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In sequence of 9 distinct numbers

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by BTGmoderatorDC » Fri Feb 07, 2020 5:15 pm
In sequence of 9 distinct numbers {a1,a2,a3................a9}, nth term is given by an = an−1 + b, where 2 ≤ n ≤ 9 and b is a constant. How many of the terms in the sequence are negative?

(1) a1 = 16

(2) a5 = 0


OA B

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Source: — Data Sufficiency |

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Re: In sequence of 9 distinct numbers

by Jay@ManhattanReview » Tue Feb 18, 2020 12:16 am
BTGmoderatorDC wrote: ↑
Fri Feb 07, 2020 5:15 pm
 In sequence of 9 distinct numbers {a1,a2,a3................a9}, nth term is given by an = an−1 + b, where 2 ≤ n ≤ 9 and b is a constant. How many of the terms in the sequence are negative?

(1) a1 = 16

(2) a5 = 0

OA B

Source: e-GMAT
Let's take each statement one by one.

(1) a1 = 16

Since we do not have any information about b, we cannot calculate the values of the terms. Insufficient.

(2) a5 = 0

Since a5 = 0, there are two possibilities:

(a) a1, a2, a3, and a4 are negative and a6, a7, a8, and a9 are positive. Thus, there are 4 negative terms.
(b) a1, a2, a3, and a4 are positive and a6, a7, a8, and a9 are negative. Thus, there are 4 negative terms.

In either case, the answer is 4. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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