Data Sufficiency

Is sq rt of (x-5)^2 = 5- x?


-x [absolute value x] > 0

5 - x > 0





OA is D.


Please explain.

Taking the square root of a squared variable/number gives us the absolute value of the number. So we want to know if the absolute value of (x-5) = 5 - x.

Statement 1:

Tells us that the absolute value of X is greater than X... aka X must be negative.

If X must be negative then if x = -3, -3 - 5 = -8, absolute value = 8. Meanhilwe for the 5 - x, 5 - x = 5 - (-3) = 5 + 3 = 8. This will hold true for all negative numbers. So Statement 1 is sufficient.

Statement 2:

Tells us that X < 5. We already know that if X < 0, that we have sufficient information. If X = 5, both statements = 0, so it holds true. If X = 3, X - 5 = -2... absolute value = 2. On the other side we have 5 - x = 2. You can try it for any other number between 5 and 0 and find that both sides of the equation will be sufficient.

Answer is D.