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505-555 (Easy)|   Algebra|      
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jsphcal
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What is the value of x? Updated on: 19 Dec 2012, 08:12
Originally posted by jsphcal on 18 Dec 2012, 22:59.
Last edited by jsphcal on 19 Dec 2012, 08:12, edited 1 time in total.
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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)!

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15% (low)

Question Stats:

72% (01:00) correct 28% (01:10) wrong based on 805 sessions

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What is the value of x?

(1) \(x^3 - x^2 = 0\)
(2) \((-x)^2 = -x^2\)
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B
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What is the value of x? 18 Dec 2012, 23:34
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jsphcal
What is the value of x?

(1) x^3 - x^2 = 0

(2) (-x)^2 = -x^2
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1) x can be either 0 or 1. Insufficient.

2) Lets say \(x^2 = a\). We are given a = -a. So, a can only be 0 and hence x can only be 0.

Answer is B
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What is the value of x? 19 Dec 2012, 02:39
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jsphcal
What is the value of x?

(1) x^3 - x^2 = 0

(2) (-x)^2 = -x^2
Show more

In this case, it is better to simplify. This is a "value" question, so our answer depends on finding the exact value of x.

(1)

\(x^3-x^2=0\)
\(x^2(x-1)=0\)
=> either x=0 or x=1
INSUFFICIENT

(2)

\((-x)^2 = -x^2\)
Simplifying left hand side,

\((-x)^2 = (-1*x)^2 = (-1)^2 * (x)^2 = x^2\)

Thus the original expression is reduced to \(x^2=-x^2\), which can only happen when x=0.
SUFFICIENT

Thus the answer is B.
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What is the value of x? 19 Dec 2012, 02:44
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What is the value of x?

(1) x^3 - x^2 = 0 --> \(x^2(x-1)=0\) --> \(x=0\) or \(x=1\). Not sufficient.

(2) (-x)^2 = -x^2 --> \(x^2=-x^2\) --> \(2x^2=0\) --> \(x=0\). Sufficient.

Answer: B.
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What is the value of x? 19 Mar 2022, 10:50
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jsphcal
What is the value of x?

(1) x³ - x² = 0
(2) (-x)² = -x²
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Target question: What is the value of x?

Statement 1: x³ - x² = 0
Factor to get: x²(x - 1) = 0
So, EITHER x = 0 OR x = 1
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (-x)² = -x²
ASIDE: Some students will assume that (-x)² and -x² are equivalent, but they are not.
(-x)² tells us to multiply x by -1, and then square the result.
-x² tells us to square x, and then multiply the result by -1.
In other words, (-x)² = [(-1)(x)]² and -x² = (-1)(x²)

So, we can rewrite the given equation as follows: [(-1)(x)]² = -x²
Rewrite the left side as follows: (-1)²(x)² = -x²
Simplify the left side: (1)(x²) = -x²
Add x² to both sides: 2x² = 0, which means x = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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What is the value of x? 10 May 2023, 11:22
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