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Three children inherited a total of X dollars. If the oldest child inherited $7,000 more than the youngest child, and the youngest child inherited $9,000 less than the middle child, what is the value of X ?

1. The middle child inherited $27,000.

2. The youngest child and the middle child together inherited a total of $45,000.


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


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答案:
D
Algebra Sim
ultaneous Equations

Let A, B, and C be the amounts inherited, respectively and in dollars, of the oldest, middle, and youngest child. It is given that A = 7,000 + C and C = B − 9,000. Then A = 7,000 +

(B − 9,000) = B − 2,000. Determine the value of A + B + C, or equivalently, determine the value of (B − 2,000) + B + (B − 9,000) = 3B − 11,000.


1. Given that B = 27,000, it follows that 3B − 11,000 = 70,000; SUFFICIENT.

2. Given that B + C = 45,000, then using C = B − 9,000 it follows that B + (B − 9,000) = 45,000, which can be solved to obtain B = 27,000. Therefore,3B − 11,000 = 70,000; SUFFICIENT.

 

The correct answer is D;

each statement alone is sufficient.


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