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

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Math Expert
Joined: 02 Sep 2009
Posts: 56256
If |x – 6| = 3, what is the value of x?  [#permalink]

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06 Dec 2016, 00:47
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If |x – 6| = 3, what is the value of x?

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

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Intern
Joined: 04 Apr 2017
Posts: 20
Re: If |x – 6| = 3, what is the value of x?  [#permalink]

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09 Jul 2017, 00:18
5
Madhavi1990 wrote:
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!

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

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Re: If |x – 6| = 3, what is the value of x?  [#permalink]

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06 Dec 2016, 02:46
1
1
Bunuel wrote:
If |x – 6| = 3, what is the value of x?

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

from stem

x is either = 9 or 3

from 1

x = 9 ... suff

from 2

x= 9 or 3 .. insuff

A
Manager
Joined: 02 Nov 2013
Posts: 81
Location: India
Re: If |x – 6| = 3, what is the value of x?  [#permalink]

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06 Dec 2016, 04:13
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.
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Posts: 6
Re: If |x – 6| = 3, what is the value of x?  [#permalink]

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07 Dec 2016, 12:03
Bunuel wrote:
If |x – 6| = 3, what is the value of x?

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

From stmt 1

X=9 only - sufficient

From Stmt2

X=3 or 9 - not Sufficient

Ans- A
Senior Manager
Joined: 15 Jan 2017
Posts: 348
Re: If |x – 6| = 3, what is the value of x?  [#permalink]

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09 Jul 2017, 00:13
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!
Math Expert
Joined: 02 Sep 2009
Posts: 56256
Re: If |x – 6| = 3, what is the value of x?  [#permalink]

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09 Jul 2017, 02:04
1
1
Madhavi1990 wrote:
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!

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.
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Re: If |x – 6| = 3, what is the value of x?  [#permalink]

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01 Sep 2017, 14:35
Bunuel wrote:
If |x – 6| = 3, what is the value of x?

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

two ways to approach abs. value

Positive
1. x-6 = 3

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

A
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Re: If |x – 6| = 3, what is the value of x?  [#permalink]

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24 Dec 2018, 21:01
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Re: If |x – 6| = 3, what is the value of x?   [#permalink] 24 Dec 2018, 21:01
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