Last visit was: 12 Jul 2024, 15:52 It is currently 12 Jul 2024, 15:52
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Is 10m > 5n - k?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94302
Own Kudos [?]: 640173 [11]
Given Kudos: 84576
Current Student
Joined: 13 Apr 2015
Posts: 1426
Own Kudos [?]: 4595 [5]
Given Kudos: 1228
Location: India
General Discussion
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 16999 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Alum
Joined: 12 Aug 2015
Posts: 2272
Own Kudos [?]: 3195 [0]
Given Kudos: 893
GRE 1: Q169 V154
Re: Is 10m > 5n - k? [#permalink]
Here is the My approach
Here we are not given much info in the question stem apart from 10m>5m-k to be proven
Statement 1 => no clue of k => not sufficient
statement 2 => it can be seen from this that k is negative but we have no clue of m and n => not sufficient
combining them => to be proven => 10m>5m-k as n=2m => 10m>10m-k or the question is asking us is k>0 or not which as per statement 2 is false.
hence C is sufficient
Intern
Joined: 29 Oct 2016
Posts: 20
Own Kudos [?]: 6 [1]
Given Kudos: 19
Re: Is 10m > 5n - k? [#permalink]
1
Kudos
Why does statement 2 imply that k can be 0? I understand that it can imply that k is negative, but not understanding why k can be 0.

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 94302
Own Kudos [?]: 640173 [1]
Given Kudos: 84576
Re: Is 10m > 5n - k? [#permalink]
1
Kudos
infinitemac wrote:
Why does statement 2 imply that k can be 0? I understand that it can imply that k is negative, but not understanding why k can be 0.

Thanks!

If k =0, then |k| = |0| = 0 and -k = -0 = 0, so |k| = -k = 0.
Tutor
Joined: 12 Oct 2010
Status:GMATH founder
Posts: 891
Own Kudos [?]: 1415 [0]
Given Kudos: 56
Re: Is 10m > 5n - k? [#permalink]
Bunuel wrote:
Is 10m > 5n - k?

(1) n = 2m
(2) |k| = -k

$$10m\,\,\mathop > \limits^? \,\,5n - k$$

$$\left( 1 \right)\,\,\,n = 2m\,\,\,\,\left\{ \matrix{\\ \,{\rm{Take}}\,\,\,\left( {n,m,k} \right) = \left( {0,0,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\, \hfill \cr \\ \,{\rm{Take}}\,\,\,\left( {n,m,k} \right) = \left( {2,1,1} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\, \hfill \cr} \right.\,$$

$$\left( 2 \right)\,\,\,\,\left| k \right| = - k\,\,\,\, \Leftrightarrow \,\,\,\,k \le 0$$

$$\left\{ \matrix{\\ \,{\rm{Take}}\,\,\,\left( {n,m,k} \right) = \left( {0,0,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\, \hfill \cr \\ \,{\rm{Take}}\,\,\,\left( {n,m,k} \right) = \left( {0,1, - 1} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\, \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{\\ 10m\,\,\mathop > \limits^? \,\,5\left( {2m} \right) - k\,\,\,\,\, \Leftrightarrow \,\,\,\,k\,\,\mathop > \limits^? \,\,0 \hfill \cr \\ k \le 0 \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{SUFF}}.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Non-Human User
Joined: 09 Sep 2013
Posts: 33952
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: Is 10m > 5n - k? [#permalink]
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).

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.
Re: Is 10m > 5n - k? [#permalink]
Moderator:
Math Expert
94302 posts