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# How many real solutions exist for the equation x2 – 11|x| - 60 = 0? 3

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CAT Forum Moderator
Joined: 29 Nov 2018
Posts: 280
Concentration: Marketing, Strategy
How many real solutions exist for the equation x2 – 11|x| - 60 = 0? 3  [#permalink]

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30 Dec 2018, 13:23
5
6
00:00

Difficulty:

75% (hard)

Question Stats:

51% (01:36) correct 49% (01:51) wrong based on 123 sessions

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How many real solutions exist for the equation x^2 – 11|x| - 60 = 0?

A 3
B 2
C 1
D 4
E 0

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General GMAT Forum Moderator
Joined: 15 Jan 2018
Posts: 739
Concentration: General Management, Finance
GMAT 1: 720 Q50 V37
Re: How many real solutions exist for the equation x2 – 11|x| - 60 = 0? 3  [#permalink]

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30 Dec 2018, 13:33
5
2
Given that x^2 – 11|x| - 60 = 0

Case 1:
When, x is greater or equal to zero, then |x| = x
x^2 – 11x - 60 = 0
x^2 – 15x + 4x - 60 = 0
(x - 15)(x + 4) = 0
x = 15, or -4
However, the initial condition is that x must be greater or equal to zero. Hence, only one solution from Case 1, i.e. x = 15

Case 2:
When, x is less zero, then |x| = - x
x^2 + 11x - 60 = 0
x^2 + 15x - 4x - 60 = 0
(x + 15)(x - 4) = 0
x = - 15, or 4
However, the initial condition is that x must be less than zero. Hence, only one solution from Case 2, i.e. x = - 15

Therefore, from Case 1 & Case 2, we get two solutions of x, i.e. x = - 15, 15. So, number of real solutions for the equation x2 – 11|x| - 60 = 0 is 2.

Hence, the Correct Answer is Option B. 2

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Re: How many real solutions exist for the equation x2 – 11|x| - 60 = 0? 3  [#permalink]

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09 Jan 2020, 06:03
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Re: How many real solutions exist for the equation x2 – 11|x| - 60 = 0? 3   [#permalink] 09 Jan 2020, 06:03
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# How many real solutions exist for the equation x2 – 11|x| - 60 = 0? 3

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