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# What is the value of (x + 3)^2 ?

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Math Expert
Joined: 02 Sep 2009
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What is the value of (x + 3)^2 ?  [#permalink]

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07 Feb 2016, 10:51
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Difficulty:

25% (medium)

Question Stats:

72% (00:53) correct 28% (00:52) wrong based on 153 sessions

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What is the value of (x + 3)^2?

(1) |x| = 3
(2) |x| + x = 0

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Joined: 30 Nov 2015
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What is the value of (x + 3)^2 ?  [#permalink]

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07 Feb 2016, 12:14
2
I: X could be 3 or -3, which results in two possible values for the original equation:
(3+3)^2 = 36
(-3+3)^2 = 0

INSUFFICIENT

II: X must be negative, but could be any negative number, which allows for unlimited possible values for the original equation

INSUFFICIENT

Both I and II: X must be -3, which means original equation = 0

SUFFICIENT

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Re: What is the value of (x + 3)^2 ?  [#permalink]

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12 Feb 2016, 00:38
I think the answer is C.

What is the value of (x + 3)^2?

(1) |x| = 3
--> x = 3 or x = -3. Therefore (x+3)^2 = 36 or (x+3)^2 = 0--> Not sufficient
(2) |x| + x = 0
--> x <=0--> cannot determine the value of (x+3)^2--> Not sufficient.

Both together --> x = -3--> (x+3)^2 =0.
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Re: What is the value of (x + 3)^2 ?  [#permalink]

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13 Feb 2016, 22:54
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the value of (x + 3)^2?

(1) |x| = 3
(2) |x| + x = 0

In the original condition, there is 1 variable(x), which should match with the number of equation. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), x=-3,3, which is not unique and not sufficient.
For 2), x<0, which is not unique and not sufficient.
When 1) & 2), x=-3, which is unique and sufficient.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously 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)^2 ?  [#permalink]

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06 Mar 2018, 05:23
Bunuel wrote:
What is the value of (x + 3)^2?

(1) |x| = 3
(2) |x| + x = 0

Question : (x + 3)^2 = ?

St 1: |x| = 3

means x = 3 or -3 Not sufficient

St 2: |x| + x = 0

means |x| = -x, which is possible when x < 0

but we don't know the value of "x" Not sufficient

Combining st I & II we get x = -3 as x < 0

(C)
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Re: What is the value of (x + 3)^2 ?   [#permalink] 06 Mar 2018, 05:23
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