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is z divisible by 9

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by gmatmachoman » Mon May 31, 2010 12:38 am
If z = x^n - 19, is z divisible by 9?
1) x = 10; n is a positive integer
2) z + 981 is a multiple of 9
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Source: — Data Sufficiency |
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by 4GMAT_Mumbai » Mon May 31, 2010 12:50 am
Hi,

z is one of -9, 81, 981, 9981, 99981 etc. Answer to the question 'Yes'.
if z + 9(109) is a multiple of 9; then z should also be a multiple of 9. Answer to the question 'Yes'.

Hence, answer is D

However, considering that gmatmachoman has posted this, something tells me that it cannot be so easy ;-D ... Am I missing something ...
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by gmatmachoman » Mon May 31, 2010 1:04 am
4GMAT_Mumbai wrote:Hi,

z is one of -9, 81, 981, 9981, 99981 etc. Answer to the question 'Yes'.
if z + 9(109) is a multiple of 9; then z should also be a multiple of 9. Answer to the question 'Yes'.

Hence, answer is D

However, considering that gmatmachoman has posted this, something tells me that it cannot be so easy ;-D ... Am I missing something ...
hahahahaha!!! OMG..i never thought I am making such a "impact" on this wonderful forum!!

But yeah it was easy question .....and OA is indeed D.
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by liferocks » Mon May 31, 2010 1:39 am
From 1
19%9=1 and 10%9=+1
hence (x^n-19)%9=0..sufficient
the thing I don't understand here is,why it is given 'n is a positive integer '..this is not really required

From 2
981%9 =0..since (z+981)%9=0...z must be divisible by 9..sufficient.

option D
"If you don't know where you are going, any road will get you there."
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