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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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Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1323
Location: Malaysia
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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08 Mar 2017, 22:54
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Difficulty:

55% (hard)

Question Stats:

58% (01:40) correct 42% (01:47) wrong based on 89 sessions

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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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Joined: 28 Dec 2011
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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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09 Mar 2017, 14:41
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1
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 $$\frac{1}{c} < 1$$

$$\frac{1}{b}+\frac{1}{c} < 2$$

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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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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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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14 May 2018, 03:08
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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- Stne

Re: If b and c do not equal 0, is a=1/b+1/c ? (1)a is an integer such that &nbs [#permalink] 14 May 2018, 03:08
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