GMAT Prep #1, Data Sufficiency In the sequence shown...

[joseph.k.lee10]

a1, a2..., an

In the sequence shown, an=an-1+ k, where n is greater or equal to 2 and less than equal to 15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10?

1.) a1=24

2.) a8=10

Can someone please explain how statement 2 alone is sufficient? Thanks.

[hiphopdidi7623]

a1, a2..., an

In the sequence shown, an=an-1+ k, where n is greater or equal to 2 and less than equal to 15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10?

1.) a1=24

2.) a8=10

Can someone please explain how statement 2 alone is sufficient? Thanks.

first of all, you have to consider that the "k" could be both positive and negative.

and then list the formula in both positive sequence and negative sequence.

if k is "positve": a9=a8+k, a8=10, a9=10+k, the following sequence must be greater than 10 until n=15 (thus, n=9,10,11,12,13,14,15. notice that n cannot be 8, because a8=10 is "not" greater than 10.)

if k is "negative": a8=a7+k, 10=a7+k (because k is negative, the sequence of "an" must be no less than 10 until "n=2", a8, a7,a6,a5,a4,a3,a2)

above, we can determine that there are "7" terms no matter k is positve or negative.

[joseph.k.lee10]

Forgot to include a8 for k less than 0. Thanks for the explanation.

[ChrisB]

Joe,

Nice work! I wouldn't add anything to the explanations provided.

As a takeaway note the use of 10 in both the problem and the statement. Why do you think the test writers included the 10 there? In the future, should you look for such connections?

Thanks,
Chris

[Viswanathan.harsha]

Doesn't the problem say greater than 10? So doesn't that mean that we cannot include a8 since it equals 10.

Hence, if k is positive, then n=9,10,11,12,13,14,15 (7 terms)

if K is negative, then n=7,6,5,4,3,2 (6 terms)

Since we do not know whether k is positive or negative, we do not know how many terms in the sequence are greater than 10. It could be either 7 or 6 terms. Wouldn't that mean it is insufficient?

[tim]

there is also an a_1 term. note that when they say n starts at 2, that is only for purposes of the recursive formula; the problem clearly demonstrates that the sequence goes from a_1 to a_15..