If a > 0, is 2/(a+b) + 2/(a-b) = 1?

From F.S 1, we know that the given expression condenses to 2/a+2/a = 4/a. The question stem asks, whether this is equal to 1. For a=4, we will have an affirmative answer, however for a=2,we would not get 1. Thus, as the answer from F.S 1, depends on the value of a, which is not unique, Statement A is not sufficient.

From F.S 2, we can simplify the given statement as\(\frac{[2(a-b)+2(a+b)]}{a^2-b^2} = \frac{4a}{a^2-b^2}\)= 4a/4a = 1[a is not equal to zero]. Thus F.S 2 is infact sufficient.

B.
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Okay...... First it is given that a>0, Now, Question asks Is 2/(a+b) +2/(a-b) = 1 ?? That means Is Left Hand Side = Right Hand Side?? Now, First Rephrase the Question.
I.e., 2/(a+b) +2/(a-b) = 1 ⇒ (2a-2b+2a+2b)/(a^2-b^2 ) = 1 ⇒ (2a+2a)/(a^2-b^2 ) = 1 ⇒ 4a/(a^2-b^2 ) =1 ?? , So the Question basically asks ::

Is 4a/(a^2-b^2 ) =1 ?

Statement: 1 Says b=0 if we plugin b=0 in the equation given, the LHS ≠ RHS. Therefore, It is clearly insufficient.
Statement: 2 says a2 – b2 = 4a, Now, when you plugin a2 – b2 = 4a in the equation provided in the Question, You will get Left Hand Side = Right Hand Side. Therefore, it is sufficient.
Hence, B only.

I am still confused. Your explanation says Statement 1 LHS is not equal to RHS ...doesn't that mean it is sufficient in saying whether the first statement is enough or not? I too selected D and cannot understand why A is not sufficient to answer the question...perhaps require an explanation from a different angle ??

Statement 1 says b=0, but there is no information on a.
If a = 4, only then we will have 2/(a+b) + 2/(a-b) = 1.
Without any information on a, neither we can say LHS = RHS, nor we can say LHS # RHS. Hence, statement 1 is insufficient.

I got the answer as D.

From Statement 1, I got the value for a=4, substituting the value of a and b in the above equation proves that the expression is equal to 1. Not sure what am I missing here.

Hi davidfrank,

In this question, we're told that A > 0. We're ASKED if 2/(A+B) + 2/(A-B) = 1. This is a YES/NO question.

Fact 1: B = 0

We don't know what A is, so let's TEST VALUES....

IF....
A = 1
2/(1) + 2/(1) = 4 and the answer to the question is NO.

IF....
A = 4
2/(4) + 2/(4) = 1 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich

I know the answer is B, but I chose A.

The question simplified: 4a = (a+b) (a-b)


1.) If b = 0, then a has to equal to 4, then we can plug in a and b to to figure if [2/(a+b)] +[2/(a-b)] = 1 ?
b+ 0
4a = (a+b) (a-b) = (a^2)-(b^2)
4a = (a+0) (a-0) = (a^2)-(0)
a = 4

2.) I understand when you simplify the question, you get the same statement as statement two. However, I am having a hard time interpreting how this helps determine if statement is equal to 1. How can I figure if 4a = (a+b) (a-b) = (a^2)-(b^2) is equal to 1 ?

Am I missing something or assuming something extra?

If a > 0, is 2/(a+b) + 2/(a-b) = 1?

Is \(\frac{2}{(a+b)} + \frac{2}{(a-b)} = 1\)?

Is \(a^2 − b^2 = 4a\)? (This is the question we want to answer).


(1) b = 0. The question becomes: is \(a^2 = 4a\)? Since given that a > 0, this is equivalent to: is \(a = 4\)? We don't know that. a can be any positive number. Not sufficient.

(2) \(a^2 − b^2 = 4a\). Directly gives an YES answer to the question. Sufficient.

Answer: B.
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The answer should be C. It is essential to mention that a not equal to b, which is not done in the given details. But if we consider the given fact a>0 and statement 1: b=0 together, this can be true only if b=0, a>0 which means a not equal to be.

Because statement 1 is INSUFF, statement 2 is SUFF, therefore the answer can't be C.

I am unable to see options for any DS question. Can anyone help as soon as possible?

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following posts:
ALL YOU NEED FOR QUANT.
Ultimate GMAT Quantitative Megathread

Hope this helps.
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With algebra ds always try to see if you can rewrite the original equation to find the hidden inference/question

2(a-b) + 2(a +b) / a^2-b^2
2a-2b +2a +2b/a^2-b^2
4a/ a^2-b^2

St 1

We don't know what A is and even if we cancel out terms we could still have different scenarios (e.x if A is 1 vs 3 the answer will be different)

insuff

St 2

Essentially

4a/4a = 1

suff

B

[quote="ahatoval"]If a > 0, is 2/(a+b) + 2/(a-b) = 1?

(1) b = 0
(2) a^2 − b^2 = 4a

the stem says whether 2a -2b +2a+2b /a^2 -b^2 =1 or, 4a = a^2 -b^2
1) when b =0, a has to be either 0 or 4 to answer the stem in YES. (4a -a^2 =0 , a(4-a)=0). Although w know a > 0, but we don't know the exact value of a. not sufficient.
2) directly answer the question. sufficient
B is the answer

Hi Bunuel,

Why is the ans not D here. From statement 1, we know that b=0, by substituting this value in the given equation, we get a=4, so both these values when substituted in the original equation, gives 1. Hence it is sufficient. I am having a hard time placing it as to why stmnt 1 is not sufficient. TIA!

The point is that when you substitute b = 0 into the QUESTION, the QUESTION becomes "does a = 4?". We don't know that, hence (1) is not sufficient. Notice that we are NOT given that 2/(a+b) + 2/(a-b) = 1. The question asks: "IS 2/(a+b) + 2/(a-b) = 1?".
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