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)

If the operation @ is defined for all a and b by the equation a @ b = a 2 * b 3 , then 2 @ (3 @ â 1) =

Sub 505 (Easy)

If x = -3, what is the value of -3x^2 ?

505-555 (Easy)

If x + y = a and x - y = b, then 2xy = ?

Sub 505 (Easy)

If the sum of 5, 8, 12, and 15 is equal to the sum of 3, 4, x, and x + 3, what is the value of x ?

Sub 505 (Easy)

(7 â + 7 â) 2 (7 + 7) 2

Sub 505 (Easy)

If 1 2 + 1 3 + 1 4 = 13 x , which of the following must be an integer? I. x 8 II. x 12 III. x 24

Sub 505 (Easy)

(2 â + 1) (2 â â 1) (3 â + 1) (3 â â 1) = (2 + 1) (2 â 1) (3 + 1) (3 â 1) =

Sub 505 (Easy)

If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y?

Sub 505 (Easy)

If 4x + 3y = -2 and 3x + 6 = 0, what is the value of y?

Sub 505 (Easy)

If x + 5y = 16 and x = -3y, then y =

Sub 505 (Easy)

If y= 4 + (x - 3)^2, then y is lowest when x =

Sub 505 (Easy)

y = 248 - 398x Which of the following values of x gives the greatest value of y in the equation above?

Sub 505 (Easy)

16 + 16 â â â â = 16 + 16 =

605-655 (Medium)

If x^4 + y^4 = 100, then the greatest possible value of x is between

Sub 505 (Easy)

If s, u, and v are positive integers and 2s = 2u + 2v, which of the following must be true? I. s = u II. u â v III. s > v

555-605 (Medium)

A bank customer borrowed

10, 000, b u t r ece i v e d y d o l l a r s l ess t han t hi s d u e t o d i sco u n t in g . I f t h er e w a s a se p a r a t e

25 service charge, then, in terms of y, the service charge was what fraction of the amount that the customer received?

555-605 (Medium)

If (t- 8) is a factor of t^2 - kt - 48, then k=

Sub 505 (Easy)

A certain grocery purchased x pounds of produce for p dollars per pound. If y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?

Sub 505 (Easy)

If (7 3 4) n = 7 , what is the value of n?

Sub 505 (Easy)

A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^4, what was the number in the population 1 hour later?

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