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What is the value of integer x? (1) x + x^2 = 0 (2) |x| + x^2 = 2x

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Bunuel
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What is the value of integer x? (1) x + x^2 = 0 (2) |x| + x^2 = 2x [#permalink] New post   22 May 2020, 02:59
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A
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C
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E

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45% (medium)

Question Stats:

58% (01:30) correct 42% (01:32) wrong based on 137 sessions
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What is the value of integer x?

(1) x + x^2 = 0
(2) |x| + x^2 = 2x


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C
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Re: What is the value of integer x? (1) x + x^2 = 0 (2) |x| + x^2 = 2x [#permalink] New post   22 May 2020, 05:20
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Bunuel wrote:
What is the value of integer x?

(1) x + x^2 = 0
(2) |x| + x^2 = 2x



Solution


Step 1: Analyse Question Stem


    • x is an integer
We need to find the value of x.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: x+x^2 = 0
    • \(x(x+1) =0 ⟹ x = 0 or x = -1\)
Since, we are getting two different values of x.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2: |x| +x^2 = 2x
    • Case 1: If \(x ≥ 0\)
      o Then,\( x + x^2 = 2x ⟹ x^2 – x = 0 ⟹x(x – 1) ⟹ x = 0\) or \(x =1\)
    • Case 2: If \(x < 0\)
      o Then, \(-x + x^2 = 2x ⟹ x^2 – 3x ⟹x(x- 3) ⟹ x = 0 or\) \(x = 3\)
         Since none of 0 and 3 are less than 0 so, we can discard these.
    • Still we are left with two values of x i.e. 0 and 1.
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining.


From statement 1: x can be 0 or -1
From statement 2: x can be 0 or 1
On combining both statements, we can say that \(x = 0\)
Thus, correct answer is Option C.
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Re: What is the value of integer x? (1) x + x^2 = 0 (2) |x| + x^2 = 2x [#permalink] New post   22 May 2020, 05:59
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Bunuel wrote:
What is the value of integer x?

(1) x + x^2 = 0
(2) |x| + x^2 = 2x




(1) \(x + x^2 = 0.........x(x+1)=0\), so x=0, or x=-1..Insufficient

(2) \(|x| + x^2 = 2x\)
Three cases..
a) \(x=0\)
b) \(x<0\)......Not possible as \(|x|+x^2>0\) while \(2x<0\), both \(|x|+x^2>0\) and \(2x<0\) cannot be equal.
c) \(x>0\).....\(|x| + x^2 = 2x........x^2+x=2x...x(x-1)=0\), so x=1
as x can be 0 or 1, insufficient

Combined
x=0

C
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Re: What is the value of integer x? (1) x + x^2 = 0 (2) |x| + x^2 = 2x [#permalink] New post   22 May 2020, 23:35
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See the attachment. Answer is C
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Re: What is the value of integer x? (1) x + x^2 = 0 (2) |x| + x^2 = 2x [#permalink] New post   21 Nov 2022, 13:04
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Re: What is the value of integer x? (1) x + x^2 = 0 (2) |x| + x^2 = 2x [#permalink]
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