Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
(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.
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).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
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 1800 practice questions - 2 full-length practice tests and other bonus offers - http://www.gmatprepnow.com/ Brent also tutors students for the GMAT
1) 1/a >1/3 since a is positive we can multiply both sides by a . therefore a <3 3<a<c , and hence c >3 ...sufficient
2) 1/a+1/b+1/c =1
we have to prove c>3 ... also means 1/c >1/3 ...also means 1/c>33.33% ( since 1/3 is 33.33% for getting rid of fraction, i have a phobia of fractions ) also 1/c>1/b>1/a ( rephrasing given data, it says 1/c should be greatest) now back to st. 2 we can write this as 1/a + 1/b +1/c =100% as we have to prove 1/c >33.33% take a case where 1/c is 30% .. then 35+35+30 =100 ( cannot happen since 1/c should be greatest) 1/c has to greater than equal to 40% in this case (21+39+40) so 1/c >33.33 % sufficient.
ans is D i hope i am right _________________
1st attempt was mock ; 2nd attempt I will rock.
Re: If a > b > c > 0, is c < 3 ?
29 Mar 2016, 01:27