Question

Find the average of 7 consecutive even numbers.

Statement I. The sum of fourth number and the sixth number is 440.

Statement II. The difference of the fifth and fourth number is 8.

1. The statement I alone is sufficient to answer the question but, statement II alone is not sufficient.
2. The statement II alone is sufficient to answer the question but, statement I alone is not sufficient.
3. Both the statements I and II together are needed to answer the question.
4. Either statement I alone or statement II alone is sufficient to answer the question.
5. Neither statement I nor statement II is sufficient to answer the question.

Answer 1

Correct Answer - Option 1 : The statement I alone is sufficient to answer the question but, statement II alone is not sufficient.

Concept:

Average = Sum of terms/Number of terms

Statement I.

Let the 7 consecutive even numbers be (x – 6, x – 4, x – 2, x, x + 2, x + 4, x + 6)

Now, x + x + 4 = 440

⇒ 2x +4 = 440

⇒ x = 218 

Numbers = (218 – 6, 218 – 4, 218 – 2, 218, 218 + 2, 218 + 4, 218 + 6)

⇒ Numbers = 212, 214, 216, 218, 220, 222, 224

Average = Sum of terms/Number of terms

⇒ Average = (212 + 214 + 216 + 218 + 220 + 222 + 224)/7

⇒ Average = 1526/7 = 218

So, Statement I alone is sufficient to answer the question

Statement II.

The difference of the fifth and fourth number is 8.

(x + 2) – x = 8

Here the variable is cancelled out so, we can't find value of x.

So, statement II is not sufficient

∴ The statement I alone is sufficient to answer the question but, statement II alone is not sufficient.