BTGmoderatorDC wrote:$$If\ x\ \ne\ 1,\ is\ y\ equal\ to\ x\ +\ 1?$$
(1) \(\frac{y - 2}{x - 1} = 1\)
(2) \(y^2 = (x + 1)^2\)
Target question: Is y equal to x+1?
Statement 1: (y - 2)/(x - 1)
Multiply both sides by (x - 1) to get: y - 2 = x - 1
Add 2 to both sides to get: y = x + 1
The answer to the target question is
YES, y IS equal to x + 1
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: y² = (x + 1)²
ASIDE: Some students will incorrectly conclude that, since y² = (x + 1)², it must also be the case that y = x + 1
This, however, is not true.
Notice, for example, that 3² = (-3)², but we can't then conclude that 3 = -3
To better see what I mean, considere these two possible cases that satisfy statement 2:
Case a: If x = 1 and y = 2, we get: 2² = (1 + 1)², which works. In this case, the answer to the target question is
YES, y IS equal to x + 1
Case b: If x = 1 and y = -2, we get: (-2)² = (1 + 1)², which also works. In this case, the answer to the target question is
NO, y is NOT equal to x + 1
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
