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Math Expert V
Joined: 02 Sep 2009
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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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Difficulty:   15% (low)

Question Stats: 80% (02:20) correct 20% (02:27) wrong based on 262 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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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, 11:42.
Last edited by snorkeler on 04 May 2016, 12:09, 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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[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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3
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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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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Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

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1

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  [#permalink]

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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

Just solve both the quadratic expressions formed when we open the modulus

$$x^2 - 5x -14 = 0$$, will give x as -2 and 7

$$x^2 - 5x + 6 = 0$$, will give x as 2 and 3

Add all the values of x to get 10

A
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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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for the equation ax^2 + bx + c = 0 ,the sum of roots is given by (-b/a)

now acc. to ques:
|x^2−5x−10|=4

=> x^2−5x−10= 4 ...... eq(1)
and x^2−5x−10= -4 ...... eq(2)

now from eq (1) and eq (2)

r1 + r2 = -(-5/1)= 5
r3 + r4 = -(-5/1)= 5

therefore , r1 + r2 + r3 + r4= 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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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

$$25|x^2−5x−10|=100$$

i.e. $$|x^2−5x−10|=4$$

i.e. $$x^2−5x−10=4$$ or i.e. $$x^2−5x−10=-4$$

i.e. $$x^2−5x−14=0$$ or i.e. $$x^2−5x−6=0$$

i.e. $$x^2−7x+2x−14=0$$ or i.e. $$x^2−6x+x−6=0$$

i.e. $$(x+2)*(x-7)=0$$ or i.e. $$(x−6)*(x+1)=0$$

i.e. x = -2, 7, 6, -1

Aum of all values of x = 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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hello folks!

if we apply the 'open up modulus' method, and find the solutions from both equations (i.e. 6, -1, 7, -2), do we need to test each one solution in the formula and check if they're correct?

or can we just take the solutions and sum them up without checking?

thanks! Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values   [#permalink] 29 Mar 2019, 11:43
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