If |x – 6| = 3, what is the value of x?

Question

(1) x is divisible by 9
(2) x is divisible by 3

yezz · Answer

from stem

x is either = 9 or 3

from 1

x = 9 ... suff

from 2

x= 9 or 3 .. insuff

A

prashantrchawla · Answer

I don't know whether this is even 600 level. 
Given that |x – 6| = 3. Removing modulus, We will get two equation, x-6=3 or x-6=-3.
Solving the two equation we will two values of X. i.e. 9 or 3.
Option 1: x is divisible by 9. Sufficient. 
Option 2: x is divisible by 3. Both the values 3 and 9 are divisible by 3. Not sufficient.

Hence answer is A.

pranab223 · Answer

From stmt 1

X=9 only - sufficient

From Stmt2

X=3 or 9 - not Sufficient

Ans- A

Madhavi1990 · Answer

so answer is A was my first thought.

|x-6| = 3

so obv x = 9 or - 3

1) x dvble 9 : so I substituted

|9-6| = 3; also |27/9 - 6| as both are dvble by 9. so X i thought could be either 27 or 9 . Insuff

2) x dvble by 3.

|x-6| =3
I put x as 9 and 18 --> |18/3 - 6| and |9/3 - 6| . so x again had two values

Answer is A. can you explain what is wrong above?
 
Also, based on reading the explanations above, it appears we consider x as dvble by something when it leaves behind a remainder one (that is why 9/3 = 3 and 3/3 = 1 hence insufficient; while 9/9 = 1 was seen as sufficient. But why can't we consider 27/9 here?)Would appreciate any reply to this!

nickrocks · Answer

Solving Question stem gives:

|x-6| = 3
x-6=3 OR x-6=-3
x=9 OR x=3
So, possible value of X can be 9 or 3, any condition which makes one value as certain will be true.

1. Div by 9 means X=9 it can't be 3 - So, it is sufficient
2. Div by 3 means X=9 or X=3 - So, it is insufficient

Answer is A

Bunuel · Answer

The logic there is not right.

If |x – 6| = 3, what is the value of x?

|x – 6| = 3 means that x is either 9 or 3. So, the question asks to find out which one of them is x.

(1) x is divisible by 9. x must be 9 because out of 9 and 3 only 9 is divisible by 9. Sufficient.

(2) x is divisible by 3. Both 9 and 3 are divisible by 3, so we cannot say whether x is 9 or 3. Not sufficient.

Answer: A.

Nunuboy1994 · Answer

two ways to approach abs. value

Positive
 1. x-6 = 3

Negative
- lx -6l =3
-x+6 =3
 -x=-3
 x= 3

A

bumpbot · Answer

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If |x – 6| = 3, what is the value of x?

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