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Sequence Problem

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Sequence Problem

by sreak1089 » Sat Mar 06, 2010 8:24 pm
In the sequence a1, a2, a3, ...., a15, an = an-1 + k (read n, n-1 as subscripts), where 2<=n<=15 and k is a non-zero constant. How many terms in the sequence are greather than 10?

1) a1 = 24
2) a8 = 10
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by spucmu » Sat Mar 06, 2010 10:30 pm
Is the answer c?

A) This tells me the value of a1 but doesn't tell me anything else so can't be the answer

B) This tells me the value of a8 but not sufficient

C) Value of k has to be negative that makes a1>a8 and as a1=24 and a8=10 (Values from a1 to a7 must be greater than 10).

So c should be the answer.

I didn't understand the usefulness extra information 2<=n<=15, I think it might be to curtail output from a2 to a7.
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by raisethebar » Mon Mar 08, 2010 2:55 am
Agree with ans C

1st gives us A1 and 2nd gives us A8.

from both of them we can find K and hence can ans the question

let me know OA
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by Fiver » Mon Mar 08, 2010 6:25 am
sreak1089 wrote:In the sequence a1, a2, a3, ...., a15, an = an-1 + k (read n, n-1 as subscripts), where 2<=n<=15 and k is a non-zero constant. How many terms in the sequence are greather than 10?

1) a1 = 24
2) a8 = 10
This is a GMAT prep question; i too marked C in my practise test but the answer to this one is B.
The sequence in question is an AP with 15 terms (given a15 is the last term), and hence a8 becomes the median.
All terms either to the left (if k<0) or to the right (if k>0) of a8 will have to be greater than 10.
Hence in any given condition (i.e. if k<0 or k>0) we will have 7 terms greater than 10.
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by spucmu » Mon Mar 08, 2010 9:50 am
Great Problem!!

Thanks for posting.

This is what I learnt:

Be sure to spend 20 seconds extra looking at A) and B) before going to choice C). This will be applicable particularly at high difficulty level.
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by Testluv » Mon Mar 08, 2010 11:23 am
Hi,

Fiver's reasoning is correct.

I discussed this question here: https://www.beatthegmat.com/terms-in-a-s ... tml#206551
Kaplan Teacher in Toronto
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by sreak1089 » Mon Mar 08, 2010 9:43 pm
Yes OA is B. This was a cool problem, which was discussed in my quant class. I enjoyed the logic behind it.
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