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Re: If a > b > c > 0, is c < 3 ? [#permalink]
23 Oct 2009, 17:01

Stmt 2 is not crystal clear..

We have here,a+b+c=abc which is only true when a,b,c=3.However,from the stem we know that a>b>c..hmmm..getting there but missing something... _________________

Re: If a > b > c > 0, is c < 3 ? [#permalink]
12 Aug 2014, 03:04

1

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If a > b > c > 0, is c < 3 ?

(1) 1/a > 1/3 --> cross-multiply (notice that we can safely do this since we know that a > 0): a < 3. As c < a, then c < a < 3. Sufficient.

(2) 1/a + 1/b + 1/c = 1. If c is more than or equal to 3, then 1/c is less than or equal to 1/3 (for example, if c is 3, then 1/c is 1/3 and if c is 4, then 1/c is 1/4). In this case both 1/b and 1/a would be less than 1/3. So, 1/a + 1/b + 1/c = (less than 1/3) + (less than 1/3) + (less than or equal to 1/3) = (less than 1), which contradicts the given statement. Therefore our assumption that c could be more than or equal to 3 was wrong, which implies that c < 3. Sufficient.

Re: If a > b > c > 0, is c < 3 ? [#permalink]
12 Oct 2015, 17:42

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a > b > c > 0, is c < 3 ? [#permalink]
10 Nov 2015, 16:19

1

This post received KUDOS

yezz wrote:

If a > b > c > 0, is c < 3 ?

(1) 1/a > 1/3 (2) 1/a + 1/b + 1/c = 1

Here's a slightly different approach . . .

Target question: Is c < 3?

Given: 0 < c < b < a

Statement 1: 1/a > 1/3 Since we can be certain that a is positive, it's safe to take the inequality 1/a > 1/3 and multiply both sides by a to get: 1 > a/3 Likewise, we can take 1 > a/3 and multiply both sides by 3 to get: 3 > a If 3 > a and c < a, then we can conclude that c < 3 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (1/a) + (1/b) + (1/c) = 1 IMPORTANT: If 0 < c < a, we can conclude that 1/a < 1/c Likewise, since 0 < c < b, we can conclude that 1/b < 1/c

In other words, 1/c is BIGGER than both 1/a and 1/b So, if we take the equation (1/a) + (1/b) + (1/c) = 1 and replace both 1/a and 1/b with 1/c, the resulting sum will be BIGGER than 1 That is, (1/c) + (1/c) + (1/c) > 1 Simplify to get: 3/c > 1 Since we know that c is positive, it's safe to take the inequality and multiply both sides by c to get: 3 > c Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers, Brent _________________

Brent Hanneson - Founder of GMAT Prep Now, a free & comprehensive GMAT course with: - over 500 videos (35 hours of instruction) - over 800 practice questions - A step-by-step Learning Guide - http://www.gmatprepnow.com/

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Re: If a > b > c > 0, is c < 3 ?
[#permalink]
10 Nov 2015, 16:19

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