 6s is equal to 3a +2s, then which of the following is equal to 2s? a. -2r + 3/2a b. -4r +3d c. -r +3/4a d. r-3/4a e. 4/3r + 3a

Answer -2r + 3/2a Set the two equations equal to each other and solve for S.

When 3x^3 - 7x + 7 is divided by x +2 the remainder is

Answer -3 Use long division

If 2 is the remainder when m is divided by 5 what is the remainder when 3m is divided by 5?

Answer 1 7 / 5 gives you a remainder of 2 so use 7 to plug into 3m / 5 = 21/5 remainder of 1

If (3^x^2) (9^x) (3) = 27 and x > 0 what is the value of x?

Answer 1.92 (3^x^2) (3^2)^x(3) = 3^3 x^2+2x+1 = 3 (x+1) (x+1) = 3 (x+1)^2 = 3 (x+1) = sqroot3

A carnival game has 9 ducks that pop up at random out of a set of holes. One duck pops up at a time and returns into its hole before the next duck comes out. There are 4 blue ducks, 3 red ducks, 1 brown duck, and 1 special gold duck. In order to win, the gamer needs to knock down the gold duck. What is the probability that the gold duck will be the third duck to pop up? a. 1/729 b. 1/120 c. 1/81 d. 1/27 e. 1/9

Answer 1/9 The third event is completely independent of the first two. 1 gold duck out of 9 total ducks

A company is selecting 4 members of its board of directors to sit on an ethics subcommittee. If the board has 9 members, any of whom may serve on the subcommittee, how many different selections of members could the company make?

Answer 126 = 9! / 4!(9-4)! 9x8x7x6x5x4x3x2x1 / 4x3x2x1x5x4x3x2x1

A certain circular stopwatch has exactly 60 second marks and a single hand. If the hand of the watch is randomly set to one of the marks and allowed to count exactly 10 seconds, what is the probability that the hand will stop less than 10 marks on either side of the 53-second mark? a. 1/6 b. 19/60 c. 1/3 d. 29/60 e. 41/60

Answer 19/60

For new car purchases, an automobile company allows the selection of the two free "extras" from a list of seven. How many different ways can a car be customized with extras? a. 21 b. 28 c. 35 d. 42 e. 49

Answer 21 You multiple 7 by 6 and not 7 by 7 because you can't pick the same thing twice. But you have to divide 7 x 6 by 2 because picking a cupholder and a basket is the same as picking a basket and a cup holder.

Five integers are listed in order from least to greatest. Beginning with the second integer in the list, each subsequent integer is 4 greater than the previous integer. If the sum of the five integers is 165, what is the first integer? a. 21 b. 25 c. 29 d. 33 e. 35

Answer 25 a b = a + 4 c = b+4 = a +8 d = c+ 4 = a +12 e = d +4 = a +16 165 = a + (a +4) + (a+8) + (a + 12) + (a+ 16) 165 = 5a + 40 a = 25

County X holds an annual math competition to which each county high school sends a team of 4 students. If school A has 6 boys and 7 girls who's math grades qualify them t be on their school team, and competition rule stipulate that the team must consist of 2 boy and 2 girls, how many different teams might school A send to the competition?

Answer 315 Your choosing 2 boys from 6 and 2 girls from 7 6!/2!4! x 7!/2!5!

A certain school has 50 students assigned to a five distinct classes so that the numbers of students in the classes are consecutive and each student is assigned to only one class What is the probability that a student selected at random from the 50 students is in one of the two largest classes? a. 38% b. 42% c. 46% d. 48% e. 56%

Answer 46% when you see the word "consecutive" it tells you the number in the series is separated from the next by a fixed amount. we have a total of 50 students. The number of students in classes are separated by one. smallest class is x, x+1, X+2, x+3, x+4 = 5x + 10. 5x +10 = 50 x = 8 the two largest student will have 8+3 and 8 + 4 = 23 23/50 students = 46%

Eight times a number equals 35 more than the number. What is the number? a. 3 b. 4 c. 5 d. 6 e. 7

Answer 5 8N = 35 + N solve for N 7N =35 n= 5

One hose can fill a pool in 2 hours and another hose can fill the pool in 3 hours. How many hours does it take both hoses operating at the same time to fill the pool? a. 2/3 b. 5/6 c. 6/5 d. 4/3 e. 7/4

Answer 6/5 1/2 + 1/3 = 5/6 and flip it (add because of the word and)

There are 6 children at a family reunion, 3 boys and 3 girls. They will be lined up single file for a photo, alternating genders. How many arrangements of the children are possible for this photo?

Answer 72 are possible arrangement of 3 boy and 3 girls alternating genders you can get bgbgbg or gbgbgb Any of the 3 boys can go in the first spot and any of the 3 girls can go in the second. 3x3x2x2x1x1 + 3x3x2x2x1x1 = 36 + 36 = 72

Company Z spent 1/4 of its revenues last year on marketing and 1/7 of the remainder on maintenance of its facilities. What fraction of last years original revenues did company Z have left after its marketing and maintenance expenditures? a. 5/14 b. 1/2 c. 17/28 d. 9/14 e. 41/56

Answer 9/14 Find a common denominator which is 28 total revenue 1/4 x 28 = 7 28-7 = 21 x 1/7 maintenance = 3 so whats left is 28-7-3 = 18/28 rewritten as 9/14

An 8-sided carousel has one horse on each vertex. 3 of the horses are red, 3 are blue and 2 are green. A child is stationary in front of one vertex while waiting to ride and waits for three rounds. For each round, the carousel turns a random number of times before stopping with one vertex directly in front of the child. What are the chances that the carousel will stop with a green horse in front of the child on the first turn, a red horse in front of the child on the second turn, and a blue horse in front of the child on the last round? a. 6/336 b. 3/225 c. 3/128 d. 9/256 e. 9/100

Answer 9/256 (2/8) x (3/8) x (3/8) = 18/512 = 9/256

What is the diameter of a circle who's perimeter intersects the four corners of a square with a perimeter of 4? a. 1/squarert 2 b. 1 c. squarert 2 d. 2 e. 2sqroot2

Answer = Sqaureroot 2 The diameter of the circle is the hypotenuse side of the triangle which is the square cut in half.

How many integers are in the solution set of abs(4x+3) < 8?

Answer is 4 -8 < 4x + 3 < 8 -3 -3 -11 < 4x < 5 -11/4 < x < 5/4 values in between is -2, -1, 0, 1

The positive difference between Sam and Lucy's ages is a, and the sum of their ages is z. If Lucy is older than sam, then which of the following represents Lucy's age? a. (z-a) / 2 b. (z + a) / 2 c. a - (z/2) d. (a-z)/ 2 e. (a+2z) / 2

Answer: (z+a)/2 plug and chug

A certain machine produces toy cars in a repeating cycle of blue, red, green, yellow and black. If a string of 6 consecutively produced cars is selected at random from all the possible strings of 6 consecutively produced cars, what is the probability that, in the string selected, two of the cars are red? a. 1/6 b. 1/5 c. 1/3 d. 2/5 e. 1/2

Answer: 1/5

A drawer contains 4 red and 8 black pens. What is the probability that a person randomly grabbing two pens at once will grab two black pens? a. 14/36 b. 14/33 c. 4/9 d. 4/8 e. 3/4

Answer: 14/33 The first chance of grabbing a black pen is 8/12 = 2/3 the second chance of grabbing a black pen is 7/11 because you have one less black pen. (7/11) (2/3) = 14/33

A crate of apples contains 1 bruised apple for every 30 apples in the crate. Three out of every four bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, then how many total apples are there in the crate? a. 270 b. 360 c. 480 d. 600 e. 720

Answer: 480 Suppose there are 360 apples in the crate. then 360/30 apples are bruised. Then, 3/4 x 12 apples or 9 apples are unsellable. (there are 12, 9 is too few). Basically tried the numbers in the answer key and see which one will give you a total of 12 apples not fit to sell.

A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is "frozen" if her opponents piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently six spaces behind player B, what is the probability that player B will be frozen after player A rolls? a. 1/36 b. 5/36 c. 1/6 d. 1/3 e. 1/2

Answer: 5/26

Ron begins reading a book 4:30 pm and reads at a steady pace of 30 pages per hour. Michelle begins reading a copy of the same book at 6:00pm. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page? a. 7pm b. 7:30pm c. 8pm d. 8:30pm e. 9pm

Answer: 8:30pm Guess and Check pick a time and see how many pages Ron and Michelle will read during that given time ex) at 8:30 which is 4 hours, Ron will read 30 x 4 = 120 pages at 830 which is 2.5 hours for Michelle, she will have read, 50 x 2.5 = 125 pages but she started 5 pages behind Ron therefore 125-5 = 120.

Carol spends 1/4 of her savings on a stereo, and then she spends 1/3 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television together?

Answer: She spent 5/12 of her savings (1/4) x 12 dollars( lowest common dominator) = 3 3 x (2/3) = 2 2/12 + 3/12 = 5/12

A car rental company charges for mileage as follows: x dollars per mile for the first n miles and x + 1 dollars per mile for each mile over n miles. How much will the mileage charge be in dollars, for a journey of d miles where d > n?

Answer: d( x + 1) - n Pick x = 4, n = 3 and d = 5 and plug in

If p, q, and r are positive integers such that q is a factor of r and r is a multiple of p, which of the following must be an integer? a. (p+q) / r b. p/q c. r(p+q) / pq d. (r +p)/q e. (rp + q)/ p

Answer: r(p+q) / pq Pick values for the variables and plug and chug

Line l contains points (-1,3) and (4,-2) which of the following is an equation of line l? a. y = x +4 b. y + x = 2 c. y +x = 3 d. y - x = 1 e. y = -x -3

Answer: y + x =2 plug the points in to see which equation works.

If y = (5x + 2)/ (x -6) for all x not equal to 6, then which of the following gives x in terms of y for all values of y where the expression for x in terms of y is defined?

Solve for x Answer x = (2 +6y)/ (y-5)

A restaurant is hanging 7 large tiles on its wall in a single row. How many arrangements of tiles are possible if there are 3 white tiles and 4 blue tiles?

answer 35 Need to divide by the number of reductants arrangements from 7! (3 white and 4 blue) 7!/4!3! 7x6x5x4x3x2x1 / 3x2x1x4x3x2x1 = 7 x 5 = 35

Each writing for the local newspaper is paid as follows: a dollars for each of the first n stories each month and a + b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits n + a stories in a month earn than a writer who submits n + b stories? a. (a-b) (a+b+n) b. a-b c. a^2 - b^2 d. n(a-b) e. n(a+b)

answer: a^2 - b^2 Choose a number for a and b and then plug it back into the equation to see which one matches

If 8^x = 16^x-1 then x =

x = 4 (2^3)^x = (2^4)^x-1 3x = 4x -1