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If b and c do not equal 0, is a=1/b+1/c ? (1)a is an integer such that

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If b and c do not equal 0, is a=1/b+1/c ? (1)a is an integer such that  [#permalink]

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New post 08 Mar 2017, 23:54
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If b and c do not equal 0, is \(a = \frac{1}{b}+\frac{1}{c}\)?

(1) a is an integer such that \(a > 2\)
(2) b and c are both integers such that \(b > 1\) and \(c > 1\)

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If b and c do not equal 0, is a=1/b+1/c ? (1)a is an integer such that  [#permalink]

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New post 09 Mar 2017, 15:41
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ziyuen wrote:
If b and c do not equal 0, is \(a = \frac{1}{b}+\frac{1}{c}\)?

(1) a is an integer such that \(a > 2\)
(2) b and c are both integers such that \(b > 1\) and \(c > 1\)

Dear ziyuen,

I'm happy to help. :-) This is a clever question.

Statement #1 tells us about a, but not about b & c, so it's not sufficient.
Statement #2 tells us about b & c, but not about a, so it's not sufficient.

Combined statement
We know that a is 3 or greater, because it's an integer greater than two.

We know b > 1 and c > 1. Since all of the numbers in these two inequalities are positive, we can take the reciprocal of both sides, which would reverse the order of the inequality.

Thus,
\(\frac{1}{b} < 1\) and \(\frac{1}{c} < 1\)

Now, add those two inequalities
\(\frac{1}{b}+\frac{1}{c} < 2\)

Since a is 3 or greater, and the sum on the right side is always less than 2, we know for a fact that the two sides NEVER can be equal. Thus, we can give a definitive NO answer to the prompt question.

We have to be careful here. Since we were able to give a definitive "NO" answer to the prompt question, that means we had sufficient information to give answer the question. Thus, the answer to the sufficiency question is, yes, the combined statements are sufficient.

OA = (C)

Does all this make sense?
Mike
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Re: If b and c do not equal 0, is a=1/b+1/c ? (1)a is an integer such that  [#permalink]

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New post 14 May 2018, 04:08
hazelnut wrote:
If b and c do not equal 0, is \(a = \frac{1}{b}+\frac{1}{c}\)?

(1) a is an integer such that \(a > 2\)
(2) b and c are both integers such that \(b > 1\) and \(c > 1\)


Dear Mike,
I am having difficulty solving this question

On simplification the question stem becomes is b+c=abc ?

I thought only b=c=1 and a=2 satisfies this equation hence when statement 1 said A>2 then I thought it to be sufficient.
Please can you how statement 1 is not sufficient by picking some numbers.

similarly I thought Statement 2 to be sufficient too as I assumed b=c=1 and a=2 are the only values that satisfy the eqn b+c=abc

if you could please show the insufficiency of the individual statements picking numbers , I would be thankful.

Thank you so much in advance.
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Re: If b and c do not equal 0, is a=1/b+1/c ? (1)a is an integer such that   [#permalink] 14 May 2018, 04:08
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