Data Sufficiency

BTGModeratorVI wrote: ↑

Thu Aug 27, 2020 12:21 pm

In a sequence of numbers in which each term is two more than the preceding term, what is the fourth term?

(1) Last term is 90
(2) First term is 2

Answer: B
Source: Official guide

Solution:

Question Stem Analysis:

We need to determine the 4th term of a sequence. Notice that this is an arithmetic sequence since each term is 2 more than the preceding term, and thus 2 is the common difference of the sequence. In any arithmetic sequence, we can find the nth term as long as we know the value of any term in the sequence and its position in the sequence. Since here we know d = 2, then to find the 4th term, all we need to know is another term in the sequence provided that we know its position in the sequence.

Statement One Alone:

Even though we know the last term is 90, however, we don’t know the number of terms in the sequence. For example, if the sequence has 10 terms, then we have a_10 = 90. However, if the sequence has 100 terms, then we have a_100 = 90. The former example will yield a different value for a_4 (the fourth term) than the latter example. Therefore, statement one alone is not sufficient.

Statement Two Alone:

Since we know the first term is 2, we can determine the fourth term. That is, if we let n = 4 and m = 1 and use the formula for the nth term of a sequence: a_n = a_1+ d(4 - 1), we have:

a_4 = a_1 + 2(4 - 1)

a_4 = 2 + 6

a_4 = 8

We see that the 4th term is 8. Statement two alone is sufficient.

Answer: B