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22 May 2020, 02:59
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
59% (01:30) correct
41%
(01:31)
wrong
based on 140
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of integer x?
(1) x + x^2 = 0
(2) |x| + x^2 = 2x
Are You Up For the Challenge: 700 Level Questions
(1) x + x^2 = 0
(2) |x| + x^2 = 2x
Are You Up For the Challenge: 700 Level Questions
22 May 2020, 05:20
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Bunuel
Solution
Step 1: Analyse Question Stem
- • x is an integer
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: x+x^2 = 0
- • \(x(x+1) =0 ⟹ x = 0 or x = -1\)
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 \(x =1\)
- 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.
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.
22 May 2020, 05:59
Kudos
Bookmarks
Bunuel
(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
