Number property problem, need explanation plz

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akpareek: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Sun Feb 14, 2010 8:53 am

by akpareek » Wed Sep 04, 2013 8:44 am

The sequence a1, a2,.....an...is such that an= 2an-1-x for all positive integers n>=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 — Problem Solving | Wed Sep 04, 2013 8:44 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Sep 04, 2013 9:18 am

akpareek wrote:The sequence a1, a2,.....an...is such that an= 2an-1-x for all positive integers n>=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

I think you may need to add some brackets here. As it stands, the question is very ambiguous.
For example, what does 2an-1-x mean?
Since we're referring to terms in a sequence, and since there are no subscript options on this forum, it may be better to write term1, term2, terms(n-1) etc rather than an-1

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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sanjoy18: Senior | Next Rank: 100 Posts; Posts: 81; Joined: Tue Jun 11, 2013 10:24 pmFollowed by: 1 member; Thanked: 7 times

by sanjoy18 » Wed Sep 04, 2013 9:27 am

an=2an-1-x
>an=2(2an-2-x)-x
>an=4an-2-2x-x
>an=4an-2-3x
put n=5
a5=4a3-3x
>>99=4*27-3x
>> 3x= 108-99
>> x= 9/3=3
hence x=3
hence A

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Sep 04, 2013 9:29 am

Here's how I might word the question to prevent ambiguity..

The sequence term1, term2,.....termn...is such that termn= 2[term(n-1)]- x for all positive integers n > 2 and for certain number x. If term5 = 99 and term3 = 27, what is the value of x ?

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

From the definition of the sequence term5= 2(term4) - x
So, what is term4?

From the definition of the sequence term4 = 2(term3) - x
Since we're told that term3 = 27, we'll plug this in to get:
term4 = 2(27) - x
In other words, term4 = 54 - x

We can now plug this into the formula for finding term5
term5 = 2(term4) - x
= 2(54 - x) - x
= 108 - 2x - x
= 108 - 3x

We're told that term5 = 99, so we can write: 99 = 108 - 3x
When we solve for x, we get [spoiler]x = 3[/spoiler]
Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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