Is |x|

Question

Is |x| < 5?

(1) x^2 < 16

(2) x(x - 5) < 0

Source: 4gmat

Bunuel · Answer

Is |x| < 5?

(1) x^2 < 16. Since both sides are nonnegative, then we can take the square root from: |x| < 4. Sufficient.

(2) x(x - 5) < 0. The "roots" are 0 and 5 and "<" sign indicates that the solution lies between the roots, so 0 < x < 5. Sufficient.

Answer: D.

BrushMyQuant · Answer

STAT 1:
x^2 < 16
=> -4 < x < 4
So, |x| < 4 so will be less than 5
So, SUFFICIENT

STAT 2:
x(x-5) < 0
two cases
case 1: x < 0 and x-5 > 0 => NO Solution
case 2: x> 0 and x-5 < 0 => 0 < x < 5
So, |x| < 5
So, SUFFICIENT

So, Answer will be D
Hope it helps!

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skysailor · Answer

Could someone help me understand why inequality x(x-5) < 0 gives us x>0 and not x<0?

mvictor · Answer

agree with the above statement.
1. can be rewritten as |x|<4.
2. x is definitely <5, but can't be negative, otherwise, it wouldn't be true 2. therefore 0<x<5
we have for each statement a definite answer.

D.

saarthak299 · Answer

hey, 
do we include negative terms also in first condition? 
in X^2 the value of x can be negative also.

pls, explain.
thank you.

Bunuel · Answer

Yes, |x| < 4 means -4 < x < 4.

AkshdeepS · Answer

x (x - 5) < 0; we have two cases ; x < 0 & x - 5 > 0 or x > 5 ; You can try some values in this range and you will see that this inequality will not hold true. x > 0 & x < 5 ; or 0 < x <5 ; solutions are between 0 and 5.

dabaobao · Answer

Hey abhimahna , how do we know the range by just looking at "x(x - 5) < 0" without having to consider the 2 scenarios (i.e. 1) x<0 & (x-5)>0 2) x>0 & (x-5)<0) as Bunuel mentioned? Is there a trick for it and can it apply to other situations as the example mentioned below? Thanks! How about x(x-5)>0? Case 1 (Both +): x>0, x-5>0 x>5 Case 2 (Both -): x<0,x-5<0 x<0

pushpitkc · Answer

Hey dabaobao You have made a mistake in the highlighted portion If x>0 and x>5, then the solution will be x > 0 Similarly, if x < 0 and x < 5, the solution is x < 5. Therefore, the solution to this inequality must be 0 < x < 5 You might want to read the following link https://gmatclub.com/forum/inequalities ... 91482.html Hope this helps you!

dabaobao · Answer

pushpitkc Thanks a lot bruh for that link. Remember studying that trick in high school but couldn't recall it. That trick makes it really easy to do such questions. Btw I don't think I made a mistake above. If we are looking at x(x-5)>0, then the solution should be x>5 or x<0 (which is what I got). I believe you mixed up x(x-5)>0 with x(x-5)<0. Irrespective of that issue, I think we should always discard the less limiting inequality. Example 1: If x>0 and x>5, then solution is x>5 Example 2: If x<0 and x<5, then solution is x<0

Is |x| < 5?

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