If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a : GMAT Data Sufficiency (DS)
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# If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a

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If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a [#permalink]

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17 May 2012, 08:42
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85% (01:42) correct 15% (00:26) wrong based on 47 sessions

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If b ≠ 0, does a equal b ?

(1) a^2 /b^2 + 4 = 5
(2) (17a + 4b)/7 = 3a

Why D is not correct above?
The first statement gives us 2 answers , either 'a' is 'b' or '-b', we have 2 specific definite answers "Yes" / "No"

statement 2 gives a better answer "Yes"

A "Yes/No" question can have multiple answers ? Am I wrong here?
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Re: If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a [#permalink]

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17 May 2012, 09:03
1MoreFinalAttempt wrote:
If b ≠ 0, does a equal b ?

(1) a^2 /b^2 + 4 = 5
(2) (17a + 4b)/7 = 3a

Why D is not correct above?
The first statement gives us 2 answers , either 'a' is 'b' or '-b', we have 2 specific definite answers "Yes" / "No"

statement 2 gives a better answer "Yes"

A "Yes/No" question can have multiple answers ? Am I wrong here?

In a Yes/No Data Sufficiency question, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

If b ≠ 0, does a equal b ?

(1) a^2 /b^2 + 4 = 5 --> a^2/b^2=1 --> a^2=b^2 --> |a|=|b|, so either a=b (answer YES) or a=-b (answer NO). Two different answers, hence not sufficient.

(2) (17a + 4b)/7 = 3a --> a=b. Sufficient.

Hope it's clear.
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Re: If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a [#permalink]

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17 May 2012, 10:17
Bunuel wrote:
In a Yes/No Data Sufficiency question, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".
That pretty much what I was looking for. Thanks!
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Re: If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a [#permalink]

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25 Oct 2012, 06:21
We need to find, if there is sufficiency to say that a always equal b or a never equals b.

Statement (1) is the equation . Subtracting 4 from both sides of this equation, we have . Multiplying both sides of this equation by b2, we have a^2 = b^2. Now having a^2 = b^2 does not mean that we must have a = b. It is also possible that a = −b. For examples, if a = 4 and b = 4, then a2 = b2, and in this case, a = b, so the answer to the question is "yes." However, if a = 4 and b = −4, then a^2 = a^2, and in this case a is not equal to b, so the answer to the question is "no." Statement (1) is insufficient. We can eliminate choices (A) and (D).

Statement (2) is the equation . Let's try to rewrite this equation. Multiplying both sides of this equation by 7, we have 17a + 4b = 21a. Subtracting 17a from both sides, we have 4b = 4a. Dividing both sides of this equation by 4, we have b = a. Thus, a = b. We can answer the question with a "yes." We have determined that a does equal b. Statement (2) is sufficient. Choice (B) is correct.
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Re: If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a   [#permalink] 25 Oct 2012, 06:21
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