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Type: Data Sufficiency

Difficulty: 4 star rating

If \(x\) and \(y\) are integers, is \(x^{2} - y^{2}\) divisible by 7?

  1. When \(x - y\) is divided by 7, the remainder is 2
  2. When \(x + y\) is divided by 7, the remainder is 5
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient