GMAT Quantitative Problem Solving: Practice with Algebra - dummies

GMAT Quantitative Problem Solving: Practice with Algebra

By Sandra Luna McCune, Shannon Reed

Some Problem Solving questions in the Quantitative section of the GMAT will involve algebra. You should be prepared to deal with polynomials, linear equations and inequalities, quadratic equations, basic function concepts, and systems of linear equations.

Practice questions

  1. Given the function,

    GMAT_0801

    which of the following expressions is equivalent to

    GMAT_0802

  2. What is the maximum value of P = 2x + 5y subject to the constraints

    GMAT_0803

    A. 3.5
    B. 8.75
    C. 12
    D. 12.25
    E. 14

Answers and explanations

  1. The correct answer is C.

    Find

    GMAT_0804

    and simplify.

    GMAT_0805

  2. The correct answer is C.

    The three constraint inequalities define a region in the xy-plane that represents their intersections. The region’s boundary equations are x = y, 3xy = 1, and 3x + y = 5. The maximum value of P will occur at one of the intersections of these three linear equations. To find the maximum value of P, systematically pair the three equations and solve for their intersections. Solving x = y and 3xy = 1 by substitution yields

    GMAT_0806

    Thus, the intersection of x = y and 3xy = 1 is

    GMAT_0807

    Solving x = y and 3x + y = 5 by substitution yields

    GMAT_0810

    Thus, the intersection of x = y and 3x + y = 5 is

    GMAT_0811

    Solving 3xy = 1 and 3x + y = 5 by elimination yields

    GMAT_0812

    Thus, the intersection of 3xy = 1 and 3x + y = 5 is (1,2). Substitute the intersection points into P = 2x + 5y to find the maximum:

    GMAT_0813

    Therefore, subject to the given constraints, the maximum value of P is 12, which occurs at (1,2).