Question

Is x>0 ? x6>x7 x7>x8 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient EACH statement ALONE is sufficient to answer the question asked

Answer 1

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

Explanation:

Statement 1 :

`x^6 > x^7`

There are two cases,

Case 1 : x > 0

eg : x =
`(1)/(2)` > 0

`\because ((1)/(2))^6 > ((1)/(2))^7`

Case 2 : x < 0

eg : x = -2,

`\because (-2)^6 > (-2)^7`

Thus, statement 1 is not alone sufficient to prove x > 0

Statement 2 :

`x^7>x^8`

There is only one case,

x > 0

Because the value of odd exponent of a negative number is always less than that of even exponent,

eg :
`(-2)^7 < (-2)^8`

Thus, Statement 2 is alone sufficient to prove x > 0