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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655-705 (Hard)

3 < x < 100

, for how many values of

x

\frac{x}{3}

the square of a prime number?

655-705 (Hard)

An object thrown directly upward is at a height of

h

feet after

t

seconds, where

h = - 16 (t - 3)^{2} + 150

. At what height, in feet, is the object 2 seconds after it reaches its maximum height?

655-705 (Hard)

David has

d

books, which is 3 times as many as Jeff and

\frac{1}{2}

as many as Paula. How many books do the three of them have altogether, in terms of

d

655-705 (Hard)

At his regular hourly rate, Don had estimated the labor cost of a repair job as

$336

and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned

$2

per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

655-705 (Hard)

To mail a package, the rate is

x

cents for the first pound and

y

cents for each additional pound, where

x > y

. Two packages weighing 3 pounds and 5 pounds, respectively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved?

655-705 (Hard)

In a certain sequence, the term

x_{n}

is given by the formula

x_{n} = 2 x_{n - 1} - \frac{1}{2} (x_{n - 2})

for all

n \geq 2

. If

x_{0} = 3

and

x_{1} = 2

, what is the value of

x_{3}

655-705 (Hard)

Last year the price per share of Stock X increased by

k

percent and the earnings per share of Stock X increased by

m

percent, where

k

is greater than

m

. By what percent did the ratio of price per share to earnings per share increase, in terms of

k

and

m

655-705 (Hard)

Last Sunday a certain store sold copies of Newspaper A for

$1.00

each and copies of Newspaper B for

$1.25

each, and the store sold no other newspapers that day. If

r

percent of the store's revenue from newspaper sales was from Newspaper A and if

p

percent of the newspapers that the store sold were copies of Newspaper A, which of the following expresses

r

in terms of

p

655-705 (Hard)

For the past

n

days, the average (arithmetic mean) daily production at a company was

50

units. If today's production of

90

units raises the average to

55

units per day, what is the value of

n

655-705 (Hard)

If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by

27

. By how much do the two digits differ?

655-705 (Hard)

In an electric circuit, two resistors with resistances

x

and

y

are connected in parallel. In this case, if

r

is the combined resistance of these two resistors, then the reciprocal of

r

is equal to the sum of the reciprocals of

x

and

y

. What is

r

in terms of

x

and

y

655-705 (Hard)

\frac{1}{x} - \frac{1}{x + 1} = \frac{1}{x + 4}

, then

x

could be

655-705 (Hard)

5 - \frac{6}{x} = x

, then

x

has how many possible values?

655-705 (Hard)

Three grades of milk are

1

percent,

2

percent, and

3

percent fat by volume. If

x

gallons of the

1

percent grade,

y

gallons of the

2

percent grade, and

z

gallons of the

3

percent grade are mixed to give

x + y + z

gallons of a

1.5

percent grade, what is

x

in terms of

y

and

z

655-705 (Hard)

When a certain tree was first planted, it was

4

feet tall, and the height of the tree increased by a constant amount each year for the next

6

years. At the end of the

6^{th}

year, the tree was

\frac{1}{5}

taller than it was at the end of the

4^{th}

year. By how many feet did the height of the tree increase each year?

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