What is the sum of the terms in a certain sequaence of

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swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Fri Aug 03, 2018 9:41 am

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Source: Economist GMAT

What is the sum of the terms in a certain sequence of consecutive integers?

(1) The least term in the sequence is 8.
(2) The average of (arithmetic mean) terms is 16.

The OA is C.

Please, can anyone explain this DS question? I can't get the correct answer. I need help. Thanks.

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Source: Beat The GMAT — Data Sufficiency | Fri Aug 03, 2018 9:41 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Thu Aug 09, 2018 7:26 am

We need the value of any term in the sequence with it's nth place in the sequence as well as the number of terms in the sequence.
Statement 1 ; The least term in the sequence is 8.
There is no Sufficient information on the number of terms the sequence has, thus statement 1 is NOT SUFFICIENT.

Statement 2; The average of (arithmetic mean) terms is 16.
The Average / arithmetic mean doesn't tell about how many term the sequence has, hence statement 2 is NOT SUFFICIENT.
Combining the two statements,
Average of sequence of consecutive terms = Median of the sequence = Average of the least and highest term = $$\frac{\left(8\ +\ highest\ terms\right)}{2}\ =\ 16$$
8 + highest term = (16 * 2)
Highest term = (16 * 2) - 8 ) = 32 - 8
Highest term = 24
The series includes all integers from 8 to 24 a total of 17 terms.
Sum of the series = 16 * 17 = 272

The two statement together are SUFFICIENT.
Option C is the correct answer.

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