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x raised to any odd integer

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x raised to any odd integer

by sanju09 » Fri Oct 15, 2010 10:47 pm
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.


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by this_time_i_will » Fri Oct 15, 2010 11:06 pm
IMO C
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by diebeatsthegmat » Fri Oct 29, 2010 7:47 pm
sanju09 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.


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C too :(
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by goyalsau » Fri Oct 29, 2010 9:04 pm
I have realized that for the last couple of days, Most of the times my answer is E

and one more E,

What is the OA ?
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by oddball » Fri Oct 29, 2010 10:04 pm
sanju09 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.


[spoiler]Source: https://www.platinumgmat.com[/spoiler]
What's the OA? I am getting A.
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by sasawlani » Fri Oct 29, 2010 10:06 pm
sanju09 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.


[spoiler]Source: https://www.platinumgmat.com[/spoiler]
Ofcourse "C".
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by Rahul@gurome » Sat Oct 30, 2010 1:33 am
sanju09 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.
[spoiler]Source: https://www.platinumgmat.com[/spoiler]
Given: x is an integer and x raised to any odd power is greater than zero.
Implies, x is a positive integer.

Statement 1: z < 25 and w = 7^x
Therefore, w - z = 7^x - z > 7^x - 25
Now, for any positive integer x
  • (1) 7^x = 7*7^(x - 1) > 5*7^(x - 1)
    (2) 5^(x + 1) is greater than or equal to 25
w - z = 7^x - z > 7^x - 25 > 5*7^(x - 1) - 25 => 5*7^(x - 1) - 5^(x + 1) = 5*[7^(x - 1) - 5^x]

Sufficient.

Statement 2: We don't know anything about w and z.

Not sufficient.

The correct answer is A.
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by sanju09 » Sat Oct 30, 2010 2:11 am
Just received a PM demanding the OA for this:

This is clear that x is a positive integer; now, w and z are some numbers we don't know, with a question:

Is w - z > 5 {7^(x - 1) - 5^x}?

[1] The minimum x is 1, which minimizes w - z to just more than -18, and turns 5 {7^(x - 1) - 5^x} to be equal to -20. Anything more than -18 is always greater than -20. For other positive integers x, greater than 1, w - z will be positive, and 5 {7^(x - 1) - 5^x} always a negative, hence keeping the statement as always true. We do not need to fix a positive integer for x in order to make w - z > 5 {7^(x - 1) - 5^x} as true. This is sufficient

[2] This alone is always insufficient, as it never tells anything about w and z.


[spoiler]IMO happens to be the suggested OA in some cases.

IMO: A[/spoiler]
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by Rezinka » Sat Oct 30, 2010 2:12 am
I'm getting A too
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