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If 25 |x square-5x-10|= 100, then what is the sum of all the possible

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Joined: 24 Nov 2018
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If 25 |x square-5x-10|= 100, then what is the sum of all the possible  [#permalink]

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New post 28 Dec 2018, 05:00
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (01:13) correct 36% (01:28) wrong based on 36 sessions

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If 25 |x square-5x-10|= 100, then what is the sum of all the possible values of x?

Options:
1) 10
2) 8
3) 2
4) -4
5) -8
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If 25 |x square-5x-10|= 100, then what is the sum of all the possible  [#permalink]

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New post Updated on: 29 Dec 2018, 19:44
1
\(25|x^2 -5x-10| = 100\)

\(|x^2-5x-10| = 4\)

\(x^2-5x-10 = +4 OR -4\)

Case (i) \(x^2-5x-10 = 4\)
\(x^2-5x-14=0\)
\(x^2-7x+2x-14=0\)
solving for x,
x = 7,-2

case (ii)
\(x^2-5x-10 = -4\)
\(x^2-5x-6=0\)
solving for x,
x = -1,6

Sum of all the values of x,
= 7-2-1+6
= 10

Option A is correct

Originally posted by Dare Devil on 28 Dec 2018, 05:14.
Last edited by Dare Devil on 29 Dec 2018, 19:44, edited 1 time in total.
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Re: If 25 |x square-5x-10|= 100, then what is the sum of all the possible  [#permalink]

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New post 28 Dec 2018, 05:58
divyadamahe wrote:
If 25 |x square-5x-10|= 100, then what is the sum of all the possible values of x?

Options:
1) 10
2) 8
3) 2
4) -4
5) -8


25 |x square-5x-10|= 100
|x square-5x-10|= 4

\(x^2\)-5x-10 = ±4

\(x^2\)-5x-10 = 4 OR \(x^2\)-5x-10 =-4

\(x^2\)-5x-14=0 OR \(x^2\)-5x-6 =0

(x-7)(x+2) =0 OR (x-6)(x+1)=0

So, possible values of x = 7, -2, 6, -1

Sum of all possible values of x = 10

Answer option 1 (Or A)
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Re: If 25 |x square-5x-10|= 100, then what is the sum of all the possible  [#permalink]

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New post 29 Dec 2018, 04:06
Use this to help formatting of fractions, exponents etc
https://gmatclub.com/forum/rules-for-po ... l#p1096628

OP is not a 700 question, but I do think it is harder than sub-600. Nice question
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Re: If 25 |x square-5x-10|= 100, then what is the sum of all the possible  [#permalink]

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New post 31 Dec 2018, 01:19
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Re: If 25 |x square-5x-10|= 100, then what is the sum of all the possible   [#permalink] 31 Dec 2018, 01:19
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If 25 |x square-5x-10|= 100, then what is the sum of all the possible

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