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
Difficult Math Problem #107 - Algebra
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its a tricky Question
Start with the innermost '$' operation
innermost : $(15) = 14 ; even !!!
next : $(14) = 16 ; even !!!
next : $(16) = 18 ; even !!!!
......
.
.
.
. 98 times
Final answer = 14 + (2 + 2 + 2 + ....... 98 times)
= 14 + ( 2*98 )
= 14 + 196
= 210
So the correct answer is (c) 210
Start with the innermost '$' operation
innermost : $(15) = 14 ; even !!!
next : $(14) = 16 ; even !!!
next : $(16) = 18 ; even !!!!
......
.
.
.
. 98 times
Final answer = 14 + (2 + 2 + 2 + ....... 98 times)
= 14 + ( 2*98 )
= 14 + 196
= 210
So the correct answer is (c) 210
- gabriel
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...$(15)= 14..... then keep adding 2s to 14.... therefore the answer is 14 + 2*98= 210... c800guy 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
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- Joined: Sun Jan 07, 2007 11:13 pm
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.
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.
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i think your right, ash. thanks!!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.
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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
$15 = 15 - 1 = 14
$ 14 = 14 + 2 = 16
$16 + 2 = 18
First time it will reduce the value by 1. For each successive time for the next 98 occasions it will increase the value by 2 So 14 + (2*98) = 210
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$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
$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