Is x = 4? (1) |x + 2| 10

Question

Is x = 4?

(1) |x + 2| < 10

(2) |x + 5| > 10

DavidTutorexamPAL · Answer

Instead of trying to explicitly solve, we'll just plug x=4 into our equation and see what happens.
This is an Alternative approach.

(1) |4+2| = 6 which is smaller than 10. So x = 4 works in the inequality.
So, (1) tells us that x could be 4. Can it be something else?
Let's try x = 3: |3+2| = 5 which is also smaller than 10.
That is, (1) tells us that x could be 4 but it could also be 3, and therefore this is not enough.
Insufficient!

(2) |4+5| = 9 which is not larger than 10. So in this case the answer to 'is x=4' is NO!
As this is a definite answer, then it is sufficient.

(B) is our answer.

Tulkin987 · Answer

I got this one wrong! Perfectly explained!!!

DavidTutorexamPAL · Answer

Glad to help

pikolo2510 · Answer

Statement 1: -
|x + 2| < 10
Case 1:-
When |x+2| >0
|x+2|=x+2

x+2<10
x<8

Case 2:-
When |x+2| <0
i.e. |x+2|= -x-2

Now
-x-2<10
x>-12

therefore, x lies between -12<x<8

x can be equal to 4 or x can be 5,6 or 7. Hence insufficient

Statement 2: -(
|x + 5| > 10
Case 1: -
When |x + 5| >0
then, |x + 5|=x + 5

Now,
x + 5>10
x>5

Case 2: -
When |x + 5|<0
then, |x + 5|=-x-5

Now,
-x-5>10
x<-15

There x>5 and x is <-15

Hence Now I can say that x can never be 4 as it does not lie in the above range. Hence sufficent

Answer is B

niks18 · Answer

Here's a number line approach that can be used to skip any form of calculation - number line.jpg Statement 1: this equation will yield -125 . In either case, x≠4 . Sufficient Option B

Raksat · Answer

simple way 1. |X+2|<10 => -10-12 10 => x+5>10 or X>5 hence X cannot be 4 or X+5 <-10 or X<-15 , hence x cannot be 4 Therefore Sufficient Answer should be B

push12345 · Answer

I) x can take values from -12 to 8
So x can be or cannot be 4
Insufficient

II) x can take values outside of -15 to 5
X cannot be 4 for sure
So sufficient

B is answer

Posted from my mobile device

bumpbot · Answer

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Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10

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