Algebra

GMAT Algebra is less about solving equations and more about choosing the fastest route: simplify first, substitute smart numbers, or backsolve from the answer choices. This set covers linear and quadratic equations, exponents and roots, functions, and algebraic translation from word problems. Watch for the classic GMAT moves — differences of squares in disguise, equations that share a common factor you should not cancel blindly, and expressions that beg to be factored rather than expanded.

Equations, exponents, absolute value.·Show:20 30 50

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Sub 505 (Easy)

The (x , y) pair (− 1 , 1) satisfies which of the following equations? I. 2 x 3 − y 2 = − 3 II. 2 x 2 − y 3 = 1 III. x 2 − 2 y 3 = − 1

505-555 (Easy)

Last year

$48, 000

of a certain store's profit was shared by its 2 owners and their 10 employees. Each of the 2 owners received 3 times as much as each of their 10 employees. How much did each owner receive from the

$48, 000

505-555 (Easy)

In the table above, what is the number of green marbles in Jar R?

505-555 (Easy)

From 2000 to 2003, the number of employees at a certain company increased by a factor of

\frac{1}{4}

. From 2003 to 2006, the number of employees at this company decreased by a factor of

\frac{1}{3}

. If there were 100 employees at the company in 2006, how many employees were there at the company in 2000?

505-555 (Easy)

A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of

$2.35

. How many of the coins have a face value of 25 cents?

505-555 (Easy)

As a salesperson, Phyllis can choose one of two methods of annual payment: either an annual salary of

$35, 000

with no commission or an annual salary of

$10, 000

plus a

20%

commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

505-555 (Easy)

1 < x < y < z

, which of the following has the greatest value?

505-555 (Easy)

Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover nonfiction books does Thabo own?

505-555 (Easy)

x > 0

\frac{x}{50} + \frac{x}{25}

is what percent of

x

505-555 (Easy)

k^{2} = m^{2}

, which of the following must be true?

505-555 (Easy)

2 x + y = 7

and

x + 2 y = 5

, then

\frac{x + y}{3} =

505-555 (Easy)

Last week Chris earned

x

dollars per hour for the first 40 hours worked plus 22 dollars per hour for each hour worked beyond 40 hours. If last week Chris earned a total of 816 dollars by working 48 hours, what is the value of

x

505-555 (Easy)

A total of

s

oranges are to be packaged in boxes that will hold

r

oranges each, with no oranges left over. When

n

of these boxes have been completely filled, what is the number of boxes that remain to be filled?

505-555 (Easy)

Company Q plans to make a new product next year and sell each unit of this new product at a selling price of

$2

. The variable costs per unit in each production run are estimated to be

40%

of the selling price, and the fixed costs for each production run are estimated to be

$5, 040

. Based on these estimated costs, how many units of the new product will Company Q need to make and sell in order for their revenue to equal their total costs for each production run?

505-555 (Easy)

A small business invests

$9, 900

in equipment to produce a product. Each unit of the product costs

$0.65

to produce and is sold for

$1.20

. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

505-555 (Easy)

When

n

liters of fuel were added to a tank that was already

\frac{1}{3}

full, the tank was filled to

\frac{7}{9}

of its capacity. In terms of

n

, what is the capacity of the tank, in liters?

505-555 (Easy)

The harvest yield from a certain apple orchard was 350 bushels of apples. If

x

of the trees in the orchard each yielded 10 bushels of apples, what fraction of the harvest yield was from these

x

trees?

505-555 (Easy)

In a certain fraction, the denominator is 16 greater than the numerator. If the fraction is equivalent to 80 percent, what is the denominator of the fraction?

505-555 (Easy)

The ratio of the amount of Alex's fuel oil bill for the month of February to the amount of his fuel oil bill for the month of January was

\frac{3}{2}

. If the fuel oil bill for February had been

$40

more, the corresponding ratio would have been

\frac{5}{3}

. How much was Alex's fuel oil bill for January?

505-555 (Easy)

f = 3 r (\frac{s}{1 , 000})^{2}

and if

s = 2, 000

, what is

r

in terms of

f

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