Inequality (flipping the sign)

Expert replies

Stockmoose16: Master | Next Rank: 500 Posts; Posts: 347; Joined: Mon Aug 04, 2008 1:42 pm; Thanked: 1 times

by Stockmoose16 » Mon Oct 27, 2008 10:28 am

Are you allowed to do the following with an inequality:

1/(k+1)>0

Multiply both sides by K+1

K+1>0

K>-1

... I've seen a couple people do this, and I'm wondering why you can multiply both sides by K+1, since you don't know whether K is positive or negative (which means you wouldn't know whether or not to flip the inequality sign).

Like this post

Source: Beat The GMAT — Data Sufficiency | Mon Oct 27, 2008 10:28 am

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Mon Oct 27, 2008 10:33 am

No you can't. You are right , you don't know the sign of K+1

But, in this case

1/(k+1)>0

since it is greater than ZERO, it means it needs to be positive. Well 1 is positive so k+1 needs to be POSITIVE as well so the equation remains valid

therefore, k+1 > 0

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

Like this post

Stockmoose16: Master | Next Rank: 500 Posts; Posts: 347; Joined: Mon Aug 04, 2008 1:42 pm; Thanked: 1 times

by Stockmoose16 » Mon Oct 27, 2008 11:35 am

logitech wrote:No you can't. You are right , you don't know the sign of K+1

But, in this case

1/(k+1)>0

since it is greater than ZERO, it means it needs to be positive. Well 1 is positive so k+1 needs to be POSITIVE as well so the equation remains valid

therefore, k+1 > 0

That is true, but the whole point of multiplying both sides by K+1 is to get K in the numerator, so you can determine whether K is positive or negative. If you already know it's positive, there's no reason to multiply it by K+1.

Like this post

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Mon Oct 27, 2008 6:40 pm

K COULD BE NEGATIVE

K= - .5

still 1/k+1 would be > 0

Like logitech mentioned k+1 has to be positive since 1/k+1 > 0 so mutlplying by k+! (a positive qty) doesnt reverse the inequality

or better yet multiply both sides by

(k+1) ^ 2 - always positive

still end up with
k+1 > 0

Hope this helps!

Like this post

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Mon Oct 27, 2008 6:44 pm

Thinkign about it a litle more, I think u would have to mutpily by

(k+1)^2 (may be thats what u meant in ur first post) if this is a data sufficiency question dealing with k

If u mutliply k+1 on both sides we will end up wiht 1>0

Not usefule info for the actual problem if is dealing with k

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review