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# Does 5^x=7^y?

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Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1324
Location: Malaysia

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08 Feb 2017, 00:28
1
6
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Difficulty:

95% (hard)

Question Stats:

37% (01:32) correct 63% (01:29) wrong based on 142 sessions

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Tricky Question.

Does $$5^x=7^y$$?

(1) $$x>y>0$$

(2) $$x$$ and $$y$$ are both even.

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Joined: 02 Aug 2009
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08 Feb 2017, 03:54
1
5
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 non-integer 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 non-integer 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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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##### General Discussion
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Joined: 26 Mar 2016
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Location: India
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21 Sep 2017, 08:31
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 non-integer 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 non-integer 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 non-integer value of x and y, both will be EQUAL..
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28 Mar 2018, 04:36
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 ??

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Joined: 02 Aug 2009
Posts: 7108

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28 Mar 2018, 05:48
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 ??

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Hi..
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..
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Intern
Joined: 09 Jun 2016
Posts: 15

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28 Mar 2018, 07:00
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.

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Joined: 09 Mar 2018
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28 Mar 2018, 07:11
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.
Senior Manager
Joined: 14 Feb 2018
Posts: 395

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28 Mar 2018, 20:24
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 app

Hi..
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 ?

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Joined: 20 Sep 2016
Posts: 547

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28 Mar 2018, 22:26
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.

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Director
Joined: 20 Sep 2016
Posts: 547

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28 Mar 2018, 22:27
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 non-integer 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 non-integer 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.

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Re: Does 5^x=7^y? &nbs [#permalink] 28 Mar 2018, 22:27
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