Data Sufficiency

a1, a2, a3,...a15
In the sequence shown, a(n) = a(n-1) + k, where 2 < n < 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

Target question: How many term in the sequence a1, a2, a3,...a15 are greater than 10?

Given: a(n) = a(n-1)+k, where 2 < n < 15
In other words, each term is derived by taking the term before it and adding k
IMPORTANT: Keep in mind that k can be either a positive or negative number. So, the sequence may be increasing (e.g., 5, 7, 9, 11...) or it may be decreasing (e.g., 20, 15, 10, ...)

Statement 1: a1 = 24
The 1st term is 24, but since we don't know the value of k, there's no way to determine the terms in the sequence that are greater than 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a8 = 10
Let's consider the 2 possible cases for k (k is POSITIVE or k is NEGATIVE)

case a: k is POSITIVE
This means that the sequence is INCREASING.
In other words, term1 < term2 < term3, etc.
The 8th term is 10, which means every term after the 8th term must be greater than 10.
So, terms 9, 10, 11, 12, 13, 14 and 15 are greater than 10.
This means that 7 terms in the sequence are greater than 10

case b: k is NEGATIVE.
This means that the sequence is DECREASING.
In other words, term1 > term2 > term3, etc.
The 8th term is 10, which means every term before the 8th term must be greater than 10.
So, terms 1, 2, 3, 4, 5, 6 and 7 are greater than 10.
This means that 7 terms in the sequence are greater than 10

Since BOTH cases yield the SAME answer to the target question, we can be certain that 7 terms in the sequence are greater than 10
Statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

Hi GMATsid2016,

Here's a remarkably similar prompt for additional practice:

https://www.beatthegmat.com/how-many-of- ... 70610.html

GMAT assassins aren't born, they're made,
Rich

GMATsid2016 wrote:In the sequence shown, a(n) = a(n-1) + k, where 2 ≤ n ≤ 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

We are given the sequence a(n)= a(n-1) + k, in which 2 n 15 and k is a nonzero constant. We need to determine how many terms in the sequence are greater than 10. We must recognize that if k is a nonzero constant, then the sequence is either an increasing sequence or a decreasing sequence. In fact, if k is positive, then it's an increasing sequence. For example, if k = 1, then each term, starting from the second term, will be 1 more than the previous term. If k is negative, then it's a decreasing sequence. For example, if k = -1, then each term, starting from the second term, will be 1 less than the previous term.

Statement One Alone:

a(1) = 24

Using the information in statement one, we know that the first term of the sequence is 24. However, without knowing the value of k, we cannot determine how many terms in the sequence are greater than 10. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

a(8) = 10

Although statement two may appear to be insufficient, we do have enough information to answer the question. First, we must recognize that a(8) is the median term of the 15 terms, and thus, there are 7 terms above 10 and 7 terms below 10 Since we know k can be either positive or negative, we can determine that in either case, 7 terms will be greater than 10 and 7 terms will be less than 10.

For instance, if k = -1, then the the last 7 terms would be less than 10 and the first 7 terms would be greater than 10. However, if k = 1, then the opposite is true: the last 7 terms would be greater than 10 and the first 7 terms would be less than 10. Either way, exactly 7 of the terms in the sequence will always be greater than 10. Thus, statement two is sufficient.

Answer: B