What is the sum of all integers x satisfying |x^2 - 5x|

Question

What is the sum of all integers x satisfying  |x^2 - 5x| < 6  ?

A. 0
B. 5
C. 10
D. 15
E. 20

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lacktutor · Accepted Answer

| x^{2} —5x | < 6 — 6 < x^{2} —5x < 6 x^{2}—5x +6 > 0 —> ( x—2)(x—3) > 0 x< 2 and x >3 x^{2} —5x —6 < 0 —> (x+ 1)(x—6) < 0 — 1 < x < 6 Taken together, — 1 < x < 2 and 3 < x < 6 0+ 1 + 4+ 5 = 10 The answer is C Posted from my mobile device

GMATinsight · Answer

|x^2 - 5x| < 6

i.e.  -6 < x^2 - 5x < 6

i.e.  -6 < x(x - 5) < 6

i.e. product of two integers separated by 5 must fall between -6 and +6

-1*(-6) does NOT lie in the range 
 0*(-5)
1*(-4) 
 2*(-3) does NOT lie in the range 
 3*(-2) does NOT lie in the range 
 4*(-1)
5*(0)

i.e. may be only {0, 1, 4 and 5}

Sum = 0+1+4+5 = 10

Answer: Option C

GMATWhizTeam · Answer

Solution: • |x^2 -5x| < 6 o -6 < x^2 -5x < 6 • Let’s break it down and solve o x^2 -5x <6 o x^2 -5x -6 <0 o x^2 -6x + x -6 <0 o (x-6)(x+1)<0  -1< x < 6 https://www.dropbox.com/s/qlh62pfth2z21e1/22.jpg?dl=1 • Now, x^2 -5x > -6 o x^2 -5x +6 >0 o x^2-3x-2x+6>0 o (x-3)(x-2)>0 o x >3 and x < 2 https://www.dropbox.com/s/c8c6dwmwr86d59l/23.jpg?dl=1 Let's combining the both result. https://www.dropbox.com/s/7oue4bboyauyl9v/24.jpg?dl=1 • Integer which satisfy both the equations are 0, 1, 4, 5 o Their sum = 0 +1 +4 +5 =10 Hence, the correct answer is Option C .

shameekv1989 · Answer

|x^2 - 5x| < 6 Case i) x^2-5x-6<0 when x^2-5x > 0 i.e. when x(x-5) > 0 i.e. x>5 or x<0 x^2-5x-6<0 = (x-6)(x+1) < 0 => -1 < x < 6 There will be no integer values within this range Case ii) x^2-5x>-6 when x^2-5x \leq 0 i.e. when x(x-5) \leq 0 i.e. 0 \leq x \leq 5 x^2-5x+6>0 = (x-3)(x-2) > 0 => x>3 or x<2 => Range is 0 \leq x < 2 and 3 < x \leq 5 Integer values = 0,1,4 and 5 Hence Sum = 10 Answer - C

shameekv1989 · Answer

Hi Can anyone confirm whether I am right in opening up the modulus?

|x^2-5x| =>

x(x−5)≤0 or x(x-5)> 0(Is it  \leq  and  \geq  for both cases? or only  \leq  while considering  \leq 0  or is it only  \geq  while taking  \geq 0 )

dave13 · Answer

lacktutor hi there

( x—2)(x—3) > 0 from here i get X=2 and x = 3 how did you x< 2 ?

lacktutor · Answer

hi,  dave13  
It’s an inequality question, not the equation. 
Well, in order (x—2)(x—3) to be greater than zero, x should be less than 2(x<2) and greater than 3(x>3).

Hope it helps

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What is the sum of all integers x satisfying |x^2 - 5x| < 6 ?

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