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

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If a > b > c > 0, is c < 3 ? [#permalink] New post 15 Aug 2009, 23:45
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If a > b > c > 0, is c < 3 ?

(1) 1/a > 1/3
(2) 1/a + 1/b + 1/c = 1
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Aug 2014, 02:52, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If a > b > c > 0, is c < 3 ? [#permalink] New post 16 Aug 2009, 07:30
IMO....D

(1) 1/a>1/3
Solution: 0 < a < 3
Since a > b > c > 0....and a < 3, then c must be < 3.
Sufficient.

2) 1/a+1/b+1/c=1

1 = 1/3 + 1/3 + 1/3
if C=3 then 1/a < 1/b < 1/3
Hence, the sum of the fraction can never reach 1....

Therefore, c has to be < 3 in order to get the sum of fractions reach 1
Sufficient.
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Re: If a > b > c > 0, is c < 3 ? [#permalink] New post 16 Aug 2009, 07:43
scarish wrote:
IMO....D

(1) 1/a>1/3
Solution: 0 < a < 3
Since a > b > c > 0....and a < 3, then c must be < 3.
Sufficient.

2) 1/a+1/b+1/c=1

1 = 1/3 + 1/3 + 1/3
if C=3 then 1/a < 1/b < 1/3
Hence, the sum of the fraction can never reach 1....

Therefore, c has to be < 3 in order to get the sum of fractions reach 1
Sufficient.


Thats D.
good job for good question. 8-)
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Re: If a > b > c > 0, is c < 3 ? [#permalink] New post 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...
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Re: If a > b > c > 0, is c < 3 ? [#permalink] New post 23 Oct 2009, 19:32
humm , for stmt 2 , is there any other way to solve the problem other than one mentioned by scarish

ab+bc+ab = abc , now can i solve from this ?
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Re: If a > b > c > 0, is c < 3 ? [#permalink] New post 04 Aug 2014, 17:36
Can some one explain Stm 2 better than the above explanations
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Re: If a > b > c > 0, is c < 3 ? [#permalink] New post 05 Aug 2014, 04:04
ashutoshbarawkar wrote:
Can some one explain Stm 2 better than the above explanations



Statement 2 : 1/a + 1/b + 1/c = 1

given a>b>c and all are positive thus == >1/c > 1/b > 1/a --(i)

let me assume values

1/a 1/b 1/c C
0.1 0.2 0.7 10/7
0.2 0.3 0.5 10/5
0.3 0.4 0.4 ---> This violates the condition--(i)

Thus C value will always be <3 ..


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Re: If a > b > c > 0, is c < 3 ? [#permalink] New post 12 Aug 2014, 03:04
Expert's post
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.

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