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题库 / Prep2007E1-DS-96
If x and y are integers greater than 1, is x a multiple of y ?
(1) 3y2 + 7y = x.
(2) x2 – x is a multiple of y.
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.
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1. y(3y + 7) = x , y is an interger, so 3y+7 is an interger, sufficient;
2. x(x - 1) is a multiple of y ,x(x - 1) is a multiple of y
-- could mean any of 3 things:
possibility a) x is a multiple of y
possibility b) x - 1 is a multiple of y
possibility c) neither x nor x - 1 is a multiple of y, but together they contain all the prime factors of y (e.g., x = 3, x - 1 = 2, y = 6)
insufficient, because we don't know whether it's possibility (a) or not