Question

If y ≠ 1, is x = 1 ? (1) x2 + y2 = 1 (2) y = 1 – x Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer 1

Statements (1) and (2) TOGETHER are NOT sufficient.

Explanation:

If y ≠ 1, is x = 1 ?

(1)
`x^2+y^2` = 1

(2) y = 1 – x

The two statements are not sufficient to assert this claim. The statement If y ≠ 1, is x = 1 only holds in the two statements if y=0 as seen below.

(1)
`x^2+y^2` = 1

`x^2+0^2=1`

x=1

(2) y = 1 – x

0=1-x

x=1

Every other value of y fails the condition. So a sufficient statement would have been:

If y ≠ 1, and y=0, is x = 1 ?

(1)
`x^2+y^2` = 1

(2) y = 1 – x