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x is an integer and x raised to any odd integer is greater

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jamifahad
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x is an integer and x raised to any odd integer is greater [#permalink] New post   Updated on: 19 Jul 2012, 02:55
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x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^(x-1)-5^x?

(1) z < 25 and w=7^x
(2) x = 4

OPEN DISCUSSION OF THIS QUESTION IS HERE: x-is-an-integer-and-x-raised-to-any-odd-integer-is-greater-95476.html
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Originally posted by jamifahad on 05 Sep 2011, 05:15.
Last edited by Bunuel on 19 Jul 2012, 02:55, edited 2 times in total.
Edited the question. Topic locked.
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Re: x is an integer and x raised to any odd integer is greater [#permalink] New post   19 Jul 2012, 02:57
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x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^(x-1)-5^x?

"x is an integer and x raised to any odd integer is greater than zero" means \(x=integer>0\).
Q: is \(w-z>5(7^{x-1}-5^x)\)?

(1) \(z<25\) and \(w=7^x\) --> is \(7^x-z>5(7^{x-1}-5^x)\)? --> is \(7^x-z>5*7^{x-1}-5^{x+1}\)? --> is \(7^x-5*7^{x-1}+5^{x+1}>z\)? --> as the lowest value of \(x\) is 1, then the lowest value of LHS is when \(x=1\): \(LHS_{min}=7^x-5*7^{x-1}+5^{x+1}=7-5+25=27\) --> so the lowest value of LHS is 27, which is more than \(z\) as \(z<25\) --> hence \(7^x-5*7^{x-1}+5^{x+1}>z\) is true. Sufficient.

(2) \(x = 4\). No info about \(w\) and \(z\). Not sufficient.

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: x-is-an-integer-and-x-raised-to-any-odd-integer-is-greater-95476.html[/quote]
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Re: Exponential [#permalink] New post   01 Oct 2011, 05:59
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jamifahad wrote:
x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7\(^(x-1)\) - \(5^x\)?

1) z < 25 and w =\(7^x\)
2) x = 4


A for me. And it took me 4 min to solve this :(

Information from the question stem: x raised to any odd integer is greater than zero ----> it implies that x>0 because x raised to even power will always greater than zero. (understanding this took most of time...after I came to this, it was easy. GMAT really is all about tricks :))

Statement 1: z <25, lets assume z = 24 (this way we will minimize the value of w-z and if even after minimizing w-z > 5(7^(x-1) - 5^x), we will get our answer)

Let x=1, w-z = 7-24 = -17
5(7^(x-1) - 5^x) = 5(1-5) = -20. YES

Let x = 3, w-z = 343 - 24 = 319
5(7^(x-1) - 5^x) = 5(49 - 125) = a negative value. Again YES

Similarly you can prove for any value of x.
Hence SUFFICIENT

A small tip: you don't need to calculate the values, you can clearly see that as the value of x increases, w-z will increase exponentially and 5(7^(x-1) - 5^x) will keep on decreasing.

Statement 2: clearly its NOT SUFFICIENT. We don't have any information about w and z.

Hope this helps.
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Re: Exponential [#permalink] New post   05 Sep 2011, 06:21
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Hey,

this is weird. The question states if w-z > 5(7x-1 - 5x), which is w-z > 10x - 5, right?

According to statement 1,

Is 7x - z > 10x - 5

When x = 2 and z = 1 then:

7(2) - 1 < 15

When x = 2 and z = -10 then:

7(2) + 10 > 15

Surely that's not enough.

The original info says that x to the power of any odd integer is greater than zero, which means x = positive
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Re: Exponential [#permalink] New post   05 Sep 2011, 06:31
Apology.
I posted question incorrectly. I have corrected it now.
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Re: x is an integer and x raised to any odd integer is greater [#permalink] New post   26 Dec 2011, 18:54
+1 A

I don't think it is a GMAT like question.
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Re: x is an integer and x raised to any odd integer is greater [#permalink] New post   18 Jul 2012, 12:44
Why can't x = 0?

0 is an integer too.

If x = 0, then 5^x+1 = 5, and statement 1 is no longer sufficient to answer the question! Please help!
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Re: x is an integer and x raised to any odd integer is greater [#permalink] New post   18 Jul 2012, 16:11
piccolina wrote:
Why can't x = 0?

0 is an integer too.

If x = 0, then 5^x+1 = 5, and statement 1 is no longer sufficient to answer the question! Please help!


read the question again. X raised to any odd number > 0..how can x be 0
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Re: x is an integer and x raised to any odd integer is greater [#permalink] New post   19 Jul 2012, 03:01
Brilliant explanation Bunuel !! Even though I got it right but your explanation is the best.

Solving a question right might not teach me anything new, but your explanation really does !!
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Re: x is an integer and x raised to any odd integer is greater [#permalink]
19 Jul 2012, 03:01
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Bunuel
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