The integers a, b, c, and d can each be equal to $0, 1, 2,$ or $3$ , independently. What is the value of $(a + 1)(b + 1)(c + 1)(d + 1)$ ?

(1) $a + 4b + 16c + 64d = 165$

(2) $64a + 16b + 4c + d = 90$

Correct answer marked below

Statement (1) ALONE is sufficient

Statement (2) ALONE is sufficient

BOTH statements TOGETHER are sufficient

EACH statement ALONE is sufficient

Correct

Statements (1) and (2) TOGETHER are NOT sufficient

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What this question tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.