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

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Intern
Joined: 24 Nov 2018
Posts: 19
Location: India
If 25 |x square-5x-10|= 100, then what is the sum of all the possible  [#permalink]

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28 Dec 2018, 05:00
2
00:00

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
Manager
Joined: 01 May 2017
Posts: 82
Location: India
If 25 |x square-5x-10|= 100, then what is the sum of all the possible  [#permalink]

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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.
Senior Manager
Joined: 17 Oct 2016
Posts: 257
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)
Re: If 25 |x square-5x-10|= 100, then what is the sum of all the possible  [#permalink]

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28 Dec 2018, 05:58
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

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Chasing the dragon
Senior Manager
Joined: 15 Feb 2018
Posts: 366
Re: If 25 |x square-5x-10|= 100, then what is the sum of all the possible  [#permalink]

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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
Math Expert
Joined: 02 Sep 2009
Posts: 58409
Re: If 25 |x square-5x-10|= 100, then what is the sum of all the possible  [#permalink]

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31 Dec 2018, 01:19
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

Discussed here: https://gmatclub.com/forum/if-25-x-2-5x ... 17821.html
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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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