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What is the value of x? (1) |x + 9| = 2x (2) |2x − 9| = x

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What is the value of x? (1) |x + 9| = 2x (2) |2x − 9| = x  [#permalink]

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New post 19 Feb 2018, 09:55
2
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

47% (01:38) correct 53% (01:43) wrong based on 99 sessions

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What is the value of x?

(1) |x + 9| = 2x

(2) |2x − 9| = x
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What is the value of x? (1) |x + 9| = 2x (2) |2x − 9| = x  [#permalink]

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New post 19 Feb 2018, 10:13
1
I don't agree with the OA.
1. 2 options:
x+9=2x.
x=9
or
-x-9=2x
-9=3x
x=-3

1 is not sufficient. So A and D are out.


2. 2 options:
2x-9=x
x=9

or
-2x+9=x
9=3x
x=3

not sufficient. B is out

1+2 => x=9

C is the answer.
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Re: What is the value of x? (1) |x + 9| = 2x (2) |2x − 9| = x  [#permalink]

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New post 19 Feb 2018, 10:16
1
mvictor wrote:
I don't agree with the OA.
1. 2 options:
x+9=2x.
x=9
or
-x-9=2x
-9=3x
x=-3

1 is not sufficient. So A and D are out.


2. 2 options:
2x-9=x
x=9

or
-2x+9=x
9=3x
x=3

not sufficient. B is out

1+2 => x=9

C is the answer.


I agree with C too, although my answer was marked wrong and OA was A. Thanks!
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What is the value of x? (1) |x + 9| = 2x (2) |2x − 9| = x  [#permalink]

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New post 19 Feb 2018, 10:22
3
1
What is the value of x?

(1) |x + 9| = 2x.

The left hand side is an absolute value, so it cannot be negative, thus the right hand side also cannot be negative, which means that x is positive or 0. If \(x \geq 0\), then x + 9 > 0, thus |x + 9| = x + 9. So, we'd have that x + 9 = 2x. Solving gives x = 9. Sufficient.

(2) |2x − 9| = x.

2x - 9 = x --> x = 9. Plug back to verify this solution: |2*9 - 9| = 9 --> OK;
2x - 9 = -x --> x = 3. Plug back to verify this solution: |2*3 - 9| = 3 --> OK.

Not sufficient.

Note that we cannot use trick we used for (1) for (2): yes, |2x − 9| = x also implies that x must be positive but 2x - 9 could be positive as well as negative for positive x.


Answer: A.
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What is the value of x? (1) |x + 9| = 2x (2) |2x − 9| = x  [#permalink]

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New post 19 Feb 2018, 10:24
1
mvictor wrote:
I don't agree with the OA.
1. 2 options:
x+9=2x.
x=9
or
-x-9=2x
-9=3x
x=-3

1 is not sufficient. So A and D are out.


2. 2 options:
2x-9=x
x=9

or
-2x+9=x
9=3x
x=3

not sufficient. B is out

1+2 => x=9

C is the answer.


For (1): x = -3 does not satisfy |x + 9| = 2x. You could spot it even without plugin back: if x is negative 2x is also negative and it cannot equal to absolute value of a number, which is non-negative.
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Re: What is the value of x? (1) |x + 9| = 2x (2) |2x − 9| = x  [#permalink]

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New post 19 Feb 2018, 10:41
1
A.

Solved it by actually plugging values.

A. This gives x+9 = 2x, x=9.
And, x+9=-2x, x=-3.

By plugging and checking for both values, we get equation stands true for only x=9. Sufficient.

B. This gives 2x-9=x, -9=-x, x=9.
And, 2x-9=-x, -3x=-9, x=3.

By plugging both values we get equation stands true for both the values of 9 and 3. No single answer. Insufficient.

Hence, A.
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Re: What is the value of x? (1) |x + 9| = 2x (2) |2x − 9| = x  [#permalink]

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New post 19 Feb 2018, 11:04
Bunuel wrote:
mvictor wrote:
I don't agree with the OA.
1. 2 options:
x+9=2x.
x=9
or
-x-9=2x
-9=3x
x=-3

1 is not sufficient. So A and D are out.


2. 2 options:
2x-9=x
x=9

or
-2x+9=x
9=3x
x=3

not sufficient. B is out

1+2 => x=9

C is the answer.


For (1): x = -3 does not satisfy |x + 9| = 2x. You could spot it even without plugin back: if x is negative 2x is also negative and it cannot equal to absolute value of a number, which is non-negative.


I see...a crucial mistake!
I remember making same mistakes before!
Thank you, Bunuel!
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Re: What is the value of x? (1) |x + 9| = 2x (2) |2x − 9| = x  [#permalink]

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New post 19 Feb 2018, 18:11
lee0706 wrote:
What is the value of x?

(1) |x + 9| = 2x

(2) |2x − 9| = x


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1):
i) x + 9 ≥ 0 or x ≥ -9
| x + 9 | = 2x
⇔ x + 9 = 2x
⇔ x = 9
Since x = 9 satisfies the assumption, we take x = 9 as an answer.

ii) x + 9 < 0 or x < -9
| x + 9 | = 2x
⇔ -( x + 9 ) = 2x
⇔ -x -9 = 2x
⇔ 3x = -9
⇔ x = -3
x = -3 doesn't satisfy the assumption x < -9.
We don'e take x = -3 as an answer.

Since we have a unique answer x = 9, the condition 1) is sufficient.


Condition 2)
i) 2x - 9 ≥ 0 or x ≥ 9/2
|2x − 9| = x
⇔ 2x -9 = x
⇔ x = 9
Since x = 9 satisfies the assumption, we take x = 9 as an answer.

ii) 2x - 9 < 0 or x < 9/2
|2x − 9| = x
⇔ -( 2x -9 ) = x
⇔ -2x + 9 = x
⇔ 3x = 9
⇔ x = 3
Since x = 3 satisfies the assumption, we take x = 3 as an answer.

Thus, we have two solutions x = 3 and x = 9.
Since we don't have a unique solution, the condition 2) is not sufficient, the condition 2) is not sufficient.

Therefore, A is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: What is the value of x? (1) |x + 9| = 2x (2) |2x − 9| = x   [#permalink] 19 Feb 2018, 18:11
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