GRE Quant Practice

If a is multiplied by 3 and the result is 4 less than 6 times b, what is the value of a - 2b? a. -12 b. -4/3 c. -3/4 d. 4/3 e. 12

b. -4/3 3a = 6b - 4 3a - 6b = -4 3(a - 2b) = -4 a - 2b = -4/3

For a certain distribution, the value 12.0 is one standard deviation above the mean and the value 15.0 is three standard deviations above the mean. What is the mean of the data set? a. 9.0 b. 9.5 c. 10.0 d. 10.5 e. 11.0

d. 10.5 15.0 - 12.0 = 3 3 / 2 standard deviations (btwn 15 and 12) = 1.5 Standard Deviation = 1.5 12 - 1.5 = 10.5 mean

Brooke wants to hang three paintings in a row on her wall. She has six paintings to choose from. How many arrangements of paintings on the wall can she create? a. 6 b. 30 c. 90 d. 120 e. 720

d. 120 i. 3 slots ii. 6 options 6 x 5 x 4 = 120

Flour, eggs, yeast, and salt are mixed by weight in the ratio of 11:9:3:2, respectively. How many pounds of yeast are there in 20 pounds of the mixture? a. 1 3/5 b. 1 4/5 c. 2 d. 2 2/5 e. 8 4/5

d. 2 2/5 F : E : Y : S = Total 11 : 9 : 3 : 2 = 25 <----------- 4/5 x 20 3 x 4/5 = 12/5 = 2 2/5

If y(x) = 10x - 1, what is y(5) - y(3)? a. 15 b. 18 c. 19 d. 20 e. 46

d. 20 y(5) = 10(5) - 1 = 50 - 1 = 49 y(3) = 10(3) - 1 = 30 - 1 = 29 y(5) - y(3) = 49 - 29 = 20

One ounce of Solution X contains only ingredients a and b in a ratio of 2:3. One ounce of a Solution Y contains only ingredients a and b in a ratio of 1:2. If Solution Z is created by mixing solutions X and Y in a ratio of 3:11, then 630 ounces of Solution Z contains how many ounces of a? a. 68 b. 73 c. 219 d. 236

d. 236 Solution X a 2 27 54 b 3 27 81 total 5 27 135 Solution Y a 1 165 165 b 2 165 330 total 3 165 495 Solution Z a 3 45 135 b 11 45 495 total 14 45 630

Dipak has a 25% chance of winning each hand of blackjack he plays. If he has $150 and bets $50 a hand, what is the probability that he will still have money after the third round? a. 1/64 b. 3/16 c. 27/64 d. 37/64 e. 3/4

d. 37/64 50 x 3 = 150 so it would take three rounds to lose all P(lose all) = 3/4 x 3/4 x 3/4 = 27/64 1-27/64 = 37/64

If x is the remainder when a multiple of 4 is divided by 6, and y is the remainder when a multiple of 2 is divided by 3, what is the greatest possible value of x + y? a. 2 b. 3 c. 5 d. 6 e. 9

d. 6 8 / 6 = 2 r4 8 / 3 = 2 r2 4 + 2 = 6

In Year X, the population of Massachusetts (40% of total) was approximately what percent of the population of Vermont (5% of total)? Year X: Total New England Population = 15 million a. 50% b. 120% c. 300% d. 800% e. 1,200%

d. 800% Mas = 15 x 0.4 = 6 Ver = 15 x 0.05 = 0.75 % = 0.75 / 6 = 8 x 100% = 800%

Quantity A: 2x^3 Quantity B: 4x^3 a. Quantity A is greater b. Quantity B is greater c. They are Equal d. Relationship cannot be determined with info given

d. Relationship cannot be determined from info given if x = 2 A = 2(2^3) = 16 B = 4(2^2) = 16 if x = 1 A = 2(1^3) = 2 B = 4(1^2) = 4 answers are absolute so if two different then must be D

5x - 2y = 2y - 3x Quantity A: x Quantity B: y a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

d. The relationship cannot be determined 5x - 2y = 2y - 3x 8x - 4y = 0 4(2x - y) = 0 2x - y = 0 y = 2x Plug-In: x = 2 and y = 4 WORKS --> Quant B > Quant A x = 0 and y= 0 WORKS --> Equal

x^2 = 144 Quantity A: x Quantity B: sqrt144 a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

d. The relationship cannot be determined x^2 = 144 --> x = 12 sqrt144 = +/- 12

Quantity A: The standard deviation of a list of data consisting of 10 integers ranging from -20 to -5 Quantity B: The standard deviation of a list of data consisting of 10 integers ranging from 5 to 20 a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

d. The relationship cannot be determined from the information given why? - standard deviation can't be negative (trick!) - unable to calculate with information

x^2 + 2x - 15 = 0 Quantity A: 2 Quantity B: x a. Quantity A is greater b. Quantity B is greater c. They are equal d. Relationship cannot be determined from info given

x^2 + 2x - 15 = 0 (x + 5) (x - 3) x = 5 and -3 d. Relationship cannot be determined from info given

If x^2 + 8x + 16 = 0, then what is the value of x?

x^2 + 8x + 16 = 0 (x+4)(x+4) or (x+4)^2 x = -4

If 0<x<10 and -10<y<-1, then what is the range for x-y?

10 - (-10) = 20 0 - (-10) = 10 10 - (-1) = 11 0 - (-1) = 1 1 < x-y < 20e

If 3^3 x 9^12 = 3^x, what is the value of x?

27 3^3 x 9^12 = 3^x 3^3 x (3^2)^12 = 3^x 3^3 x 3^24 = 3^x 3^27 = 3^x

If x≠ 0 and 64^3 = 8^x, then what is the value of x^2? a. 5 b. 6 c. 25 d. 36 e. 64

d. 36 64^3 = 8^x (8^2)^3 = 8^x x = 6 x^2 = 6^2 = 36

Which of the following is the units digit for the sum of all the distinct prime integers less than 20? a. 4 b. 5 c. 6 d. 7 e. 8

d. 7 Prime #'s = 2, 3, 5, 7, 11, 13, 17, 19

If the cost of a one-hour telephone call is $7.20, what would be the cost in dollars of a 10-minute telephone call at the same rate?

$1.20 $7.20 / 60 min = x / 10 min 60x = 10($7.20) 60x = 72 x = 6/5 or $1.20 $7.20/1 hour * 1 hour/60 min = $0.12 / min $0.12/min * 10-min = $1.20

Each month, Renaldo earns a commission of 10.5% of his total sales for the month, plus a salary of $2,500. If Renaldo earns $3,025 in a certain month, what were his total sales?

$5,000 3025-2500 = 525 10.5% = 525 / total sales 0.105x = 525 x = 525/0.105 = 5,000

Sadie sells half the paintings in her collection, gives one-third of her paintings to her friends, and keeps the remaining paintings for herself. What fraction of her collection does Sadie keep?

1/6 1 - 1/2 - 1/3 6/6 - 3/6 - 2/6 = 1/6

The original selling price of an item at a store is 40 percent more than the cost of the item to the retailer. If the retailer reduces the price of the item by 15 percent of the original selling price, then the difference between the reduced price and the cost of the item to the retailer is what percent of the cost of the item to the retailer?

19% Retail = 100 Original Selling = 100*0.4 = 40 + 100 = 140 Reduced = 140 *0.15 = 21 -140 = 119 119 - 100 = 19 19/100 = 19%

At a recent dog show, there were 5 finalists. One of the finalists was awarded "Best in Show" and another finalist was awarded "Honorable Mention". In how many ways could the two awards be given out?

20 Order Matter i. 2 slots ii. 5 options 5 x 4 = 20

If 6k - 5l = 27 and 3l - 2k = -13 and 5k - 5l = j, what is the value of j?

25 3l - 2k = -13 3l = -13 + 2k l = (-13 + 2k)/3 6k - 5[ (-13 + 2k)/3 ] = 27 18/3k + 65/3 - 10/3k = 27 8/3k + 65/3 = 27 8k + 65 = 81 8k = 16 k = 2 3l - 2(2) = -13 l = -3 j = 5k - 5l = 5(2) - 5(-3) = 25

-2, 3, -5, -2, 3, -5, -2, 3, -5,... In the sequence above, the first 3 terms repeat without end. What is the product of the 81st term through the 85th term?

300 81 / 3 = 27 --> 81st is end of series = -5 81 = -5 82 = -2 83 = 3 84 = -5 85 = -2

When a pair of six-sided dice, each with faces numbered 1 to 6, is rolled once, what is the probability that the result is either a 3 and a 4 or a 5 and a prime number? Give your answer in a fraction.

7/36 P(3 and 4 OR 5 and Prime) = P(3 and 4) + P(5 and P) 1. 2. 3. 4. 5. 6. 1 - x. x. x. x. x. x. 2 - x. x. x. x. Y. x. 3 - x. x. x. Y. Y. x. 4 - x. x. Y. x. x. x. 5 - x. Y. Y. x. Y. x. 6 - x. x. x. x. x. x. Y = 7/36

Quantity A: The greatest number of consecutive nonnegative integers which have a sum less than 22 Quantity B: 6 a. quantity A is greater b. quantity B is greater c. they are equal d. the relationship cannot be determined from the info given

a. quantity A is greater *nonnegative integers start at 0*

Nicole needs to form a committee of 3 from a group of 8 research attorneys to study possible changes to the Superior Court. If two of the attorneys are too inexperienced to serve together on the committee, how many different arrangements of the committees can Nicole form? a. 20 b. 30 c. 50 d. 56 e. 336

Order NOT Matter All Exp i. 3 slots ii. 6 options iii. divide by 3! (6 x 5 x 4)/(3 x 2 x1) = 20 One Inexp i. 2 slots ii. 6 options iii. divide by 2! (6 x 5)/(2 x 1) = 15 15 x 2 options for inexperienced = 30 Total Combos = 30 + 20 = 50

If the product of two distinct integers is 91, then which of the following could be the sum of the two integers? Indicate ALL such sums. a. -92 b. -91 c. 7 d. 13 e. 20

a. -92 e. 20 Factors = 1, 7, 13, 91

At a meeting of 376 members of a neighborhood association, 1/5 of the participants have lived in the community for less than 5 years and 2/3 of the attendees have lived in the neighborhood for at least 10 years. If a member of the meeting is selected at random, what is the probability that the person has lived in the neighborhood for at least 5 years but less than 10? a. 2/15 b. 4/15 c. 3/10 d. 1/2 e. 8/15

a. 2/15 Less than 5 years = 375 * 1/5 = 75 Lived for at least 10 years = 375 * 2/3 = 250 250 + 75 = 325 375 - 325 = 50 More than 5 but Less Than 10 50/375 = 2/15

A merchant sells three different sizes of canned tomatoes. A large can costs the same as 5 medium cans or 7 small cans. If a customer purchases an equal number of small and large cans of tomatoes for the same amount of money needed to buy 200 medium cans, how many cans does she purchase? a. 35 b. 45 c. 72 d. 199 e. 208

a. 35 Large Cans = $5 (small) x $7 (med) = $35 Medium = $35/$5 = $7 Small = $35/$7 = $5 200 x $7 = $1400 Plug in... 72 x $5 = $360 and 72 x $35 = $2520 NO 35 x $5 = $175 and 35 x $35 = $1225 $175 + $1225 = $1400 YES

Dale gives Miranda x bottles of water. He gives Marcella two fewer bottles of water than he gives to Miranda and he gives Mary three more bottles of water than he gives to Marcella. How many bottles of water did Dale give to Miranda, Marcella, and Mary, in terms of x? a. 3x - 1 b. 3x c. 3x + 1 d. 3x + 2 e. x - 2

a. 3x - 1 Miranda = x Marcella = x-2 Mary = x+3 x + x - 2 + x + 3 = 3x -1

What is the value of sqrt75/sqrt27? a. 5/3 b. 25/9 c. 3 d. 3sqrt3 e. 3sqrt5

a. 5/3 sqrt75/sqrt27 sqrt(25*3)/sqrt(9*3) 5sqrt3/3sqrt3 5/3

An elected official wants to take five members of his staff to an undisclosed secure location. What is the minimum number of staff members the elected official must employ in order to have at least 20 different groups that could be taken to the location? a. 7 b. 8 c. 9 d. 10 e. 11

a. 7 Order Not Matter i. 5 slots ii. x options iii. divide by 5! = 5 x 4 x 3 x 2 x 1 = 120 7 x 6 x 5 x 4 x 3 = 2520 / 120 = 21 MINIMUM NUMBER

Quantity A: 2^-4/4^-2 Quantity B: sqrt64/-2^3 a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

a. Quantity A is greater A = 2^-4/4^-2 = 2^-4/(2^-2)^-2 = 2^-4/2^-4 = 1 B = sqrt64/-2^3 = 8/-2^-3 = 8/-8 = -1

Towns A, B, C, and D are all in the same voting district. Towns A and B have 3,000 people each who support referendum R and the referendum has an average (arithmetic mean) of 3,500 supporters in towns B and D and an average of 5,000 supporters in Towns A and C. Quantity A: The average # of supporters of Referendum R in Towns C and D Quantity B: The average # of supporters of Referendum R in Towns B and C a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

a. Quantity A is greater Average = Total / Parts Total = Average x Parts = 3500 x 2 = 7000 B+D 7000 - 3000 (in B) = 4,000 support in D Total = Average x Parts = 5000 x 2 = 10,000 C+A 10,000 - 3,000 = 7,000 support in C A = (7,000 + 4,000)/2 = 5,500 B = (7,000 + 3,000)/2 = 5,000

Quantity A: 15^15 - 15^14 Quantity B: 15^14(14) - 1 a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

a. Quantity A is greater FACTOR A - 15^15 - 15^14 = 15^14 (15-1) = 15^14(14) B = 15^14(14) - 1

Set F = {4, 2, 7, 11, 8, 9} Quantity A: The range of set F Quantity B: The median of set F a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

a. Quantity A is greater Reorder: 2, 4, 7, 8, 9, 11 Median = (7 + 8)/2 = 7.5 Range = 11 - 2 = 9

Company X budgets $90,000 total on advertising for all of its products per year. Company X budgets $40,000 for all advertising for product A and $30,000 for all advertising for product B. From the budgets for products A and B, $15,000 is budgeted for advertisements that feature both products used as a system. QA: The total amount Company X budgets for advertising products other than products A and B QB: $20,000 a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

a. Quantity A is greater Total = G1 + G2 - B + N 90,000 = 40,000 + 30,000 - 15,000 + N 20,000 = N - 15,000 35,000 = N

A recent survey of registered voters in City X found that 1/3 of the respondents support the mayor's property tax plan. Of those who did not support the mayor's plan, 1/8 indicated they would not vote to reelect the mayor if the plan were implemented. Of all the respondents, what fraction indicated that they would not vote for the major if the plan were enacted? a. 1/16 b. 1/12 c. 1/6 d. 1/3 d. 2/3

b. 1/12 Easy Total = 75 1/3 of 75 = 25 support 2/3 of 75 = 50 no support 1/8 of 50 = 25/4 (6.25) no reelect of no support (25/4)/75 or 25/4 * 1/75 = 1/12 not vote for mayor

During a sale, a store decreases the prices on all of its scarves by 25 to 50 percent. If all of the scarves in the store were originally priced at $20, which of the following prices could be the sale price of a scarf? a. $8 b. $10 c. $12 d. $14 e. $16

b. 10 c. 12 d. 14 20 *0.25 = 5 --> 20-5 = 15 50 *0.50 =10 --> 20-10 = 10 30% = 14 35% = 13 40% = 12 45% = 11

A jar contains 12 marbles. Each is either yellow or green and there are twice as many yellow marbles as green marbles. If two marbles are to be selected from the jar at random, what is the probability that exactly one of each color is selected? a. 8/33 b. 16/33 c. 1/2 d. 17/33 e. 25/33

b. 16/33 Green = x Yellow = 2x Total = Green + Yellow 12 = x + 2x 12 = 3x x = 4 Green = 4 Yellow = 2(4) = 8 P(Yellow then Green) = 4/12 x 8/11 = 32/132 = 8/33 P(Green then Yellow) = 8/12 x 4/11 = 32/132 = 8/33 8/33 + 8/33 = 16/33

An office supply store sells binder clips that cost 14 cents each and binder clips that cost 16 cents each. If a customer purchases 85 binder clips from this store at a total cost of $13.10, how many 14-cent binder clips does the customer purchase? a. 16 b. 25 c. 30 d. 35 e. 65

b. 25 x + y = 85 0.14x + 0.16y = 13.10 x = 85 - y (plug into ^^) y = 60 (16-cent clips) x + y = 85 --> x + 60 = 85 ---> x = 25 (14-cent clips)

Lee randomly selects a 2-digit prime number less than 50. What is the probability that the tens digit is greater than the units digit? a. 3/14 b. 3/11 c. 3/8 d. 1/2 e. 8/11

b. 3/11 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 = 11 31, 41, 43 3/11

Quantity A: 1/16 + 1/7 + 1/4 Quantity B: 1/4 + 1/16 + 1/6 a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

b. Quantity B is greater 1/6 > 1/7

11x + 14y = 30 and 3x + 4y = 12 Quantity A: x + y Quantity B: (x + y)^-2 a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

b. Quantity B is greater 3x + 4y = 12 3x = 12 - 4y x = 4 - 4/3y 11(4 - 4/3y) + 14y = 30 44 - 44/5y + 14y = 30 -44/5y + 42/3y = -14 -2/3y = -14 y = 21 x = 4 - 4/3(21) = 4 - 28 = -24 A = x + y = -24 + 21 = -3 B = (-3)^-2 = 1/-3^2 = 1/9

A set of 10 points lies in a plane such that no three points are collinear. QA: The # of distinct triangles that can be created from the set QB: The # of distinct quadrilaterals that can be created from the set a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

b. Quantity B is greater QA i. 3 slots ii. 10 options iii. divide by 3! 10 x 9 x 8 / 3 x 2 x 1 = 120 QB i. 4 slots ii. 10 options iii. divide by 4! 10 x 9 x 8 x 7 / 4 x 3 x 2 x 1 = 210

x^2 + 8x = -7 Quantity A: x Quantity B: 0 a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

b. Quantity B is greater x^2 + 8x + 7 = 0 (x + 7) (x + 1) = 0 x = -7, -1

For all positive integer values of x, ≠x = 2^-x? QA: ≠8 QB: ≠4 a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

b. Quantity B is greater ≠8 = 2^-x = 2^-8 = 1/2^8 = 1/256 ≠4 = 2^-x = 2^-4 = 1/2^4 = 1/16

If y ≠ 0, which of the following is equivalent to y^9/y(y^2)^3 a. y b. y^2 c. y^3 d. y^4 e. y^5

b. y^2 y^9/y(y^2)^3 = y^9/y(y^6) = y^9/y^7 = y^2

If -3 ≤ g ≤ 2 and f(g) = -2g and g is an integer, then which of the following integers could be a value of f(g)? Indicate ALL. a. -6 b. -5 c. -2 d. 0 e. 2 f. 4 g. 6

c, d, e, f, g f(g) = -6 = -2g --> g = 3 NO f(g) = -5 = -2g --> g = 5/2 No f(g) = -2 = -2g --> g = 1 YES f(g) = 0 = -2g --> g = 0 YES f(g) = 6 = -2g --> g = -3 YES

What is the value of the expression 3sqrt80 - 2sqrt5? a. 4sqrt5 b. 5sqrt3 c. 10sqrt5 d. 12sqrt3 e. 20sqrt5

c. 10sqrt5 3sqrt80 - 2sqrt5 sqrt80 = sqrt(4*20) = 2sqrt20 = 2sqrt(4*5) = 4sqrt5 3(4sqrt5) - 2sqrt5 = 12sqrt5 - 2sqrt5 = 10sqrt5

A water jug with a capacity of 20 gallons is 20 percent full. At the end of every third day, water is added to the jug. If the amount of water added is equal to 50 percent of the water in the jug at the beginning of the day, how many days does it take for the jug to be at least 85% full? a. 4 b. 6 c. 12 d. 15 e. 20

c. 12 20 x 0.2 = 4 gallons 3 days = (4 + 2) / 20 = 30% 6 days = (6 + 3) / 20 = 45% 9 days = (9 + 4.5) / 20 = 67.5% 12 days = (13.5 + 6.75) / 20 = >100%

A machine can stamp 20 envelopes in 4 minutes. How many of these machines, working simultaneously, are needed to stamp 60 envelopes per minute? a. 5 b. 10 c. 12 d. 20 e. 24

c. 12 Amount = Rate x Time Rate = Amount / Time Rate = 20 envelopes / 4 min = 5 per min 60 / 5 = 12 machines needed

It takes Carla three hours to drive to her brother's house at an average speed of 50 miles per hour. If she takes the same route home, but her average speed is 60 miles per hour, what is the time in hours, that it takes her to drive home? a. 2 hours b. 2 hours and 14 minutes c. 2 hours and 30 minutes d. 2 hours and 45 minutes e. 3 hours

c. 2 hours and 30 minutes Distance = Rate x Time Distance = 50 mph x 3 hours = 150 miles Distance = Rate x Time Time = Distance / Rate Time = 150 miles / 60 mph = 2.5 hours

If 1/12 < x < 1/6, then which of the following could be the value of x? Indicate ALL such values. a. 2/9 b. 1/5 c. 2/15 d. 1/10 e. 2/25

c. 2/15 and d. 1/10

If A = 2x - (y - 2c) and B = (2x - y) -2c, then A - B = ? a. -2y b. -4c c. 0 d. 2y c. 4c

c. 4c A - B = [2x - y + 2c] - [2x - y - 2c] A - B = 2x - y + 2c - 2x + y + 2c = 4c

If a prime number, p, is squared and the result is added to the next prime number greater than p, which of the following integers could be the resulting sum? Indicate ALL such integers. a. 3 b. 4 c. 7 d. 14 e. 58 f. 60 g. 65 h. 69

c. 7 d. 14 e. 60

A bowl contains 15 marbles, all of which are either red or blue. If the number of red marbles is one more than the number of blue marbles, what is the probability that a marble selected at random is blue? a. 1/15 b. 2/15 c. 7/15 d. 1/2 e. 8/15

c. 7/15 Red = x + 1 Blue = x Total = Red + Blue 15 = x + 1 + x 15 = 2x + 1 14 = 2x x = 7 Red = x + 1 = 7 + 1 = 8 Blue = x = 7

A biologist is studying breeding groups noted that of 225 birds tagged for the study, 85 birds made nests in pine trees, 175 made nests in oak trees, and 40 birds did not build nests in either type of tree. How many birds built nests in both types of trees? a. 45 b. 60 c. 75 d. 80 e. 125

c. 75 Total = G1 + G2 - B + N 225 = 85 + 175 - B + 40 225 = 300 - B -75 = - B B = 75

A pizza may be ordered with any of eight possible toppings. Quantity A: The # of different ways to order a pizza with 3 toppings Quantity B: The # of different ways to order a pizza with 5 toppings a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

c. They are Equal ORDER NOT MATTER Ai. 3 slots Aii. 8 options Aiii. divide by 3! (8 x 7 x 6 )/(3 x 2 x 1) = 56 Bi. 5 slots Bii. 8 options Biii. divide by 5! (8 x 7 x 6 x 5 x 4) / (5 x 4 x 3 x 2 x 1) = 56

Quantity A: (4 + sqrt6)(4 - sqrt6) Quantity B: 10 a. Quantity A is greater b. Quantity B is greater c. They are equal d. Relationship cannot be determined from info given

c. They are equal (4 + sqrt6)(4 - sqrt6) 16 + 4sqrt6 - 4sqrt6 - 6 16 - 6 = 10

The average (arithmetic mean) of a set of 6 numbers is 28. If a certain number, y, is removed from the set, the average of the remaining numbers in the set is 24. Quantity A: y Quantity B: 48 a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

c. They are equal Average = Total / Parts Total = Average x Parts = 6 x 28 = 168 Total = 5 x 24 = 120 168-120 = 48 was removed

Quantity A: 12!/11! Quantity B: 4!/2! a. Quantity A is greater b. Quantity B is greater c. They are equal d. The relationship cannot be determined

c. They are equal QA 12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 12/1 = 12 QB 4! = 4 x 3 x 2 x 1 2! = 2 x 1 4 x 3 / 1 = 12 / 1 = 12

A bookstore will only order books that come in complete cases. Each case has 150 books and costs $1,757. Quantity A: The number of books that can be ordered for $10,550 Quantity B: The number of books that can be ordered for $12,290 a. quantity A is greater b. quantity B is greater c. they are equal d. the relationship cannot be determined from the info given

c. they are equal

Quantity A: 4( 1/2x + 2y) Quantity B: 2x + 8y a. quantity A is greater b. quantity B is greater c. they are equal d. the relationship cannot be determined from the info given

c. they are equal

A company paid $500,000 in merit raises to employees whose performances were rated A, B, or C. Each employee rated A received twice the amount of the raise that was paid to each employee rated C; and each employee rated B received one-and-a-half times the amount of the raise that was paid to each employee rated C. If 50 workers were rated A, 100 were rated B, and 150 were rated C, how much was the raise paid to each employee rated A? a. $350 b. $625 c. $740 d. $1,250 e. $2,500

e. $2500 A = 2C and B = 3/2C 50A + 100B + 150C = 500,000 50(2C) + 100(3/2C) + 150C = 500,000 100C + 150C + 150C = 500,000 400C = 500,000 C = 1250 A = 2 (1250) = 2500

12 - (6/3 - 4 x 3) - 8 x 3 a. -46 b. -30 c. -18 d. -6 e. -2

e. -2 12 - (6/3 - 12) - 8 x 3 12 - (2 - 12) - 8 x 3 12 - (-10) - 8 x 3 12 + 10 - 8 x 3 12 + 10 - 24 22 - 24 -2

The average (arithmetic mean) of seven numbers is 9 and the average of three of these numbers is 5. What is the average of the other 4 numbers? a. 4 b. 5 c. 7 d. 10 e. 12

e. 12 Average = Total / Parts Total = Average x Parts = 9 x 7 = 63 Total = 5 x 3 = 15 63 - 15 = 48 Average = Total / Parts = 48 / 4 = 12

If x = 3a and y = 9b, then all of the following are equal to 2(x + y) EXCEPT a. 3(2a + 6b) b. 6(a + 3b) c. 24(1/4a + 3/4b) d. 1/3(18a + 54b) e. 12(1/2a + 3/4b)

e. 12(1/2a + 3/4b) 2x + 2y = 2(3a) + 2(9b) = 6a + 18b 3(2a + 6b) = 6a + 18b 6(a + 3b) = 6a + 18b 24(1/4a + 3/4b) = 6a + 18b 1/3(18a + 54b) = 6a + 18b 12(1/2a + 3/4b) = 6a + 9b NOT SAME

If x and y are positive integers, and if x^2 + 2xy + y^2 = 25, then what is the value of (x+y)^3 a. 5 b. 15 c. 50 d. 75 e. 125

e. 125 x^2 + 2xy + y^2) = (x+y)^2 = 25 (x+y) = 5 (x+y)^3 = 5^3 = 125

Approximately what was the percent increase in the price of aluminum from 1985 ($1900) to 1995 ($2700)? a. 8% b. 16% c. 23% d. 30% e. 40%

e. 40% Percent Change = Difference / Original x 100% % = (2700-1900) / 1900 x 100% = 42%

Mara has six more than twice as many apples as Robert and half as many apples as Sheila. If Robert has x apples, then, in terms of x, how may apples do Mara, Robert, and Sheila have combined? a. 2x + 6 b. 2x + 9 c. 3x + 12 d. 4x + 9 e. 7x + 18

e. 7x + 18 Robert = x Mara = 2x + 6 Sheila = 2 (2x + 6) = 4x + 12 x + 2x + 6 + 4x + 12 = 7x + 18

For all real numbers x and y, if x≠y = x(x-y), then x≠(x ≠ y) = ? a. x^2 - xy b. x^2 - 2xy c. x^3 - x^-2 - xy d. x^3 - (xy)^2 e. x^2 - x^3 + x^2y

e. x^2 - x^3 + x^2y x≠y = x(x - y) = x^2 - xy x≠(x≠y) = x[ x - (x^2 - xy)] = x^2 - x^3 - x^2y