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GMAT Quantitative Practice, Problem Solving

Question 4

If p Ο q = p(qp), which of the following specific operations yields 2p – 4 ?

  1. 2p Ο 2
  2. p Ο 2
  3. 2p Ο p
  4. 2 Ο 2p
  5. 2 Ο p

Explanatory Answer

This problem involves a defined operation and is essentially an exercise in algebraic substitution. For each answer choice, "plug" the given values into the expression p(qp).

You can eliminate the first three listed operations because each one yields a quadratic expression containing a p2 term. The operation given in choice (E) is the one that yields 2p – 4:

p(qp) = 2(p – 2) = 2p – 4

The correct answer is (E).