Author 
Message 
TAGS:

Hide Tags

Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1286
Location: Malaysia

Does 5^x=7^y? [#permalink]
Show Tags
08 Feb 2017, 01:28
1
This post received KUDOS
6
This post was BOOKMARKED
Question Stats:
33% (01:14) correct 67% (02:54) wrong based on 138 sessions
HideShow timer Statistics
Tricky Question. Does \(5^x=7^y\)? (1) \(x>y>0\) (2) \(x\) and \(y\) are both even.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
"Be challenged at EVERY MOMENT."
“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”
"Each stage of the journey is crucial to attaining new heights of knowledge."
Rules for posting in verbal forum  Please DO NOT post short answer in your post!



Math Expert
Joined: 02 Aug 2009
Posts: 5780

Re: Does 5^x=7^y? [#permalink]
Show Tags
08 Feb 2017, 04:54
1
This post received KUDOS
Expert's post
5
This post was BOOKMARKED
ziyuenlau wrote: Tricky Question. Does \(5^x=7^y\)? (1) \(x>y>0\) (2) \(x\) and \(y\) are both even. Hi When can \(5^x=7^y\)?.. When x=y=0, both are EQUAL to 1.. Also for a certain noninteger value of x and y, both will be EQUAL..
Let's see the statements... (1) \(x>y>0\) X=y=0 is ruled out but still for a certain noninteger value of x and y, both will be EQUAL otherwise they will not be same.. Insufficient.. (2) \(x\) and \(y\) are both even.[/quote] x=y=0, and is YES.. x=0, y=2, ans is NO.. Insufficient.. Combined.. Both are even and not ZERO, so ans will always be NO.. Sufficient C
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor



Manager
Joined: 26 Mar 2016
Posts: 59
Location: India
Concentration: Strategy, General Management
GRE 1: 313 Q166 V147
GPA: 3.3
WE: Other (Consulting)

Re: Does 5^x=7^y? [#permalink]
Show Tags
21 Sep 2017, 09:31
chetan2u wrote: ziyuenlau wrote: Tricky Question. Does \(5^x=7^y\)? (1) \(x>y>0\) (2) \(x\) and \(y\) are both even. Hi When can \(5^x=7^y\)?.. When x=y=0, both are EQUAL to 1.. Also for a certain noninteger value of x and y, both will be EQUAL..
Let's see the statements... (1) \(x>y>0\) X=y=0 is ruled out but still for a certain noninteger value of x and y, both will be EQUAL otherwise they will not be same.. Insufficient.. (2) \(x\) and \(y\) are both even. x=y=0, and is YES.. x=0, y=2, ans is NO.. Insufficient.. Combined.. Both are even and not ZERO, so ans will always be NO.. Sufficient C[/quote] Hello Chetan, Could you please explain on this Also for a certain noninteger value of x and y, both will be EQUAL..
_________________
23 Kudos left to unlock next level. Help me by Contributing one for cause .. Please
My failed GMAT experience ... https://gmatclub.com/forum/gmatbadexperience640needsuggestionsonverbalimprovement251308.html
My review on EmpowerGMAT : https://gmatclub.com/reviews/comments/empowergmatonlinecourse345355767



Manager
Joined: 14 Feb 2018
Posts: 198

Re: Does 5^x=7^y? [#permalink]
Show Tags
28 Mar 2018, 05:36
But how do we know that apart from 0 if there is/are another value which satisfies the equation is even or not. If one pair is even, then answer will be C, but if more than one, it might be E. How can we conclude in this way without knowing other possible values of x and y ?? Sent from my Lenovo K53a48 using GMAT Club Forum mobile app



Math Expert
Joined: 02 Aug 2009
Posts: 5780

Re: Does 5^x=7^y? [#permalink]
Show Tags
28 Mar 2018, 06:48
SonalSinha803 wrote: But how do we know that apart from 0 if there is/are another value which satisfies the equation is even or not. If one pair is even, then answer will be C, but if more than one, it might be E. How can we conclude in this way without knowing other possible values of x and y ?? Sent from my Lenovo K53a48 using GMAT Club Forum mobile appHi.. If x and y are integer.. 5^x will have only 1 and 5 as factor and 7^y will have 1 and 7 as factor.. So they both cannot be equal ever.. Only possiblity is if both are 1 when x and y are 0.. Also there is always some non integer value where 5°x could be 7..
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor



Intern
Joined: 09 Jun 2016
Posts: 15

Re: Does 5^x=7^y? [#permalink]
Show Tags
28 Mar 2018, 08:00
Chetan2u... can you please elaborate which all non integer values are available wherein 5^x equals 7... as if as a layman I solve question then I would have marked A without knowing the values of non integers. Sent from my SMG935F using GMAT Club Forum mobile app



Intern
Joined: 09 Mar 2018
Posts: 1

Re: Does 5^x=7^y? [#permalink]
Show Tags
28 Mar 2018, 08:11
why is it not A? Since, x and y are greater than 0, 5 to any power cannot be equal to 7 to any power.



Manager
Joined: 14 Feb 2018
Posts: 198

Re: Does 5^x=7^y? [#permalink]
Show Tags
28 Mar 2018, 21:24
chetan2u wrote: SonalSinha803 wrote: But how do we know that apart from 0 if there is/are another value which satisfies the equation is even or not. If one pair is even, then answer will be C, but if more than one, it might be E. How can we conclude in this way without knowing other possible values of x and y ?? Sent from my Lenovo K53a48 using GMAT Club Forum mobile appHi.. If x and y are integer.. 5^x will have only 1 and 5 as factor and 7^y will have 1 and 7 as factor.. So they both cannot be equal ever.. Only possiblity is if both are 1 when x and y are 0.. Also there is always some non integer value where 5°x could be 7.. Okay got it.....and now I know decimals cannot be even or odd....this is where I was confused.... thankyou so much ? Sent from my Lenovo K53a48 using GMAT Club Forum mobile app



Manager
Joined: 20 Sep 2016
Posts: 120

Re: Does 5^x=7^y? [#permalink]
Show Tags
28 Mar 2018, 23:26
lilyb wrote: why is it not A? Since, x and y are greater than 0, 5 to any power cannot be equal to 7 to any power. There is always some NON integer (decimal) value for which the entities will be equal. If you want to know this for sure. Apply logarithm to both sides of equation. After applying look into the log table for log 5 and log 7. And for some certain value the product on both the values will be equal. Sent from my XT1562 using GMAT Club Forum mobile app



Manager
Joined: 20 Sep 2016
Posts: 120

Re: Does 5^x=7^y? [#permalink]
Show Tags
28 Mar 2018, 23:27
chetan2u wrote: ziyuenlau wrote: Tricky Question. Does \(5^x=7^y\)? (1) \(x>y>0\) (2) \(x\) and \(y\) are both even. Hi When can \(5^x=7^y\)?.. When x=y=0, both are EQUAL to 1.. Also for a certain noninteger value of x and y, both will be EQUAL..
Let's see the statements... (1) \(x>y>0\) X=y=0 is ruled out but still for a certain noninteger value of x and y, both will be EQUAL otherwise they will not be same.. Insufficient.. (2) \(x\) and \(y\) are both even. x=y=0, and is YES.. x=0, y=2, ans is NO.. Insufficient.. Combined.. Both are even and not ZERO, so ans will always be NO.. Sufficient C[/quote] The best point chetan2u does not fail to consider like the rest is x and y in statement 1 can be non integers. Sent from my XT1562 using GMAT Club Forum mobile app










