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

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Intern
Joined: 16 Aug 2012
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If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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28 Apr 2013, 19:10
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If a > 0, is 2/(a+b) + 2/(a-b) = 1?

(1) b = 0
(2) a^2 − b^2 = 4a

[Reveal] Spoiler:
My answer was D. I thought that STATEMENT 1 was SUFFICIENT to answer the question, because the question is not asking if the equation is 1 or not. It is asking if the info provided is SUFFICIENT to answer the question or not.

Thanks
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Apr 2013, 23:14, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Special a & b [#permalink]

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28 Apr 2013, 21:04
ahatoval wrote:
Hey guys,

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

(1) b = 0
(2) a^2 − b^2 = 4a

My answer was D. I thought that STATEMENT 1 was SUFFICIENT to answer the question, because the question is not asking if the equation is 1 or not. It is asking if the info provided is SUFFICIENT to answer the question or not.

Thanks

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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Re: Special a & b [#permalink]

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28 Apr 2013, 22:45
ahatoval wrote:
Hey guys,

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

(1) b = 0
(2) a^2 − b^2 = 4a

My answer was D. I thought that STATEMENT 1 was SUFFICIENT to answer the question, because the question is not asking if the equation is 1 or not. It is asking if the info provided is SUFFICIENT to answer the question or not.

Thanks

-----------------------------------

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.
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Intern
Joined: 30 Apr 2013
Posts: 34
Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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30 Apr 2013, 20:10
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 ??
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Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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30 Apr 2013, 20:22
rsworase wrote:
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.
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Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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02 Mar 2015, 02:08
ahatoval wrote:
If a > 0, is 2/(a+b) + 2/(a-b) = 1?

(1) b = 0
(2) a^2 − b^2 = 4a

[Reveal] Spoiler:
My answer was D. I thought that STATEMENT 1 was SUFFICIENT to answer the question, because the question is not asking if the equation is 1 or not. It is asking if the info provided is SUFFICIENT to answer the question or not.

Thanks

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.
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Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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02 Mar 2015, 13:33
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Expert's post
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

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Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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16 Jul 2017, 22:56
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?
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Posts: 43361
Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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16 Jul 2017, 23:21
1
KUDOS
Expert's post
thealchemist89 wrote:
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.

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Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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23 Aug 2017, 09:34
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.
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Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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24 Aug 2017, 23:44
viswanathnittala wrote:
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.
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Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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24 Aug 2017, 23:53
I am unable to see options for any DS question. Can anyone help as soon as possible?
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Posts: 43361
Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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24 Aug 2017, 23:58
aksh5900 wrote:
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.
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.

Hope this helps.
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Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1? [#permalink]

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10 Sep 2017, 12:09
ahatoval wrote:
If a > 0, is 2/(a+b) + 2/(a-b) = 1?

(1) b = 0
(2) a^2 − b^2 = 4a

[Reveal] Spoiler:
My answer was D. I thought that STATEMENT 1 was SUFFICIENT to answer the question, because the question is not asking if the equation is 1 or not. It is asking if the info provided is SUFFICIENT to answer the question or not.

Thanks

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
Re: If a > 0, is 2/(a+b) + 2/(a-b) = 1?   [#permalink] 10 Sep 2017, 12:09
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