Difficult Data Sufficiency Questions
WXYZ Remainder
If w, x, y, and z are the digits of the four-digit number N, a positive integer, what is the remainder when N is divided by 9?
1) w + x + y + z = 13 2) N + 5 is divisible by 9 A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
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If x and y are distinct positive integers, what is the value of x4 - y4?
1) (y2 + x2)(y + x)(x - y) = 240 2) xy = yx and x > y A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
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May be distributed freely, but not modified.
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Counting 9s
If z = xn - 19, is z divisible by 9? 1) x =