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# What is the value of |x -3| ? (1) x^2 - 6x = 16 (2) -3 < x < 9

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Math Expert
Joined: 02 Sep 2009
Posts: 47033
What is the value of |x -3| ? (1) x^2 - 6x = 16 (2) -3 < x < 9 [#permalink]

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02 Apr 2018, 21:28
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35% (medium)

Question Stats:

60% (00:48) correct 40% (01:04) wrong based on 124 sessions

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What is the value of |x -3| ?

(1) x^2 - 6x = 16
(2) -3 < x < 9

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Manager
Joined: 05 Feb 2016
Posts: 117
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: What is the value of |x -3| ? (1) x^2 - 6x = 16 (2) -3 < x < 9 [#permalink]

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02 Apr 2018, 21:44
Bunuel wrote:
What is the value of |x -3| ?

(1) x^2 - 6x = 16
(2) -3 < x < 9

from 1: solving eq (x+2)(x-8)=0
x=-2,8
solving for both value of x
|-2-3|=5
|8-3|=5

Hence sufficient.

from 2 : 1,2,3
|x-3| is different.

Hence A
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Re: What is the value of |x -3| ? (1) x^2 - 6x = 16 (2) -3 < x < 9 [#permalink]

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03 Apr 2018, 01:11
Bunuel wrote:
What is the value of |x -3| ?

(1) x^2 - 6x = 16
(2) -3 < x < 9

Question : What is the value of |x -3| ?

Statement 1: x^2 - 6x = 16

i.e. x^2 - 6x - 16 = 0

i.e. x^2 -8x + 2x - 16 = 0

i.e. (x+2)(x-8) = 0

i.e. x = -2 or 8

i.e. |x -3| = |-2 -3| or |8 -3| = 5 in both cases hence

SUFFICIENT

Statement 2: -3 < x < 9

i.e. |x -3| = |-2 -3| or |-1 -3| or other cases = 5 or 4 or other cases hence

NOT SUFFICIENT

Answer: option A
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Re: What is the value of |x -3| ? (1) x^2 - 6x = 16 (2) -3 < x < 9 [#permalink]

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03 Apr 2018, 02:23
kunalcvrce wrote:
Bunuel wrote:
What is the value of |x -3| ?

(1) x^2 - 6x = 16
(2) -3 < x < 9

from 1: solving eq (x+2)(x-8)=0
x=-2,8
solving for both value of x
|-2-3|=5
|8-3|=5

Hence sufficient.

from 2 : 1,2,3
|x-3| is different.

Hence A

kunalcvrce, your answer is absolutely correct.

I just want to add my points to your answer.

NOTE: x is not an integer. Hence the value of |x-3| can also be a decimal like1.5 or 2.3 or 5.1.

This is a very common mistake during the exam.
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Re: What is the value of |x -3| ? (1) x^2 - 6x = 16 (2) -3 < x < 9 [#permalink]

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03 Apr 2018, 02:31

Solution

Given:
• We are given an expression |x-3|.

To find:
• We need to find the values of |x-3|.

Statement-1: “$$x^2 - 6x = 16$$“

We can write $$x^2 - 6x = 16$$ as $$x^2 - 6x-16=0$$.
• $$x^2-8x+2x-16=0$$
• x (x - 8) +2 (x - 8) =0
• (x-8) (x+2) =0
• Thus, x= 8, -2.

For x=8, the value of |x-3| is:
• |8-3|= 5

For x=-2, the value of |x-3| is:
• |-2-3|= 5

Since the value of |x-3| is unique for x=8 and x= -2, Statement 1 alone is sufficient to answer the question.

Statement-2:-3 < x < 9

Please Note: x is not an integer. Thus, x can be any real number.

Thus, the value of x can be 1.5 or 4.3 or -0.3 or. 2.7 or real number that lies between -3 to 9.

In the range -3 to 9, x can take infinite values, hence, we can have infinite values of |x-3|.

Thus, Statement 2 alone is not sufficient to answer the question.

Hence, the correct answer is option A.

Answer: A
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Re: What is the value of |x -3| ? (1) x^2 - 6x = 16 (2) -3 < x < 9 [#permalink]

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09 Apr 2018, 17:22
A
S1 ) x = -2 or 8 . If we caluclate |x-3| using the two values 2 and 8 , the result is always 5 hence sufficient
S2) ISF , it clearly provides more than 1 solution . In addition x can be a fraction as well.
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Re: What is the value of |x -3| ? (1) x^2 - 6x = 16 (2) -3 < x < 9 [#permalink]

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11 Apr 2018, 23:29
Bunuel wrote:
What is the value of |x -3| ?

(1) x^2 - 6x = 16
(2) -3 < x < 9

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)
x^2 -6x = 16
⇔ x^2 -6x-16 = 0
⇔ (x+2)(x-8) = 0
⇔ x = -2 or x = 8
⇔ |x-3| = |-2-3| = |-5| = 5 or |x-3| = |8-3| = |5| = 5.
Since we have a unique solution, condition 1) is sufficient.

Condition 2)
Since we don't have a unique solution, condition 1) is not sufficient.

Therefore, the answer is A.

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 -3| ? (1) x^2 - 6x = 16 (2) -3 < x < 9   [#permalink] 11 Apr 2018, 23:29
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