GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 27 Jan 2020, 06:07

### 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

# Is 10m > 5n - k?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60687
Is 10m > 5n - k?  [#permalink]

### Show Tags

07 Mar 2016, 08:57
2
5
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:15) correct 33% (01:35) wrong based on 269 sessions

### HideShow timer Statistics

Is 10m > 5n - k?

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

_________________
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1683
Location: India
Re: Is 10m > 5n - k?  [#permalink]

### Show Tags

08 Mar 2016, 03:25
2
1
St1: n = 2m
Is 5n > 5n - k
Is 0 > -k ? We do not know this as it depends on the value of k. If k is -ve or 0 then the answer is no. If k is +ve then the answer is yes.
Not sufficient

St2: |k| = -k
This implies that -k is positive or 0. Therefore k has to be negative value or 0.
But is 10m > 5n - k ? We cannot answer this because we have 3 unknown values.
Not sufficient

Combining St1 and St2 we have,
Is 0 > -k ?
From St2, if k is -ve in value, then is 0 > -(-k) ? Answer is No
but if k is 0, then is 0 > 0 ? Answer is still No.
Since we get a unique answer 'No' when both the statements are combined, it is sufficient.

Intern
Joined: 29 Oct 2016
Posts: 23
Re: Is 10m > 5n - k?  [#permalink]

### Show Tags

10 Dec 2017, 17:49
1
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: 60687
Re: Is 10m > 5n - k?  [#permalink]

### Show Tags

10 Dec 2017, 20:55
1
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.
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is 10m > 5n - k?  [#permalink]

### Show Tags

08 Mar 2016, 17:33
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is 10m > 5n - k?

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

In the original condition, there are 3 variables(m,n,k), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), 10m>10m-k? -> -k<0? -> k>0?. In 2), k<=0, which is no and sufficient.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Current Student
Joined: 12 Aug 2015
Posts: 2547
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: Is 10m > 5n - k?  [#permalink]

### Show Tags

09 Mar 2016, 08:41
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
_________________
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Is 10m > 5n - k?  [#permalink]

### Show Tags

23 Sep 2018, 08:20
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.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: Is 10m > 5n - k?   [#permalink] 23 Sep 2018, 08:20
Display posts from previous: Sort by