Multiple choice

x is a multiple of 5 and is a positive integer. What is the remainder of x divided by 7? 1) The remainder of x divided by 4 is 3 2) The remainder of x divided by 14 is 1

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

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A Correct answer
Explanation

x = 5n, n is a positive integer. 1)  only, assume x = 4m + 3, m is a positive integer, so 5n = 4m + 3. If m = 3, n = 3, x = 15, the remainder will be 1. But if m = 8, n = 7, x = 35, the remainder will be 0. We don't know the value of x, so we don't know the remainder of x divided by 7, insufficient. 2)  only, assume x = 14p + 1, p is a positive integer, so x/7 = (14p + 1)/7 = 2p + 1/7, the remainder is 1, sufficient.

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