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If 25|x^2−5x−10|=100, then what is the sum of all the possible values

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If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

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04 May 2016, 10:08
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Difficulty:

25% (medium)

Question Stats:

82% (02:06) correct 18% (02:01) wrong based on 90 sessions

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If $$25|x^2−5x−10|=100$$, then what is the sum of all the possible values of x?

A. 10
B. 8
C. 2
D. -4
E. -8

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Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

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Updated on: 04 May 2016, 11:09
It is 10.

|expression| = 4
exp = +4 => on solving x=7 and -2
exp = -4 => on solving x = 3 and 2
7 - 2 + 2 + 3 = 10

updated *roots for 2nd exp are wrong, that should be 6 or -1 instead of +3 or -2*

7-2+6-1 = 10 is correct

oa pls
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Originally posted by snorkeler on 04 May 2016, 10:42.
Last edited by snorkeler on 04 May 2016, 11:09, edited 3 times in total.
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Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

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04 May 2016, 10:56
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1
[quote="Bunuel"]If $$25|x^2−5x−10|=100$$, then what is the sum of all the possible values of x?

A. 10
B. 8
C. 2
D. -4
E. -8

x^2-5x-10=4 will give you x=-2 and 7
-(x^2-5x-10)= 4 will give you x =-1 and 6
-2+7+-1+6=10
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If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

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04 May 2016, 12:49
2
x² - 5x - 10 = 4 => x² - 5x - 14 = 0 => (x - 7) (x + 2) = 0 => x = 7 or x = -2
x² - 5x - 10 = - 4 => x² - 5x - 6 = 0 => (x + 1) (x- 6) = 0 => x = 6 or x = -1

7 -2 + 6 - 1 = 10
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Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

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31 Dec 2018, 03:51
Bunuel wrote:
If $$25|x^2−5x−10|=100$$, then what is the sum of all the possible values of x?

A. 10
B. 8
C. 2
D. -4
E. -8

$$25|x^2−5x−10|=100$$

|x^2−5x−10|=4

x^2−5x−10=4
x=7 & -2
or say
-(x^2−5x−10)=4
x=3,+2

sum = 7-2+2+3 = 10

IMO A
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Posts: 2460
Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

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02 Jan 2019, 04:18

Solution

Given:
• $$25|x^2 - 5x - 10| = 100$$

To find:
• The sum of all the possible values of x

Approach and Working:
$$|x^2 - 5x - 10| = \frac{100}{25}= 4$$
• This implies, $$x^2 - 5x – 10 = 4$$ or $$x^2 - 5x – 10 = -4$$
o $$x^2 - 5x – 14 = 0$$, implies, x = 7 or -2
o $$x^2 - 5x – 6 = 0$$, implies, x = 6 or -1

Therefore, sum of all possible values of x = 7 – 2 + 6 – 1 = 10

Hence, the correct answer is Option A

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Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values &nbs [#permalink] 02 Jan 2019, 04:18
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