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

Question

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

Alex75PAris · Accepted Answer

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

Himanshu9818 · Answer

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

Answer is A

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

snorkeler · Answer

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

Archit3110 · Answer

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

EgmatQuantExpert · Answer

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

Answer: A

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Free-Session-Algebra-e1533292089856.jpg

KanishkM · Answer

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

93soni · Answer

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

GMATinsight · Answer

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

Answer: Option A

im9572 · Answer

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!

Saiharish98 · Answer

x^2-5x-10=4... Sum is -b/a=5
x^2-5x-10=-4... Sum=5
So sum of all possible values is 10

Posted from my mobile device

Saiharish98 · Answer

x^2-5x-10=4... Sum is -b/a=5
x^2-5x-10=-4... Sum=5
So sum of all possible values is 10

Posted from my mobile device

preetamsaha · Answer

|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

correct answer A

ThrivingWind · Answer

Hi All,

I've been using TTP for my quant prep and I'm having some difficulties in understanding this concept. Apparently when solving for for equations with absolute values, I need to split the equation into positive and negative then find all of the potential solutions. Then, I need to plug the solutions back into the original equation to determine what the actual solutions are. However, in the practice question solutions, TTP only does the check half of the time.

For this question specifically, I keep trying to plug the potential solutions into the original equation and I keep getting 3 of the potential solutions as false. However, that is not the answer provided by TTP. Could someone help me solve this?

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

When I solve for this, I get all of the potential solutions from TTP (7, -2, 6, -1), but when I plug 7, 6, and -1 back into the equation, it doesn't equal which makes me thing they aren't real solutions

Thank you so much,

DashingNightmare2 · Answer

25 |x^2 - 5x - 10| = 100 => |x^2-5x-10| = 4

We have 2 cases:

Case 1 : x^2-5x-10 >0
=> x^2-5x-10 = 4
=> x^2-5x-14 =0
=>x^2 - 7x+2x-14 =0
=>x(x-7) +2(x-7) =0
=>(x+2)(x-7)=0
=> x=-2 or x=7

Case 2 : x^2-5x-10 <0
=> x^2-5x-10 = -4
=> x^2-5x-6 =0
=>x^2-6x+x-6=0
=>x(x-6)+1(x-6)=0
=>(x+1)(x-60=0
=> x=-1 or x=6

Adding all 4 values -2+7+6-1 = 10
Hence A

For plugging in values:

25 |x^2 - 5x - 10| = 100 =>
 
|x^2-5x-10| = 4

x=7, |49-35-10| = |49-45| = 4 Correct 
x= 6, |36 -30 -10| =|-4| =4 Correct
and x = -1, |1+5-10| = |-4| = 4 Correct

sivatx2 · Answer

We can rewrite the equations as |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

solving each equations separately,

(x-7)(x+2) = 0

or

(x-6)(x+1) = 0

so possible values of x is 7, -2, 6, -1.

Sum of all possible values = 7-2+6-1 = 10.

So the correct choice is A

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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

Prep Toolkit

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