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Does 5^x = 7^y? (1) x > y > 0 (2) x and y are both even. 08 Feb 2017, 01:28
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C
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85% (hard)

Question Stats:

33% (01:25) correct 67% (01:20) wrong based on 236 sessions

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Does \(5^x=7^y\)?

(1) \(x>y>0\)

(2) \(x\) and \(y\) are both even.
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C
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Does 5^x = 7^y? (1) x > y > 0 (2) x and y are both even. 08 Feb 2017, 04:54
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ziyuenlau

Tricky Question.



Does \(5^x=7^y\)?

(1) \(x>y>0\)

(2) \(x\) and \(y\) are both even.
Show more


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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Does 5^x = 7^y? (1) x > y > 0 (2) x and y are both even. 21 Sep 2017, 09:31
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chetan2u
ziyuenlau

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.
Show more
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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Does 5^x = 7^y? (1) x > y > 0 (2) x and y are both even. 28 Mar 2018, 05:36
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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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Does 5^x = 7^y? (1) x > y > 0 (2) x and y are both even. 28 Mar 2018, 06:48
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SonalSinha803
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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Show more

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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Does 5^x = 7^y? (1) x > y > 0 (2) x and y are both even. 28 Mar 2018, 08:00
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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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Does 5^x = 7^y? (1) x > y > 0 (2) x and y are both even. 28 Mar 2018, 08:11
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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.
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Does 5^x = 7^y? (1) x > y > 0 (2) x and y are both even. 28 Mar 2018, 21:24
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chetan2u
SonalSinha803
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..
Show more
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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Does 5^x = 7^y? (1) x > y > 0 (2) x and y are both even. 28 Mar 2018, 23:26
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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.
Show more
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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Does 5^x = 7^y? (1) x > y > 0 (2) x and y are both even. 28 Mar 2018, 23:27
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chetan2u
ziyuenlau

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.
Show more
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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Does 5^x = 7^y? (1) x > y > 0 (2) x and y are both even. 23 Jul 2025, 00:29
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