Carcass wrote:
If |d - 9| = 2d, then d=
(A) -9
(B) -3
(C) 1
(D) 3
(E) 9
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math BookWe have two cases to consider:
d - 9 = 2d and d - 9 = -2d
case a: If d - 9 = 2d, then d =
-9When we check this solution for extraneous roots, we get: |
-9 - 9| = (2)(
-9)
Simplify to get: |-18| = -18
NO GOOD!
So, d = -9 is NOT a valid solution
case b: If d - 9 = -2d, then d =
3When we check this solution for extraneous roots, we get: |
3 - 9| = (2)(
3)
Simplify to get: |-6| = 6
WORKS!
So, d = 3 IS a valid solution.
Answer: D