Data Sufficiency

BTGModeratorVI wrote: ↑

Fri Jul 03, 2020 7:11 am

What is the value of |x + 7|?

(1) |x + 3|= 14
(2) (x + 2)^2 = 169

Answer: C
Source: GMAT paper tests

Target question: What is the value of |x+7|?

Statement 1: |x+3| = 14
When solving questions involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug in the solutions to check for extraneous roots

So, x+3 = 14
OR
x+3 = -14
When we solve the two equations, we get x = 11 OR x = -17

NOTE: Although we got two different answers, we must check whether we get 2 different answers to the target question.

If x = 11, then |x + 7| = |11 + 7| = 18
If x = -17, then |x + 7| = |-17 + 7| = 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (x+2)² = 169
This means EITHER (x+2) = 13 OR (x+2) = -13
When we solve the two equations, we get x = 11 OR x = -15
If x = 11, then |x + 7| = |11 + 7| = 18
If x = -15, then |x + 7| = |-15 + 7| = 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that |x + 7| = 18 OR 10
Statement 2 tells us that |x + 7| = 18 OR 8
So, if BOTH statements are true, then |x + 7| must equal 18
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C