If a and b are not zero, is 1/a + 1/b = 2?

Question

(1) 2ab = a + b
(2) a/1 + b/1 = 2

Kurtosis · Answer

St1: 2ab = a + b --> 2 = 1/b + 1/a --> Sufficient

St2: a + b = 2 --> Clearly insufficient.

Answer: A

korrag · Answer

From statement 1, 2ab = a +b
dividing both sides by ab, we get, 2 = 1/b + 1/a.

Statement 2 is not sufficient.

Hence, the answer is (A).

Bombsante · Answer

Hi, If we simplify the equation is question stem, it gives a+b = 2ab. Therefore, the Q is asking "is a+b = 2ab?"

Statement 1 says exactly that, therefore sufficient. Now here is when the doubt arises in my head. The Q is a yes / no Q.
If we are able to answer the Q in a definite Y or a definite N, the statements should be sufficient.

Statement 2 says that a+b = 2. Why is this not sufficient? It does help us in answering "is a+b = 2ab" in a definite no IMO.
I am definitely missing out something,  Bunuel  plz help.

Bunuel · Answer

Two things:

1. On the GMAT, two data sufficiency statements always provide TRUE information and these  statements never contradict each other . So, if you were right and (2) were also sufficient with a NO answer to the question, then the question would be flawed because we cannot have an YES answer from (1) and a NO answer from (2). The statements in this case would clearly contradict each other.

2. The question asks is a + b = 2ab and (2) says that a + b = 2. But a + b = 2ab and a + b = 2 could be true simultaneously when a = b = 1, and in this case a + b = 2ab would be true, giving an YES answer to the question. While all other values of a and b satisfying a + b = 2, will give a NO answer to the question. So, we can have both a NO and an YES answers, which makes (2) not sufficient.

Hope it helps.

bumpbot · Answer

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If a and b are not zero, is 1/a + 1/b = 2?

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GMAT Data Sufficiency (DS) Questions

If a and b are not zero, is 1/a + 1/b = 2?

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