Difficult Math Problem #107 - Algebra

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

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

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

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.

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!!

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

$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