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If a + b + c = 12, what is the value of b ?

1. a + b = 8

2. b + c = 6


    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:
C

Algebra Simu

ltaneous Equations


1.Given that a + b = 8, it follows from (a + b) + c = 12 that 8 + c = 12, or c = 4. However, the value of b still cannot be determined. For example, if a = 6, b = 2, and c = 4, then a + b + c = 12 and a + b = 8. On the other hand, if a = 4, b = 4, and c = 4, then a + b + c = 12 and a + b = 8; NOT sufficient.

2.Given that b + c = 6, it follows from a + (b + c) = 12 that a + 6 = 12, or a =6. However, the value of b still cannot be determined. For example, if a = 6, b = 3, and c = 3, then a + b + c = 12 and b + c = 6. On the other hand, if a = 6, b = 2, and c = 4, then a + b + c = 12 and b + c = 6; NOT sufficient.


Taking (1) and (2) together, it follows from (1) that c = 4 and it follows from (2) that a = 6. Substituting these values in a + b + c = 12 gives 6 + b + 4 = 12, or b = 2.


The correct answer is C;

both statements together are sufficient.


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