GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2018, 21:06

### 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

# If m = (3^x)^(2+3+4+6) and n = (3^y)^3, is m/n > 1 ?

Author Message
TAGS:

### Hide Tags

Senior RC Moderator
Status: Perfecting myself for GMAT
Joined: 22 May 2017
Posts: 759
Concentration: Nonprofit
Schools: Haas '21
GPA: 4
WE: Engineering (Computer Software)
If m = (3^x)^(2+3+4+6) and n = (3^y)^3, is m/n > 1 ?  [#permalink]

### Show Tags

23 Sep 2018, 06:07
2
00:00

Difficulty:

85% (hard)

Question Stats:

44% (02:33) correct 56% (02:11) wrong based on 45 sessions

### HideShow timer Statistics

If $$m = (3^x)^{(2+3+4+6)}$$ and $$n = (3^y)^3$$, is $$\frac{m}{n}$$ >1?

(1) $$x^2 + y^2 = 5^2$$

(2) $$\frac{x}{y} = \frac{1}{6}$$

_________________

If you like my post press kudos +1

New - RC Butler - 2 RC's everyday

Tag me in RC questions if you need help. Please provide your analysis of the question in the post along with the tag.

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 365
Re: If m = (3^x)^(2+3+4+6) and n = (3^y)^3, is m/n > 1 ?  [#permalink]

### Show Tags

23 Sep 2018, 13:34
workout wrote:
If $$m = (3^x)^{(2+3+4+6)}$$ and $$n = (3^y)^3$$, is $$\frac{m}{n}$$ >1?

(1) $$x^2 + y^2 = 5^2$$

(2) $$\frac{x}{y} = \frac{1}{6}$$

$$\frac{m}{n} = {3^{15x - 3y}}\,\,\mathop > \limits^? \,\,{3^0}\,\,\,\,\mathop \Leftrightarrow \limits^{{\text{base}}3\, > \,1} 15x - 3y\,\,\mathop > \limits^? \,\,0\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\boxed{5x\,\,\mathop > \limits^? \,\,y}$$

$$\left( 1 \right)\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {x,y} \right) = \left( {0,5} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{No}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,\left( {x,y} \right) = \left( {3,4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{Yes}}} \right\rangle \hfill \\ \end{gathered} \right.$$

$$\left( 2 \right)\,\,\,\left\{ \begin{gathered} \,x = k \hfill \\ \,y = 6k \hfill \\ \end{gathered} \right.\,\,\,\,\left( {k \ne 0} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,k = 1\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{No}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,k = - 1\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{Yes}}} \right\rangle \hfill \\ \end{gathered} \right.$$

$$\left( {1 + 2} \right)\,\,\,37{k^2} = 25\,\,\,\, \Rightarrow \,\,\,\,\left\{ \begin{gathered} \,k = \sqrt {\frac{{25}}{{37}}} \,\,\,\,\, \Rightarrow \,\,\,\,\,5\sqrt {\frac{{25}}{{37}}} \,\,\mathop {\, > }\limits^? \,\,\,6\sqrt {\frac{{25}}{{37}}} \,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{No}}} \right\rangle \hfill \\ \,k = - \sqrt {\frac{{25}}{{37}}} \,\,\,\,\, \Rightarrow \,\,\,\,\, - 5\sqrt {\frac{{25}}{{37}}} \,\,\mathop {\, > }\limits^? \,\,\, - 6\sqrt {\frac{{25}}{{37}}} \,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{Yes}}} \right\rangle \hfill \\ \end{gathered} \right.$$

The correct answer is therefore (E).

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

Regards,
Fabio.
_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

Re: If m = (3^x)^(2+3+4+6) and n = (3^y)^3, is m/n > 1 ? &nbs [#permalink] 23 Sep 2018, 13:34
Display posts from previous: Sort by