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GMAT Quantitative Practice, Data Sufficiency

Question 1

What is the value of m?

(1)  3/2m + n = 6

(2)  2/3n + m = 4

  1. Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is NOT sufficient.
  2. Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is NOT sufficient.
  3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
  4. Each statement ALONE is sufficient to answer the question.
  5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question.

Explanatory Answer

Statements (1) and (2) actually provide the same equation. (One way to confirm this is to multiply each term in the second equation by 3/2.) Given one linear equation in two variables, you cannot determine the value of one variable without knowing the value of the other. Thus, m may carry an infinite number of possible values. The correct response is (E).