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M08-35 If operation @X is defined as @X=X+2 if X is even and

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M08-35 If operation @X is defined as @X=X+2 if X is even and [#permalink]  09 Sep 2013, 16:59
If operation @X is defined as @X=X+2 if X is even and @X=X−1 if X is odd, what is @(...@(@(@(15)))...) 99 times?

A. 120
B. 180
C. 210
D. 225
E. 250

[Reveal] Spoiler:
Bunuel, wouldn't operation become an AP sequence after the second term? So you have n = 98 and a = 14, therefore, you should end up with 208 -----> 14+97*2 (a+(n-1)d).

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Re: M08-35 If operation @X is defined as @X=X+2 if X is even and [#permalink]  10 Sep 2013, 04:57
Expert's post
vaishnogmat wrote:
Q) If operation @X is defined as @X=X+2 if X is even and @X=X−1 if X is odd, what is @(...@(@(@(15)))...) 99 times?

a) 120
b) 180
c) 210
d) 225
e) 250

Bunuel, wouldn't operation become an AP sequence after the second term? So you have n = 98 and a = 14, therefore, you should end up with 208 -----> 14+97*2 (a+(n-1)d).

@(15)=14. We have to compute @(...@(@(@(14)))...) 98 times. Each @ just adds 2 to the previous result. Therefore, @(...@(@(@(14)))...)98 times=14+2∗98=210.

Consider this: @(@(@14)) = @(@16) = @18 = 20 = 14+2*3 (for 3 @'s). So, for 98 @ we'll have 14+2*98=210.
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Re: M08-35 If operation @X is defined as @X=X+2 if X is even and   [#permalink] 10 Sep 2013, 04:57
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M08-35 If operation @X is defined as @X=X+2 if X is even and

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