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Is 7^7/7^x an integer?

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Is 7^7/7^x an integer?  [#permalink]

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New post 19 Mar 2010, 19:35
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A
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Is \(\frac{7^7}{7^x}\) an integer?

(1) \(0\leq{x}\leq{7}\)
(2) \(|x|=x^2\)

(C) 2008 GMAT Club - m04#26

Statement (1) by itself is insufficient. S1 says that x can be between 0 and 7, so it can be an integer or any fraction.

Statement (2) by itself is sufficient. S2 implies that x is one of (-1, 0, 1). .

The correct answer is B.


WHY CAN THIS BE AN INTEGER OR ANY FRACTION, ISN'T IT ANY INTEGER ALL THE WAY. BECAUSE THE LEAST WHEN X= 7 IS 1 AND X=0 IS 7 * 7*7*7*7*7*7
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Re: Is 7^7/7^x an integer?  [#permalink]

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New post 20 Mar 2010, 07:53
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aramjung wrote:
Is \(\frac{7^7}{7^x}\) an integer?

(1) \(0\leq{x}\leq{7}\)
(2) \(|x|=x^2\)


stmt1: x can be fraction between 0 to 7 so insuff.
stmt2: |x| = x^2
-x = x^2 => x(x+1) = 0 => x = 0 or x = -1
or
x = x^2 => x(x-1) = 0 => x = 0 or x = 1
in any of the three cases 0, 1 , -1 it is going ot be an integer to sufficient.
Hence, B is the answer.
it cannot be fraction all the way, take for example x = 1/2 it is between 0 to 7 but 7^7/7^1/2 is not an integer
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Re: Is 7^7/7^x an integer?  [#permalink]

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New post 20 Mar 2010, 10:37
S1. It is not specified that x is an integer. Using a value such as x=3.5 in the original function will result in a non-integer. Insufficient.
S2. x can only be equal to -1, 0. or 1. Using these values in the original function will always result in an integer. Sufficient.

Answer is B
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Re: Is 7^7/7^x an integer?  [#permalink]

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New post 20 Mar 2010, 11:08
1.) x can be any value from 0-7 including decimals. so this is Insuff

2.) using B x= -1, 0, 1, -2, 2.....x is an integer.

Hence B
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Re: Is 7^7/7^x an integer?  [#permalink]

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New post 07 Oct 2015, 03:41
stmt1: x can be fraction between 0 to 7 so insuff.
stmt2: |x| = x^2
-x = x^2 => x(x+1) = 0 => x = 0 or x = -1
or
x = x^2 => x(x-1) = 0 => x = 0 or x = 1
in any of the three cases 0, 1 , -1 it is going ot be an integer to sufficient.
Hence, B is the answer.


hii please tell me how do we get just those 3 values for x.
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Re: Is 7^7/7^x an integer?  [#permalink]

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New post 07 Oct 2015, 05:35
shreeya wrote:
stmt1: x can be fraction between 0 to 7 so insuff.
stmt2: |x| = x^2
-x = x^2 => x(x+1) = 0 => x = 0 or x = -1
or
x = x^2 => x(x-1) = 0 => x = 0 or x = 1
in any of the three cases 0, 1 , -1 it is going ot be an integer to sufficient.
Hence, B is the answer.


hii please tell me how do we get just those 3 values for x.


Square \(|x| = x^2\):

\(x^2 = x^4\);

\(x^2 - x^4 = 0\);

\(x^2(1 - x^2) = 0\);

\(x^2(1 - x)(1 + x) = 0\);

\(x = 0\), \(x = 1\), or \(x = -1\).

Hope it's clear.
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Re: Is 7^7/7^x an integer?  [#permalink]

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New post 18 Sep 2019, 04:24
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Re: Is 7^7/7^x an integer?   [#permalink] 18 Sep 2019, 04:24
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