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07 Oct 2021, 06:56
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
45% (01:35) correct
55%
(01:33)
wrong
based on 251
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of x2 + 4x - 5?
(1) |x - 2| = 1
(2) |x + 2| = 3
(1) |x - 2| = 1
(2) |x + 2| = 3
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07 Oct 2021, 08:17
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BrentGMATPrepNow
I call this question a fool me once question (FMO). The mistake many students will make is to conclude that, in order to answer the target question, we need only determine the value of x. So, when those students see that each statement yields two different possible value of x, they (incorrectly) conclude that each statement alone is insufficient. Remember that the target question is not asking us to find the value of x; it's asking us to find the value of x² + 4x - 5, and we can't answer that question without first plugging values of x into the expression.
Once you make this mistake, you're less likely to make it again (thus the FMO designation)
Target question: What is the value of x² + 4x - 5?
Statement 1: |x - 2| = 1
This means EITHER x - 2 = 1 OR x - 2 = -1
Let's examine each possible case...
Case a: If x - 2 = 1, then x = 3. In this case, the answer to the target question is x² + 4x - 5 = 3² + 4(3) - 5 = 16
Case b: If x - 2 = -1, then x = 1. In this case, the answer to the target question is x² + 4x - 5 = 1² + 4(1) - 5 = 0
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: |x + 2| = 3
This means EITHER x + 2 = 3 OR x + 2 = -3
Let's examine each possible case...
Case a: If x + 2 = 3, then x = 1. In this case, the answer to the target question is x² + 4x - 5 = 1² + 4(1) - 5 = 0
Case b: If x + 2 = -3, then x = -5. In this case, the answer to the target question is x² + 4x - 5 = (-5)² + 4(-5) - 5 = 0
So, it MUST be the case that x² + 4x - 5 = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
General Discussion
07 Oct 2021, 07:52
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(1) |x - 2| = 1
x - 2 = 1
x = 3
or
-x + 2 = 1
-x = -1
x = 1 INSUFFICIENT
(2) |x + 2| = 3
x + 2 = 3
x = 1
or
-x -2 = 3
-x = 5
x = -5 INSUFFICIENT
1+2) Putting them together tells us that x = 1.
x² + 4x - 5
(1)² + 4(1) - 5
= 0
Answer C
x - 2 = 1
x = 3
or
-x + 2 = 1
-x = -1
x = 1 INSUFFICIENT
(2) |x + 2| = 3
x + 2 = 3
x = 1
or
-x -2 = 3
-x = 5
x = -5 INSUFFICIENT
1+2) Putting them together tells us that x = 1.
x² + 4x - 5
(1)² + 4(1) - 5
= 0
Answer C
