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How many common points have \(y=|x|\) and \(y=|x^2 - 4|\)?
A. 0
B. 1
C. 2
D. 4
E. Infinitely many
Are You Up For the Challenge: 700 Level Questions
A. 0
B. 1
C. 2
D. 4
E. Infinitely many
Are You Up For the Challenge: 700 Level Questions
18 Jan 2022, 06:41
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Bunuel
Equation:
Now
\(y=|x|=|x^2-4|\)
As both sides are positive, we can square the two sides.
\(x^2=x^4-8x^2+16……..x^4-9x^2+16=0\)
An equation of degree 4 will have 4 values of x. We can find the values through determinant of factorisation but can be left as it will not be in scope of GMAT to find 4 factors. In some cases, however, we can have same values of x leading to lesser than 4. For example \(x^4=16\) has only two different values 2 and -2.
Answer is 4
Graphic solution
y=|x| will give you a linear equation. But as y is non negative for all values of x, we will have the line in shape of V above x axis and symmetrical to y axis.
Next \(y=|x^2-4|\) will be a parabola. If it were \(y=x^2-4\) the parabola would have cut these lines twice. However due to MOD, the parabola will once again move up above x-axis and we will have TWO more intersections.
Thus, total 4.
D
General Discussion
anish777
Joined: 18 Feb 2021
Last visit: 09 Jan 2025
Posts: 102
Own Kudos:
Given Kudos: 143
Location: India
Schools: IIM Calcutta '26
GMAT Focus 1: 635 Q88 V79 DI77 
GPA: 7.98
22 May 2024, 23:44
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chetan2u, the graph solution proposed by you is very good.
