Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Dec 1511:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.
Dec 1608:00 AM PST
-11:59 PM PST
GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes!- Dec 17
09:00 AM PST
-10:00 AM PST
Join Manhattan Prep instructor Whitney Garner for a fun—and thorough—review of logic-based (non-math) problems, with a particular emphasis on Data Sufficiency and Two-Parts. - Dec 18
10:00 AM PST
-11:00 AM PST
Here is the essential guide to securing scholarships as an MBA student! In this video, we explore the various types of scholarships available, including need-based and merit-based options.
05 Mar 2019, 12:53
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (01:43) correct
28%
(01:56)
wrong
based on 173
sessions
History
Date
Time
Result
Not Attempted Yet
GMATH practice exercise (Quant Class 14)
Is \(xy >3\) ?
(1) \(7^x > 729\)
(2) \(9^y = 7\)
P.S.: this IS in GMAT´s quant section scope.
Is \(xy >3\) ?
(1) \(7^x > 729\)
(2) \(9^y = 7\)
P.S.: this IS in GMAT´s quant section scope.
05 Mar 2019, 14:22
Kudos
Bookmarks
fskilnik
GMATH practice exercise (Quant Class 14)
Is \(xy >3\) ?
(1) \(7^x > 729\)
(2) \(9^y = 7\)
\(xy\,\,\mathop > \limits^? \,\,3\)Is \(xy >3\) ?
(1) \(7^x > 729\)
(2) \(9^y = 7\)
\(\left( 1 \right)\,\,{7^x} > 729\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,0} \right)\,\,\,\,\,\left[ {{7^4} = {{49}^2}} \right]\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \\
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\)
\(\left( 2 \right)\,\,{9^y} = 7\,\,\,\, \Rightarrow \,\,\,y = {y_p}\,\,\,{\rm{unique}}\,\,{\rm{,}}\,\,\,{1 \over 2}\,\,{\rm{ < }}\,\,{y_p} < 1\,\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0,{y_p}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \\
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {6,{y_p}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\)
\(\left( {1 + 2} \right)\,\,\,{3^6} = 729\,\,\,\mathop < \limits^{\left( 1 \right)} \,\,\,{7^x}\,\,\mathop = \limits^{\left( 2 \right)} \,\,\,{\left( {{9^y}} \right)^x} = {3^{2xy}}\,\,\,\,\,\mathop \Rightarrow \limits^{3\,\, > \,\,1} \,\,\,2xy > 6\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle\)
The correct answer is (C).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
General Discussion
fskilnik
GMATH practice exercise (Quant Class 14)
Is \(xy >3\) ?
(1) \(7^x > 729\)
(2) \(9^y = 7\)
P.S.: this IS in GMAT´s quant section scope.
Is \(xy >3\) ?
(1) \(7^x > 729\)
(2) \(9^y = 7\)
P.S.: this IS in GMAT´s quant section scope.
If YOU FIND MY SOLUTION HELPFUL, PLEASE GIVE ME KUDOS
This question is testing, among other things, our ability to estimate
(1) Notice, that powers of 7 give us 7, 49, 353, 2479 Now 729? 353, therefore 3<x<4, (although we should estimate that x is closer to 3 than 4). Lets say x = a little more than 3. Y can still = ANYTHING NS
(2) 9^Y = 7. Notice that 9^0 =1 and 9^1 =9,therefore y is a little less than 1, however X can = ANYTHING NS
(1) and (2) x is between 3 and 4, and y is a little less than 1. Assuming the numbers picked for estimation are accurate enough (y is very close to 3.4), we will get an unequivocal YES as 3.4(.9) = 3.06> 3
The problem I have with this question, is it requires us to estimate exponential relationships to a level of precision that is unrealistic on this test. For example, what if the test taker estimated x to be 3.1, and y to be .9. That would give us xy> approx 2.6, which could give the reader a potential YES and NO.
Overall this is a high quality question as far as the skills the question tests, however.
