Absolute value

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Bronson: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Thu Dec 27, 2007 3:48 am; Thanked: 1 times

by Bronson » Wed Jan 09, 2008 4:37 am

Is 1/(a-b) < b-a ?

Stat1) a<b
Stat2) 1<!a-b!

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Source: Beat The GMAT — Data Sufficiency | Wed Jan 09, 2008 4:37 am

StarDust845: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Dec 03, 2007 8:32 am; Thanked: 7 times

by StarDust845 » Wed Jan 09, 2008 10:51 am

Is the answer A?

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cris: Master | Next Rank: 500 Posts; Posts: 128; Joined: Sat Nov 17, 2007 11:59 am; Thanked: 1 times

by cris » Wed Jan 09, 2008 5:32 pm

I think is C (together are sufficient).

What is the answer?

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jaiswaln: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Nov 12, 2007 11:20 am

by jaiswaln » Wed Jan 09, 2008 9:07 pm

The answer should be E.

1 <a> (a-b)^2

which is not a true statement. so its not possible to get an answer to the question even by using any of the option or together.

BUMMER....

What is the answer?????

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camitava: Legendary Member; Posts: 645; Joined: Wed Sep 05, 2007 4:37 amFollowed by: 5 members; Location: India; Thanked: 34 times

by camitava » Wed Jan 09, 2008 9:11 pm

Guys I am having some other opinion at all. The Qs is saying that -
Is 1/(b - a) < (a - b) - But this we can reformat to 1/-(a - b) <a> -1. So we have to show - Is (a - b)^2 > -1?
This we can conclude when option - 1 and option - 2 independently holds true. So IMO D. What's the OA?

Correct me If I am wrong

Regards,

Amitava

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sagar: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Jun 07, 2007 12:44 am

by sagar » Wed Jan 09, 2008 9:59 pm

the ans is D. both fact statements individually hold good. such problems r best solved by substitution.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: Absolute value

by Stuart@KaplanGMAT » Wed Jan 09, 2008 10:22 pm

Bronson wrote:Is 1/(a-b) < b-a ?

Stat1) a<b
Stat2) 1<!a-b!

(1) if a is less than b, then (a-b) is negative. So, 1/(a-b) is also negative.

Also, if a - b is negative, then b-a is positive.

So, 1/(a-b) is negative and b-a is positive.. therefore, 1/(a-b) is definitely less than b-a. Statement (1) is sufficient.

(2) if 1 is less than the abs val of (a-b), then a-b is greater than 1 or a-b is less than -1. However, this doesn't tell us the relationship between a and b, so statement 2 is insufficient.

For example, we could choose the values:

a=10 b=5, since 1 is less than 5. We then ask the original question:

is 1/(10-5) greater than (5-10)? Or is 1/5 greater than -5. Yes it is!

We could also choose the values a= -10 and b = -5 (since 1 is less than 5). We then ask the original question:

Is 1/(-10 --5) greater than (-5 --10)?

In other words, is 1/-5 greater than +5 ? No, it isn't!

Since we can get both a yes and a no, statement (2) is insufficient.

1 is sufficient, 2 isn't.. choice (A) is correct.

ps: I had to edit this post 8 times to finally get it to format correctly - any time I used a greater than or less than sign it messed everythign up.. very frustrating!

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camitava: Legendary Member; Posts: 645; Joined: Wed Sep 05, 2007 4:37 amFollowed by: 5 members; Location: India; Thanked: 34 times

by camitava » Wed Jan 09, 2008 10:59 pm

Hey Stuart, if I interpret the Qs

Is 1/(a-b) < b-a ?

in the following way -
1/-(b - a) < (b - a)
so -1 < (b - a)^2
So the Qs is coming like -

Is -1 < (b-a)^2 ?

what wrong I am doing? Am I missing something or doing something wrong? Stuart, looking for ur suggestion/ concern...

Correct me If I am wrong

Regards,

Amitava

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gabriel: Legendary Member; Posts: 986; Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member; Location: India; Thanked: 51 times

Re: Absolute value

by gabriel » Thu Jan 10, 2008 12:42 am

Bronson wrote:Is 1/(a-b) < b-a ?

Stat1) a<b
Stat2) 1<!a-b!

Answer should be A .. a<b means a-b is negative which makes 1/(a-b) negative and also a<b means (b-a) is positive so 1/(a-b)<(b-a).

the second statement could mean a-b is positive or negative so it is insufficient.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Thu Jan 10, 2008 1:41 am

You need to be very careful when manipulating inequalities.

In this question, to get to your final statement, you're multiplying both sides by (b-a). However, if b-1 turns out to be negative, you have to change the direction of the inequality, so you'd actually end up with:

Is -1 greater than (b-a)^2

to which the answer is "no".

So, if b-a is positive, then the answer will be yes. However, if b-a is negative, the answer will be no. That's another way to deal with statement (2) and decide that it's insufficient.

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beatthegmat: Site Admin; Posts: 6778; Joined: Mon Feb 13, 2006 8:30 amFollowed by: 994 members; Location: Los Angeles, CA; Thanked: 1249 times

by beatthegmat » Thu Jan 10, 2008 12:31 pm

Hi Stuart:

gabriel just let me know about your issues with posting. My apologies for your frustration, I'm investigating right now what the problem is with the greater then, less then symbols...

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beatthegmat: Site Admin; Posts: 6778; Joined: Mon Feb 13, 2006 8:30 amFollowed by: 994 members; Location: Los Angeles, CA; Thanked: 1249 times

by beatthegmat » Thu Jan 10, 2008 12:35 pm

Quick update. I ran some tests with the symbols and didn't encounter any issues. I'll keep investigating, but this might have been a fluke incident.

Again, my apologies!

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Thu Jan 10, 2008 2:36 pm

beatthegmat wrote:Quick update. I ran some tests with the symbols and didn't encounter any issues. I'll keep investigating, but this might have been a fluke incident.

Again, my apologies!

I disabled HTML, I think that should fix it (since HTML uses < and > for tags).

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jaiswaln: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Nov 12, 2007 11:20 am

by jaiswaln » Thu Jan 10, 2008 3:28 pm

sorry, i meant the answer is D not E. since -1 > (a-b)^2. So the answer is obvious without the choices.

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beatthegmat: Site Admin; Posts: 6778; Joined: Mon Feb 13, 2006 8:30 amFollowed by: 994 members; Location: Los Angeles, CA; Thanked: 1249 times

by beatthegmat » Thu Jan 10, 2008 6:08 pm

Stuart Kovinsky wrote:
beatthegmat wrote:Quick update. I ran some tests with the symbols and didn't encounter any issues. I'll keep investigating, but this might have been a fluke incident.

Again, my apologies!
I disabled HTML, I think that should fix it (since HTML uses <and> for tags).

That did it. Thanks for the QA work, Stuart.

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