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by smagish » Sat Aug 18, 2012 2:31 am
In the sequence of nonzero numbers t1, t2, t3, ..., tn, ..., tn+1 = tn / 2 for all positive integers
n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16
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by das.ashmita » Sat Aug 18, 2012 4:36 am
Hi Smagish

IMO D

Given tn+1 = tn / 2
Therefore the series is a GP with r = 1/2

(1) t3 = 1/4
t4 = t3/2 and t5 = t4/2 = t3/4 ... SUFF

(2) t1 - t5 = 15/16 ... (a)
t5 = t1[1-(1/2)^5]....by nth term formula of GP...(b)
2 equations 2 unknown... SUFF

ANS D
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by neelgandham » Sat Aug 18, 2012 5:31 am
In the sequence of nonzero numbers t1, t2, t3, ..., tn, ..., tn+1 = tn / 2 for all positive integers
n. What is the value of t5?
(1) t3 = 1/4
t5 = (t4)/2
t4 = (t3)/2
So, t5 = (t3)/4 = 1/16
Statement 1 is sufficient to answer the question.
(2) t1 - t5 = 15/16[/quote
t5 = t4/2; t4 = 2*t5
t4 = t3/2; t3 = 2*t4
t3 = t2/2; t2 = 2*t3
t2 = t1/2; t1 = 2*t2
t1 = 2*t2 = 2*2*t3 = 2*2*2*t4 = 2*2*2*2*t5 = 16*t5

If t1 - t5 = 15/16
16*t5 - t5 = 15/16
15*t5 = 15/16
t5 = 1/16.
Statement 2 is sufficient to answer the question.

IMO D
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by Brent@GMATPrepNow » Sat Aug 18, 2012 7:46 am
smagish wrote:In the sequence of nonzero numbers t1, t2, t3, ..., tn, ..., tn+1 = tn / 2 for all positive integers
n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16

The given information tells us that every term in the sequence is half the term before it.
So, the sequence might look like this: 80, 40, 20, 10, 5, 2.5,...
Or like this: 36, 18, 9, 4.5,...
As you can see, there are many possible sequences here, which means there a many possible values of t5.

Okay, onto the statements:

Statement 1: t3 = 1/4
Once we know the value of the 3rd term, we can find the value of the 4th term, and once we know the value of the 4th term, we can find the value of the 5th term.
Of course, we don't need to actually find the value of the 5th term. All we need to determine is whether we have sufficient information to find that value.
That said, we can conclude that t3 = 1/4, t4 = 1/8, and t5 = 1/16
So, statement 1 is SUFFICIENT

Statement 2: t1 - t5 = 15/16
If we let t1 = A, we can see that:
t1 = A
t2 = (1/2)A
t3 = (1/2)(1/2)A
t4 = (1/2)(1/2)(1/2)A
t5 = (1/2)(1/2)(1/2)(1/2)A

So, if t1 - t5 = 15/16, we can write the equation: (1/2)(1/2)(1/2)(1/2)A - A = 15/16
At this point, we need only recognize that we could solve this equation for A.
Once we know the value of A (the first term), we can find the value of t2, then t3, etc all the way to t5.
So, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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