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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555-605 (Medium)

A certain fruit stand sold apples for

0.70 e a c han d banana s f or

0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?

Sub 505 (Easy)

Which of the following equations is NOT equivalent to 10 y 2 = (x + 2) (x â 2) ?

Sub 505 (Easy)

y = k x + 3 In the equation above, k is a constant. If y = 17 when x = 2, what is the value of y when x = 4 ?

Sub 505 (Easy)

If the operation @ is defined by x @ y = â x y x @ y = x y â â for all positive numbers x and y, then (5@45)@60 =

555-605 (Medium)

(x + 1 x â 1) 2 If x â 0 and x â 1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to

505-555 (Easy)

If T = 5/9 * (K - 32), and if T = 290, then K =

Sub 505 (Easy)

If y (3 x â 5 2) = y and y â 0 , then x =

Sub 505 (Easy)

A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?

Sub 505 (Easy)

If 1.5 0.2 + x = 5 , then x =

505-555 (Easy)

Of the 50 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?

Sub 505 (Easy)

If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?

505-555 (Easy)

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

555-605 (Medium)

If 0.0015 * 10 m 0.03 * 10 k = 5 * 10 7 , then m - k =

Sub 505 (Easy)

If x = 1- 3t and y = 2t - 1, then for what value of t does x = y?

Sub 505 (Easy)

If 1 + 1/x = 2 - 2/x, then x =

505-555 (Easy)

As x increases from 165 to 166, which of the following must increase? I. 2x - 5 II. 1 - 1/x III. 1/(x^2 - x)

505-555 (Easy)

If (x - 1)^2 = 400, which of the following could be the value of x - 5?

505-555 (Easy)

If n is positive, which of the following is equal to 1 â n + 1 â â n 1 n + 1 â â â â n â

705-805 (Hard)

If x, y, and k are positive numbers such that x x + y * 10 + y x + y * 20 = k and if x < y, which of the following could be the value of k?

555-605 (Medium)

If s is the product of the integers from 100 to 200 inclusive, and if t is the product of the integers from 100 to 201 inclusive, what is 1/s + 1/t in terms of t?

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