Data Sufficiency

lheiannie07 wrote:Sequence A is defined by the equation An = 3n + 7, where n is an integer greater than or equal to 1. If set B is comprised of the first x terms of sequence A, what is the median of set B ?

(1) The sum of the terms in set B is 275.
(2) The range of the terms in set B is 30

Which of the statements is sufficient? can some experts explain why?

OA D

We have

Sequence A is defined by the equation An = 3n + 7, where n ≥ 1

Set B is comprised of the first x terms of sequence A

We have to get the value of median of Set B.

If we get the values of first x terms of Set B, we can calculate the value of the median.

Let's take each statement one by one.

(1) The sum of the terms in set B is 275.

The first term of Set A = 3*1 + 7 = 10;
The second term of Set A = 3*2 + 7 = 13;
The third term of Set A = 3*3 + 7 = 16;

So Set B: {10, 13, 16, 19, ... }

If we keep adding the terms of Set B (10 + 13 + 16 + 19 + 22 + ...), we will certainly reach 275; thus, the number of terms would be known. When the numbers of terms would be known, the middle-most term can be identified and thus, we can get the unique value of median. Sufficient.

Since this is a DS question and we only need to be sure that there would be a unique answer to the question, we need not necessarily calculate the value.

(2) The range of the terms in set B is 30.

Range = Highest term - Smallest term

30 = Highest term - (3*1 + 7)

Highest term = 30 + 10 = 40

Set B: {10, 13, 16, 19, 22, ... 40}

Again, we have the finite number of terms, thus, the unique value of median can be computed. Sufficient.

The correct answer: D

Hope this helps!
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