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505-555 (Easy)|   Algebra|      
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1MoreFinalAttempt
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If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a 17 May 2012, 09:42
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

77% (01:10) correct 23% (01:19) wrong based on 214 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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B
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Bunuel
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If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a 17 May 2012, 10:03
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1MoreFinalAttempt
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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Welcome to GMAT Club. Below is an answer to your question.

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.

Answer: B.

Hope it's clear.
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If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a 17 May 2012, 11:17
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Bunuel

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".
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That pretty much what I was looking for. Thanks!
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If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a 25 Oct 2012, 07:21
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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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If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a 31 Jul 2021, 10:38
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Statement 1 : Insufficient
\(\frac{a^2 }{b^2} + 4 = 5\)
\(\frac{a^2 }{b^2} = 1\)
\(a^2 = b^2\)
\(a = b\) or \(a = -b\)
Two different values

Statement 2 : Sufficient
\(\frac{(17a + 4b)}{7} = 3a\)
\(17a + 4b = 21a\)
\( 4b = 4a\)
\( a = b\)

Hence, OA is (B).
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If b ≠ 0, does a equal b? (1) a^2 /b^2+4=5 (2) (17a+4b)/7=3a 15 Nov 2023, 21:14
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