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Register now and save up to $200 Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code ## Difficult Math Problem #107 - Algebra This topic has 7 member replies 800guy Master | Next Rank: 500 Posts Joined 27 Jun 2006 Posted: 354 messages Followed by: 5 members Thanked: 11 times #### Difficult Math Problem #107 - Algebra Fri Mar 09, 2007 10:49 am Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) If operation$ is defined as
$X = X + 2 if X is even$X = X - 1 if X is odd,
what is $(...$($($(15)))...) 99 times?

(A) 120
(B) 180
(C) 210
(D) 225
(E) 250

from diff math doc, oa coming when people reply with explanations

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Badri Junior | Next Rank: 30 Posts
Joined
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Fri Mar 09, 2007 11:15 am
its a tricky Question

Start with the innermost '$' operation innermost :$(15) = 14 ; even !!!

next : $(14) = 16 ; even !!! next :$(16) = 18 ; even !!!!
......
.
.
.
. 98 times

Final answer = 14 + (2 + 2 + 2 + ....... 98 times)
= 14 + ( 2*98 )
= 14 + 196
= 210

So the correct answer is (c) 210

gabriel Legendary Member
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Fri Mar 09, 2007 11:18 am
800guy wrote:
If operation $is defined as$X = X + 2 if X is even
$X = X - 1 if X is odd, what is$(...$($($(15)))...) 99 times? (A) 120 (B) 180 (C) 210 (D) 225 (E) 250 from diff math doc, oa coming when people reply with explanations ...$(15)= 14..... then keep adding 2s to 14.... therefore the answer is 14 + 2*98= 210... c

800guy Master | Next Rank: 500 Posts
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Mon Mar 12, 2007 12:01 pm
oa:

don't really understand the oa provided in the doc, but here it is..

$15 gives 14 After that it is an AP with d=2, a=14 and n =99 ash_maverick Senior | Next Rank: 100 Posts Joined 07 Jan 2007 Posted: 31 messages Tue Mar 13, 2007 11:23 am The Oa ur r talking abt is not right. That gives the summation of all the numbers in that series. But here it is not asking asking about the summation of all the number in tht series. Just 2*98+14 should give the answer. 800guy Master | Next Rank: 500 Posts Joined 27 Jun 2006 Posted: 354 messages Followed by: 5 members Thanked: 11 times Tue Mar 13, 2007 11:25 am ash_maverick wrote: The Oa ur r talking abt is not right. That gives the summation of all the numbers in that series. But here it is not asking asking about the summation of all the number in tht series. Just 2*98+14 should give the answer. i think your right, ash. thanks!! Cybermusings Legendary Member Joined 27 Mar 2007 Posted: 559 messages Followed by: 2 members Thanked: 5 times Wed Mar 28, 2007 2:58 am Attack bracket by bracket -$15 = 15 - 1 = 14

$14 = 14 + 2 = 16$16 + 2 = 18

First time it will reduce the value by 1. For each successive time for the next 98 occasions it will increase the value by 2 So 14 + (2*98) = 210

### Top Member

Roland2rule Master | Next Rank: 500 Posts
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Fri Sep 29, 2017 3:22 pm
$X = X + 2 if X is even -----------(1)$X = X - 1 if X is odd, -------------(2)

from the question, it can be deduce that if x is an even number, we will use (1) but if it is odd number, we will use (2).
what is $(...$($($(15)))...) 99 times?
X=15 (an odd number)
eqn (2) is applicable here, substitute x=15
$15= 15-4 = 14 i will have to compute the progression$(...$($($(14)))...) p to 98 times and for each$, it just add 2 to the previous result.
so for the 98th timeprogression,
$15= (15-1) + (2*98)$15= 14 *+ 196
\$15= 210

Hence, the correct answer is C

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