Mar 19 08:00 AM PDT  09:00 AM PDT Beat the GMAT with a customized study plan based on your needs! Learn how to create your preparation timeline, what makes a good study plan and which tools you need to use to build the perfect plan. Register today! Mar 20 07:00 AM PDT  09:00 AM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Mar 20 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Wednesday, March 20th at 9 PM EDT Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score.
Author 
Message 
TAGS:

Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 902

Is xy>3?
[#permalink]
Show Tags
05 Mar 2019, 12:53
Question Stats:
72% (01:41) correct 28% (01:32) wrong based on 29 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



Manager
Joined: 16 Oct 2011
Posts: 82
GMAT 1: 620 Q37 V38 GMAT 2: 640 Q36 V41 GMAT 3: 650 Q42 V38 GMAT 4: 650 Q44 V36 GMAT 5: 570 Q31 V38

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: 902

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: 82
GMAT 1: 620 Q37 V38 GMAT 2: 640 Q36 V41 GMAT 3: 650 Q42 V38 GMAT 4: 650 Q44 V36 GMAT 5: 570 Q31 V38

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: 902

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: 902

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



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 902

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: 82
GMAT 1: 620 Q37 V38 GMAT 2: 640 Q36 V41 GMAT 3: 650 Q42 V38 GMAT 4: 650 Q44 V36 GMAT 5: 570 Q31 V38

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?



CEO
Joined: 12 Sep 2015
Posts: 3506
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: 902

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










