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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505-555 (Easy)

The formula

F = \frac{9}{5} C + 32

gives the relationship between the temperature in degrees Fahrenheit,

F

, and the temperature given in degrees Celsius,

C

. If the temperature is 85 degrees Fahrenheit, what is the temperature, to the nearest degree, in degrees Celsius?

505-555 (Easy)

Which of the following is equal to the average (arithmetic mean) of

(x + 2)^{2}

and

(x - 2)^{2}

505-555 (Easy)

In Western Europe,

x

bicycles were sold in each of the years 1990 and 1993. The bicycle producers of Western Europe had a 42 percent share of this market in 1990 and a 33 percent share in 1993. Which of the following represents the decrease in the annual number of bicycles produced and sold in Western Europe from 1990 to 1993?

505-555 (Easy)

p \neq = 0

and

p - \frac{1 - p ^{2}}{p} = \frac{r}{p}

, then

r =

505-555 (Easy)

\frac{∣ z ∣}{w} = 1

, which of the following must be true?

505-555 (Easy)

What number is

108

more than two-thirds of itself?

505-555 (Easy)

A service provider charges

c

dollars for the first 50 hours of service used per month and 40 cents for each 30 minutes in excess of 50 hours used during the month. If

x

is an integer greater than 50, which of the following expressions gives this service provider’s charge, in dollars, for a month in which

x

hours of service were used?

505-555 (Easy)

5 x - 8 = 12

and

x = y + 3

, then

y =

505-555 (Easy)

A dance troupe has a total of 50 dancers split into 2 groups. The costumes worn by Group A cost

$80

each, and those worn by Group B cost

$90

each. If the total cost of all the costumes is

$4, 270

, what is the total cost of the costumes worn by Group B?

505-555 (Easy)

35%

of a number is decreased by 15, then the result is

25%

of the original number. What is the original number?

505-555 (Easy)

A certain method for calculating pediatric drug dosages states that if

d

is the adult dosage, in milligrams, and

y

is the child’s age, in years, then the child’s dosage, in milligrams, is

d (\frac{y + 1}{24})

. If the adult dosage for a particular drug is 800 milligrams, what is an 8-year-old child’s dosage, in milligrams, according to this method?

605-655 (Medium)

To rent a tractor, it costs a total of

x

dollars for the first 24 hours, plus

y

dollars per hour for each hour in excess of 24 hours. Which of the following represents the cost, in dollars, to rent a tractor for 36 hours?

605-655 (Medium)

z \neq = 0

and

z + \frac{1 - 2 z ^{2}}{z} = \frac{w}{z}

, then

w =

605-655 (Medium)

a (a + 2) = 24

and

b (b + 2) = 24

, where

a \neq = b

, then

a + b =

605-655 (Medium)

In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If

N

is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?

605-655 (Medium)

Last year a state senate consisting only of Republican and Democrat members had 20 more Republican members than Democrat members. This year it has the same total membership but 2 fewer Republican members. If this year the number of Republican members is

\frac{2}{3}

the number of senate members, how many members does the senate have this year?

605-655 (Medium)

The cost

C

, in dollars, to remove

p

percent of a pollutant is

C = \frac{100 , 000 p}{100 - p}

. How much more would it cost to remove 90 percent than 80 percent?

605-655 (Medium)

x y \neq = 0

and

x^{2} y^{2} - x y = 6

, which could be

y

in terms of

x

? I.

\frac{1}{2 x}

II.

- \frac{2}{x}

III.

\frac{3}{x}

605-655 (Medium)

A certain high school has 5,000 students. Of these students,

x

are taking music,

y

are taking art, and

z

are taking both music and art. How many students are taking neither music nor art?

605-655 (Medium)

The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?

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