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What is the value of x² + 4x - 5?

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BrentGMATPrepNow
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What is the value of x² + 4x - 5? [#permalink] New post  07 Oct 2021, 06:56
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45% (01:35) correct 55% (01:34) wrong based on 211 sessions
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What is the value of x² + 4x - 5?

(1) |x - 2| = 1
(2) |x + 2| = 3
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BrentGMATPrepNow
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Re: What is the value of x² + 4x - 5? [#permalink] New post  07 Oct 2021, 08:17
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BrentGMATPrepNow wrote:
What is the value of x² + 4x - 5?

(1) |x - 2| = 1
(2) |x + 2| = 3


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
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Re: What is the value of x² + 4x - 5? [#permalink] New post  07 Oct 2021, 07:52
(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
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Re: What is the value of x² + 4x - 5? [#permalink] New post  07 Oct 2021, 10:53
x² + 4x - 5
(x+5)(x-1)
#1
|x - 2| = 1
x= 3 and x = 1
We get two different values insufficient
#2
|x + 2| = 3
x= 1 and x=-5
for target we get 0
Sufficient
Option B

BrentGMATPrepNow wrote:
What is the value of x² + 4x - 5?

(1) |x - 2| = 1
(2) |x + 2| = 3


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rishabh195
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Re: What is the value of x² + 4x - 5? [#permalink] New post  07 Oct 2021, 13:44
Can someone explain how (B) is correct?

Upon substituting the equation, I got x= 1 or -5
Upon inserting 1 in option A, it satisfies the statement 1 and the equation too and upon inserting 1 in option B, it again satisfies the statement 2 and hence the equation. In both of the statements, I am getting 1 as the only answer to satisfy both of the statements. [We definitely can't put -5 in any of the statements because if we put that, then we get 2 answers proving both of the statements individually insufficient]

Hence, I got (D). Where am I going wrong?
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Re: What is the value of x² + 4x - 5? [#permalink] New post  07 Oct 2021, 14:03
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rishabh195 wrote:
Can someone explain how (B) is correct?

Upon substituting the equation, I got x= 1 or -5
Upon inserting 1 in option A, it satisfies the statement 1 and the equation too and upon inserting 1 in option B, it again satisfies the statement 2 and hence the equation. In both of the statements, I am getting 1 as the only answer to satisfy both of the statements. [We definitely can't put -5 in any of the statements because if we put that, then we get 2 answers proving both of the statements individually insufficient]

Hence, I got (D). Where am I going wrong?


Which equation did you solve to conclude that x = 1 or x = -5?

I have a feeling that you may have "solved" the expression in the target question, x² + 4x - 5
Keep in mind that x² + 4x - 5 is simply an expression. That is, there's nothing to solve.

I've seen a lot of students take an expression like x² + 4x - 5 and convert it to an equation set equal to zero to get x² + 4x - 5 = 0 (which they then solve).
Since x² + 4x - 5 isn't an equation, it can't be solved.

However, we CAN find the value of the expression x² + 4x - 5 for various values of x.
For example, if x = 0, then the expression x² + 4x - 5 evaluate to equal -5 (since 0² + 4(0) - 5 = -5

Does that help?
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Re: What is the value of x² + 4x - 5? [#permalink] New post  07 Oct 2021, 14:09
BrentGMATPrepNow wrote:
rishabh195 wrote:
Can someone explain how (B) is correct?

Upon substituting the equation, I got x= 1 or -5
Upon inserting 1 in option A, it satisfies the statement 1 and the equation too and upon inserting 1 in option B, it again satisfies the statement 2 and hence the equation. In both of the statements, I am getting 1 as the only answer to satisfy both of the statements. [We definitely can't put -5 in any of the statements because if we put that, then we get 2 answers proving both of the statements individually insufficient]

Hence, I got (D). Where am I going wrong?


Which equation did you solve to conclude that x = 1 or x = -5?

I have a feeling that you may have "solved" the expression in the target question, x² + 4x - 5
Keep in mind that x² + 4x - 5 is simply an expression. That is, there's nothing to solve.

I've seen a lot of students take an expression like x² + 4x - 5 and convert it to an equation set equal to zero to get x² + 4x - 5 = 0 (which they then solve).
Since x² + 4x - 5 isn't an equation, it can't be solved.

However, we CAN find the value of the expression x² + 4x - 5 for various values of x.
For example, if x = 0, then the expression x² + 4x - 5 evaluate to equal -5 (since 0² + 4(0) - 5 = -5

Does that help?


Yes, now I got it. I was solving the expression initially for which I got 2 values of x. But now I have completely understood that I have to input the values of x in the expression from the statements given. Thanks!!
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Re: What is the value of x² + 4x - 5? [#permalink] New post  29 Oct 2021, 08:16
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We can rewrite the equation as \(x^2 + 4x - 5\) = \(x^2 + 4x +4 - 9\) => \((x+2)^2 - 9\)

With statement 1 we get |x-2| = 1 which does not give 1 value to solve the equation. Insuff!

Statement 2 gives us |x+2| = 3 which does help in deducing the equation to \((x+2)^2 - 9\) = \(9-9 = 0\). Sufficient!

Answer: B
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Re: What is the value of x² + 4x - 5? [#permalink]
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