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

 It is currently 26 Jan 2020, 07:16

### 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

# m and n are two different numbers selected from the integers between

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
m and n are two different numbers selected from the integers between  [#permalink]

### Show Tags

30 Oct 2018, 18:35
1
00:00

Difficulty:

5% (low)

Question Stats:

95% (00:58) correct 5% (00:54) wrong based on 45 sessions

### HideShow timer Statistics

[Math Revolution GMAT math practice question]

$$m$$ and $$n$$ are two different numbers selected from the integers between $$11$$ and $$20$$, inclusive. What is the maximum value of $$\frac{mn}{(m-n)}$$?

$$A. 320$$
$$B. 340$$
$$C. 360$$
$$D. 380$$
$$E. 400$$

_________________
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" GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: m and n are two different numbers selected from the integers between [#permalink] ### Show Tags 30 Oct 2018, 19:00 MathRevolution wrote: [Math Revolution GMAT math practice question] $$m$$ and $$n$$ are two different numbers selected from the integers between $$11$$ and $$20$$, inclusive. What is the maximum value of $$\frac{mn}{(m-n)}$$? $$A. 320$$ $$B. 340$$ $$C. 360$$ $$D. 380$$ $$E. 400$$ Beautiful problem, Max. Congrats! $$m,n\,\,{\rm{distinct}}\,\, \in \left\{ {11,12, \ldots ,20} \right\}$$ $$? = \max \left( {{{mn} \over {m - n}}} \right)$$ $$\left( {\rm{I}} \right)\,\,m > n\,\,\,\,\left( {{\rm{otherwise}}\,\,{{mn} \over {m - n}} < 0\,\,,\,\,{\rm{not}}\,\,\max } \right)$$ $$\left( {{\rm{II}}} \right)\,\,0 < {{mn} \over {m - n}} \le \max \left( {{{mn} \over {m - n}}} \right)\,\,\,\,\, \Leftrightarrow \,\,\,\,\,{1 \over n} - {1 \over m} = {{m - n} \over {mn}} \ge {\left[ {\max \left( {{{mn} \over {m - n}}} \right)} \right]^{ - 1}}$$ $$\left( {{\rm{III}}} \right)\,\,\,?\,\,\,\, \Leftrightarrow \,\,\,\,\min \left( {{1 \over n} - {1 \over m}} \right)\,\,\,\,\, \Leftrightarrow \,\,\,\left( {m,n} \right) = \left( {20,19} \right)$$ $$\left( {{\rm{IV}}} \right)\,\,\,? = {\left( {{{20 - 19} \over {20 \cdot 19}}} \right)^{ - 1}} = 20 \cdot 19 = 380$$ 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: m and n are two different numbers selected from the integers between [#permalink] ### Show Tags 01 Nov 2018, 00:36 => To obtain the maximum value for $$\frac{mn}{(m-n)}$$, $$m-n$$ must be the smallest possible positive number and $$mn$$ must be the largest possible product. $$mn$$ is largest when both $$m$$ and $$n$$ are largest, that is, when $$m = 20$$ and $$n – 19$$. In this case, $$m – n = 1$$ is as small as possible and $$mn = 20*19 = 380$$ is as large as possible. Thus, the maximum value of $$\frac{mn}{(m-n)}$$ is $$\frac{20*19}{(20-19)} = \frac{380}{1} = 380.$$ Therefore, D is the answer. Answer: 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"
Re: m and n are two different numbers selected from the integers between   [#permalink] 01 Nov 2018, 00:36
Display posts from previous: Sort by