Question

Does the equation y = (x - a)(x - b) intercept the x-axis at the point (2,0)?

(1) ab = -8

(2) -2 - a = b

• A. IF statement (1) alone is sufficient, but statement (2) is not or If Statement (2) alone is sufficient but statement (1) is not
• B. If Both statements TOGETHER are sufficient, but neither statement ALONE is sufficient
• C. If Each statement ALONE is sufficient
• D. Statement s (1) and (2) TOGETHER are not sufficient

Answer 1

The correct option is B

If Both statements TOGETHER are sufficient, but neither statement ALONE is sufficient

At y = 0
0 = (x - a)(x - b). This product would only be zero when xis equal to a or b. thus, we need to find out if a or b = 2. Both statements are required to answer this
(1) INSUFFICIENT: We can't find the value of a or b from this equation.
(2) INSUFFICIENT: We can't find the value of a or b from this equation.
(1) AND (2) SUFFICIENT: we have 2 simultaneous eqns which can be solved.

If b = 2, a = -4 and if b = -4, a = 2. Either way either a or b is equal to 2.