Function Data Sufficiency question

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Striver: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Tue May 29, 2012 3:30 pm

by Striver » Sun Sep 09, 2012 1:21 pm

The sequence a1, a2....., an,...is such that an = 2an-1 - X for all positive integers n is greater than or equal to 2 and for certain number X. If a5 = 99 and a3 = 27, what is the value of X?

A. 3
B. 9
C. 18
D. 36
E. 45

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Source: Beat The GMAT — Data Sufficiency | Sun Sep 09, 2012 1:21 pm

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by GMATGuruNY » Sun Sep 09, 2012 2:56 pm

Striver wrote:The sequence a1, a2....., an,...is such that an = 2an-1 - X for all positive integers n is greater than or equal to 2 and for certain number X. If a5 = 99 and a3 = 27, what is the value of X?

A. 3
B. 9
C. 18
D. 36
E. 45

aâ‚… = 2aâ‚„ - x
Since aâ‚… = 99, we get:
99 = 2aâ‚„ - x
x = 2aâ‚„ - 99.

aâ‚„ = 2aâ‚ƒ - x
Since aâ‚ƒ = 27, we get:
aâ‚„ = 2(27) - x
aâ‚„ = 54 - x.

Substituting aâ‚„ = 54 - x into x = 2aâ‚„ - 99, we get:
x = 2(54-x) - 99
x = 108 - 2x - 99
3x = 9
x = 3.

The correct answer is A.

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Javoni: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sat Jul 09, 2011 1:45 pm; Location: Tajikistan, Dushanbe; Thanked: 2 times

by Javoni » Mon Sep 10, 2012 2:15 am

As per question stem we can find that a5 = 2a4 - X and a4 = 2a3 - X, from here replacing the existing values we get: a4 = 2a3 - X = 2*27 - X = 54 - X. Consequently, a5 = 2a4 - X = 2*(54 - X) - X = 99
From this straightforward equation we get that 108 - 3X = 99, or 9 = 3X or X = 3, HENCE the answer would be (A)

Correct me if I went awry bro.

Striver wrote:The sequence a1, a2....., an,...is such that an = 2an-1 - X for all positive integers n is greater than or equal to 2 and for certain number X. If a5 = 99 and a3 = 27, what is the value of X?

A. 3
B. 9
C. 18
D. 36
E. 45

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