Consider the given question and decide which of the following statement(s) is/are sufficient to answer the question. Average of nine numbers is equal to 40. Find the last number. Statements 1. Average of first 6 numbers is 30 and sum of 7th and 9th numbers is 40 more than 8th number. 2. Average of first 8 terms is 36.?

Option 2 : 2 alone is sufficient while 1 alone is not sufficient to answer the question.

Given:

Average of nine terms = 40

Solution:

Sum of all numbers = 40 × 9

⇒ Sum of all numbers = 360

From statement 1

Average of first 6 numbers = 30

⇒ Sum of 6 numbers = 30 × 6 = 180

Sum of remaining 3 numbers = 360 – 180

⇒ Sum of remaining 3 numbers = 180

Let eight number be x

⇒ 7_th number + 9_th number = x + 40

⇒ Sum of remaining numbers = x + x + 40 = 180

⇒ 2x = 140

⇒ x = 70

From here we cannot find the value of last term.

Statement 1 is not sufficient to answer the question

From statement 2

Average of first 8 numbers = 36

⇒ Sum of first 8 numbers = 36 × 8

⇒ Sum of the first 8 numbers = 288

⇒ 9_th number = Total sum – Sum of first 8 numbers

⇒ 9_th number = 360 – 288

⇒ 9_th number = 72

∴  Only statement 2 alone is sufficient while 1 alone is not sufficient to answer the question.