Is lx^3-23x^2+132xl=x^3-23x^2+132x? 1. x0 2. lx-2l5

Question

Is lx^3-23x^2+132xl=x^3-23x^2+132x?

1. x>0
2. lx-2l>5

eschn3am · Answer

|x(x-11)(x-12)| = x(x-11)(x-12)

for this to work we need to keep the answer positive on the right side because the left side will have to end up positive or 0. If the equation comes out negative then they won't be equal to each other.

for that to happen X must be >=0, but <11 OR > 12. Look at it like this. This equation will work for any number greater than or equal to 0 unless it's between 11 and 12, if that happens we'll end up with 1 negative in the equation, making the whole thing negative when multiplied out.

if X = 1. then it's +(-)(-) which = +
if X = 11 then it's +(0)(-) which = 0 
if X = 13 then it's +(+)(+) which is +

BUT if X = 11.5 then it's +(+)(-) which will give us a negative number on the right and a positive number on the left (due to ||)

so we just want to see if X is greater than or equal to 0, but not between 11 and 12 (non inclusive).

1. X>0 on the right track, but insufficicent
2. |x-2|>5 X is less than -3or greater than 7, insufficient

combined we see that X must be greater than 7

still not enough to determine if X is between 11 and 12 though.

INSUFFICIENT

 Answer E 


This seems rather long and drawn out for the GMAT. Is this an official question? or maybe I'm completely off point and missed an obvious short cut?

deparis · Answer

how did you understand that it was a number between 11 and 12 - how can you do this quickly? thanks

mtgmat · Answer

I solved this problem with the help of number line. Made portion of the line bold where absolute value was +ve. Like for Q stem between 0 & 11 and then beyond 12. St 1 is simple. For st 2 reached at point 2 of the no. line and then counted five on right as well as left. Bolded the line beyond 7 and less than -3. It helped in reducing the time taken to solve the Q.

walker · Answer

E 

|x³-23x²+132x|=x³-23x²+132x is true when x³-23x²+132x>=0

f(x)=x³-23x²+132x=x(x-11)(x-12)

f(x) intersects x-axis in 3 points: x=0, x=11, and x=12 and change its sign.

at x→-∞ f(x)→-∞. So, we start with sign "-"
 1st interval: x e (-∞,0): "-" and answer is "no" 
 2nd interval: x e  : "+" and answer is "yes" 
 3td interval: x e (11,12): "-" and answer is "no" 
 4th interval: x e  

1. x>0 means x e (0,+∞) and we have 2,3,4 intervals with different signs. INSUFF.

2. lx-2l>5 means x e (-∞,-3)&(7,+∞) and we have 1,2,3,4 intervals with different signs. INSUFF.

1&2. x e (7,+∞) and we have 2,3,4 intervals with different signs. INSUFF.

Is lx^3-23x^2+132xl=x^3-23x^2+132x? 1. x>0 2. lx-2l>5

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