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

Question

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

mikemcgarry · Accepted Answer

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

stne · Answer

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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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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards