Oct 22 08:00 AM PDT  09:00 AM PDT Join to learn strategies for tackling the longest, wordiest examples of Counting, Sets, & Series GMAT questions Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Is xy>3?
[#permalink]
Show Tags
05 Mar 2019, 12:53
Question Stats:
71% (01:49) correct 29% (01:54) wrong based on 117 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net




GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: Is xy>3?
[#permalink]
Show Tags
05 Mar 2019, 14:22
fskilnik wrote: GMATH practice exercise (Quant Class 14)
Is \(xy >3\) ?
(1) \(7^x > 729\) (2) \(9^y = 7\)
\(xy\,\,\mathop > \limits^? \,\,3\) \(\left( 1 \right)\,\,{7^x} > 729\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,0} \right)\,\,\,\,\,\left[ {{7^4} = {{49}^2}} \right]\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\) \(\left( 2 \right)\,\,{9^y} = 7\,\,\,\, \Rightarrow \,\,\,y = {y_p}\,\,\,{\rm{unique}}\,\,{\rm{,}}\,\,\,{1 \over 2}\,\,{\rm{ < }}\,\,{y_p} < 1\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0,{y_p}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {6,{y_p}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\) \(\left( {1 + 2} \right)\,\,\,{3^6} = 729\,\,\,\mathop < \limits^{\left( 1 \right)} \,\,\,{7^x}\,\,\mathop = \limits^{\left( 2 \right)} \,\,\,{\left( {{9^y}} \right)^x} = {3^{2xy}}\,\,\,\,\,\mathop \Rightarrow \limits^{3\,\, > \,\,1} \,\,\,2xy > 6\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle\) The correct answer is (C). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net




Manager
Joined: 16 Oct 2011
Posts: 107
GMAT 1: 570 Q39 V41 GMAT 2: 640 Q38 V31 GMAT 3: 650 Q42 V38 GMAT 4: 650 Q44 V36 GMAT 5: 570 Q31 V38
GPA: 3.75

Is xy>3?
[#permalink]
Show Tags
Updated on: 05 Mar 2019, 14:12
fskilnik wrote: 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. 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.
Originally posted by ocelot22 on 05 Mar 2019, 13:23.
Last edited by ocelot22 on 05 Mar 2019, 14:12, edited 3 times in total.



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: Is xy>3?
[#permalink]
Show Tags
05 Mar 2019, 13:42
ocelot22 wrote: (1) and (2) x>3 and 0<y<1. Then 0<XY<3, which gives us a definite NO
Hi ocelot22 ! Thanks for joining! The two inequalities you mentioned (repeated above) are enough for your conclusion (in red)? Another thing: I guarantee (1+2) is enough for a definite YES!! My solution is short but very instructive. Think a bit more before I present it! Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Manager
Joined: 16 Oct 2011
Posts: 107
GMAT 1: 570 Q39 V41 GMAT 2: 640 Q38 V31 GMAT 3: 650 Q42 V38 GMAT 4: 650 Q44 V36 GMAT 5: 570 Q31 V38
GPA: 3.75

Re: Is xy>3?
[#permalink]
Show Tags
05 Mar 2019, 13:59
fskilnik wrote: ocelot22 wrote: (1) and (2) x>3 and 0<y<1. Then 0<XY<3, which gives us a definite NO
Hi ocelot22 ! Thanks for joining! The two inequalities you mentioned (repeated above) are enough for your conclusion (in red)? Another thing: I guarantee (1+2) is enough for a definite YES!! My solution is short but very instructive. Think a bit more before I present it! Regards, Fabio. You are right. I use potentially inappropriate interval techniques for this problem, and have corrected my mistakes from before. Can you please however, look over my edited post, which points out some concerns I have pointed out about this problem



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: Is xy>3?
[#permalink]
Show Tags
05 Mar 2019, 14:13
ocelot22 wrote: You are right. I use potentially inappropriate interval techniques for this problem, and have corrected my mistakes from before. Can you please however, look over my edited post, which points out some concerns I have pointed out about this problem I am glad your interest in my problem continues, ocelot22 . ocelot22 wrote: 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 would be A NO answer to the question. This would be true only if you had no choice but to insist on your approach... higherlevel problems are harder (also) because a proper way of dealing with them are not always seen at first! Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: Is xy>3?
[#permalink]
Show Tags
05 Mar 2019, 14:17
ocelot22 wrote: 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. Thanks for the comment in blue. I guess you will find the question much more interesting after analysing my solution. I will post it below right now!
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Manager
Joined: 16 Oct 2011
Posts: 107
GMAT 1: 570 Q39 V41 GMAT 2: 640 Q38 V31 GMAT 3: 650 Q42 V38 GMAT 4: 650 Q44 V36 GMAT 5: 570 Q31 V38
GPA: 3.75

Is xy>3?
[#permalink]
Show Tags
05 Mar 2019, 15:12
fskilnik wrote: fskilnik wrote: GMATH practice exercise (Quant Class 14)
Is \(xy >3\) ?
(1) \(7^x > 729\) (2) \(9^y = 7\)
\(xy\,\,\mathop > \limits^? \,\,3\) \(\left( 1 \right)\,\,{7^x} > 729\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,0} \right)\,\,\,\,\,\left[ {{7^4} = {{49}^2}} \right]\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\) \(\left( 2 \right)\,\,{9^y} = 7\,\,\,\, \Rightarrow \,\,\,y = {y_p}\,\,\,{\rm{unique}}\,\,{\rm{,}}\,\,\,{1 \over 2}\,\,{\rm{ < }}\,\,{y_p} < 1\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0,{y_p}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {6,{y_p}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\) \(\left( {1 + 2} \right)\,\,\,{3^6} = 729\,\,\,\mathop < \limits^{\left( 1 \right)} \,\,\,{7^x}\,\,\mathop = \limits^{\left( 2 \right)} \,\,\,{\left( {{9^y}} \right)^x} = {3^{2xy}}\,\,\,\,\,\mathop \Rightarrow \limits^{3\,\, > \,\,1} \,\,\,2xy > 6\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle\) The correct answer is (C). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. This is a very succinct solution. I Appreciate the compact notation used. This of course avoids the estimation pitfall that I ran into in my solution. I am guessing that you teach this kind of notation in your course?



GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4015
Location: Canada

Re: Is xy>3?
[#permalink]
Show Tags
05 Mar 2019, 15:27
fskilnik wrote: Is \(xy >3\) ?
(1) \(7^x > 729\) (2) \(9^y = 7\)
Target question: Is xy > 3 ? Statement 1: (7^x) > 729Since there's no information about y, we cannot answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: (9^y) = 7Since there's no information about x, we cannot answer the target question with certainty. Statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that (7^x) > 729 Statement 2 tells us that (9^y) = 7 Take the inequality ( 7^x) > 729, and replace 7 with 9^y to get: ( 9^y)^x > 729 Simplify to get: 9^xy > 729 Rewrite 729 as 9^3 to get: 9^xy > 9^3 From this, we can conclude that xy > 3Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C Cheers, Brent
_________________
Test confidently with gmatprepnow.com



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: Is xy>3?
[#permalink]
Show Tags
05 Mar 2019, 15:57
ocelot22 wrote: This is a very succinct solution. I Appreciate the compact notation used. This of course avoids the estimation pitfall that I ran into in my solution. I am guessing that you teach this kind of notation in your course? Hi, ocelot22 ! First of all, thanks for the kudos (both in the question stem and also in my solution)! I am glad you liked our notation/solution. YES, the precision and brevity of our exclusive notation is an IMPORTANT part of our method, especially in Data Sufficiency! I will not come into details here, due to respect for all companies, teachers, and students who have their own (probably different) opinions on the matter (or never thought about it). In our "test drive" you will earn two credits for questions. Feel free to use one of them to ask me about this at your free trial! (*) Regards, Fabio. (*) P.S.: although the number of question credits is limited per student (to avoid someone asking me, say, 10 questions a day "to avoid" thinking by himself/herself beforehand), I usually reimburse each credit used. (I am the sole creator of the method and the only person who answers questions in our preparation.)
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



VP
Joined: 23 Feb 2015
Posts: 1262

Is xy>3?
[#permalink]
Show Tags
29 Mar 2019, 11:58
fskilnik wrote: fskilnik wrote: GMATH practice exercise (Quant Class 14)
Is \(xy >3\) ?
(1) \(7^x > 729\) (2) \(9^y = 7\)
\(xy\,\,\mathop > \limits^? \,\,3\) \(\left( 1 \right)\,\,{7^x} > 729\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,0} \right)\,\,\,\,\,\left[ {{7^4} = {{49}^2}} \right]\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\) \(\left( 2 \right)\,\,{9^y} = 7\,\,\,\, \Rightarrow \,\,\,y = {y_p}\,\,\,{\rm{unique}}\,\,{\rm{,}}\,\,\,{1 \over 2}\,\,{\rm{ < }}\,\,{y_p} < 1\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0,{y_p}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {6,{y_p}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\) \(\left( {1 + 2} \right)\,\,\,{3^6} = 729\,\,\,\mathop < \limits^{\left( 1 \right)} \,\,\,{7^x}\,\,\mathop = \limits^{\left( 2 \right)} \,\,\,{\left( {{9^y}} \right)^x} = {3^{2xy}}\,\,\,\,\,\mathop \Rightarrow \limits^{3\,\, > \,\,1} \,\,\,2xy > 6\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle\) The correct answer is (C). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. fskilnik, Sir, do you want to mean 2>1 (talking about statement) in the red part? Regards, Asad
Attachments
solution.PNG [ 57.29 KiB  Viewed 716 times ]
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”― Henry Wadsworth LongfellowDo you need official questions for Quant?3700 Unique Official GMAT Quant Questions SEARCH FOR ALL TAGSGMAT Club Tests



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: Is xy>3?
[#permalink]
Show Tags
29 Mar 2019, 16:09
@AsadAbu wrote: fskilnik, Sir, do you want to mean 2>1 (talking about statement) in the red part? Regards, Asad Hi, Asad (@AsadAbu)! Sorry for the delay (very busy)! Thank you for your REAL interest in my solution. Answering your (important) question: I said \({3^6} < {3^{2xy}}\,\,\,\mathop \Rightarrow \limits^{3\, > \,1} \,\,\,6 < 2xy\) Meaning: from the fact that the exponential function \(y = 3^x\) has a base that is greater than 1 (=3), it is an (strictly) increasing function: \(x < y\,\,\,\, \Rightarrow \,\,\,{3^x} < {3^y}\) From this fact, please note that: \(6 \ge 2xy\,\,\,\mathop \Rightarrow \limits^{3\, > \,1} \,\,\,{3^6} \ge {3^{2xy}}\,\,\,\left( {{\rm{impossible,}}\,\,{\rm{because}}\,\,{3^6} < {3^{2xy}}} \right)\) That´s (finally!) the reason for the validity of the implication \({3^6} < {3^{2xy}}\,\,\,\mathop \Rightarrow \limits^{3\, > \,1} \,\,\,6 < 2xy\) ... Best Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



VP
Joined: 23 Feb 2015
Posts: 1262

Re: Is xy>3?
[#permalink]
Show Tags
02 Apr 2019, 11:17
Thank you so much...
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”― Henry Wadsworth LongfellowDo you need official questions for Quant?3700 Unique Official GMAT Quant Questions SEARCH FOR ALL TAGSGMAT Club Tests



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: Is xy>3?
[#permalink]
Show Tags
02 Apr 2019, 13:27
AsadAbu wrote: Thank you so much...
Our pleasure, AsadAbu. If you (and other readers) liked our approach and explanations, we invite you to try our test drive ("Free Trial"), so that you will have a MUCH better understanding of our METHOD, that is, our systematic (and very deep!) way of looking into the GMAT´s contents with all objectivity, subtleness and "venom" that characterizes highlevel performances in the quant section of the test. We create and post new questions there (such as this one) on an almost daily basis, by the way. Regards and success in your studies, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



VP
Joined: 23 Feb 2015
Posts: 1262

Re: Is xy>3?
[#permalink]
Show Tags
02 Apr 2019, 14:08
fskilnik wrote: AsadAbu wrote: Thank you so much...
Our pleasure, AsadAbu. If you (and other readers) liked our approach and explanations, we invite you to try our test drive ("Free Trial"), so that you will have a MUCH better understanding of our METHOD, that is, our systematic (and very deep!) way of looking into the GMAT´s contents with all objectivity, subtleness and "venom" that characterizes highlevel performances in the quant section of the test. We create and post new questions there (such as this one) on an almost daily basis, by the way. Regards and success in your studies, Fabio. I'm going to try ""Free Trial"" from tomorrow. Thanks__
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”― Henry Wadsworth LongfellowDo you need official questions for Quant?3700 Unique Official GMAT Quant Questions SEARCH FOR ALL TAGSGMAT Club Tests



Intern
Joined: 10 Apr 2019
Posts: 18

Re: Is xy>3?
[#permalink]
Show Tags
20 May 2019, 14:01
GMATPrepNow wrote: fskilnik wrote: Is \(xy >3\) ?
(1) \(7^x > 729\) (2) \(9^y = 7\)
Target question: Is xy > 3 ? Statement 1: (7^x) > 729Since there's no information about y, we cannot answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: (9^y) = 7Since there's no information about x, we cannot answer the target question with certainty. Statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that (7^x) > 729 Statement 2 tells us that (9^y) = 7 Take the inequality ( 7^x) > 729, and replace 7 with 9^y to get: ( 9^y)^x > 729 Simplify to get: 9^xy > 729 Rewrite 729 as 9^3 to get: 9^xy > 9^3 From this, we can conclude that xy > 3Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C Cheers, Brent Hi Brent, Could you please clarify if it is always possible to replace one part of the inequality completely, just like you are doing in your solution Quote: Take the inequality (7^x) > 729, and replace 7 with 9^y to get: (9^y)^x > 729










