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# If (x+2)^2 = 225, which of the following could be the value of x−2?

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
If (x+2)^2 = 225, which of the following could be the value of x−2?  [#permalink]

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04 Aug 2017, 08:17
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Difficulty:

25% (medium)

Question Stats:

77% (01:12) correct 23% (01:42) wrong based on 198 sessions

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If (x+2)^2 = 225, which of the following could be the value of x−2?

A. 15
B. 13
C. -13
D. -17
E. -19

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Joined: 24 Apr 2016
Posts: 331
Re: If (x+2)^2 = 225, which of the following could be the value of x−2?  [#permalink]

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04 Aug 2017, 09:10
1
(x+2)^2 = 225 = 15^2

therefore, |x+2| = 15

x+2 = 15 or x+2 = -15

x = 13 or x = -17

x-2 = 13-2 = 11 or x-2 = -17 - 2 = -19

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Posts: 730
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
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Re: If (x+2)^2 = 225, which of the following could be the value of x−2?  [#permalink]

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04 Aug 2017, 09:59
1
Bunuel wrote:
If (x+2)^2 = 225, which of the following could be the value of x−2?

A. 15
B. 13
C. -13
D. -17
E. -19

$$(x+2)^2 = 225$$

$$(x+2)^2 = (15)^2$$ or $$(-15)^2$$

Therefore;

$$x + 2 = (+15)$$ or $$(-15)$$

Lets check both options.

$$x + 2 = 15$$

$$x = 15 - 2 => 13$$

$$x-2 => 13 - 2 = 11$$

There is no option with this answer.

$$x + 2 = -15$$

$$x = -15 - 2 => -17$$

$$x - 2 => -17 - 2 = -19$$

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Re: If (x+2)^2 = 225, which of the following could be the value of x−2?  [#permalink]

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05 Aug 2017, 10:20
Bunuel wrote:
If (x+2)^2 = 225, which of the following could be the value of x−2?

A. 15
B. 13
C. -13
D. -17
E. -19

(x+2)^2 = 225
=> x+2 = 15 or x+2 = -15
=> x-2 = 11 or x-2 = -19

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Joined: 10 Jul 2018
Posts: 6
Re: If (x+2)^2 = 225, which of the following could be the value of x−2?  [#permalink]

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10 Jul 2018, 14:34
Skywalker18 wrote:
Bunuel wrote:
If (x+2)^2 = 225, which of the following could be the value of x−2?

A. 15
B. 13
C. -13
D. -17
E. -19

(x+2)^2 = 225
=> x+2 = 15 or x+2 = -15
=> x-2 = 11 or x-2 = -19

How did the number 15 come about?
sorry, I started a study for the GMAt today
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: If (x+2)^2 = 225, which of the following could be the value of x−2?  [#permalink]

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10 Jul 2018, 19:20
joaolucas193 wrote:
Skywalker18 wrote:
Bunuel wrote:
If (x+2)^2 = 225, which of the following could be the value of x−2?

A. 15
B. 13
C. -13
D. -17
E. -19

(x+2)^2 = 225
=> x+2 = 15 or x+2 = -15
=> x-2 = 11 or x-2 = -19

How did the number 15 come about?
sorry, I started a study for the GMAt today

Hi joaolucas193,

We can write 225 in prime factorization form; $$225=5^2*3^2$$
Now $$\sqrt{{225}}=\sqrt{5^2*3^2}$$=$$\sqrt{5^2}*\sqrt{3^2}$$=$$5*3=15$$
Hope it's clear.
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PKN

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Posts: 2830
Re: If (x+2)^2 = 225, which of the following could be the value of x−2?  [#permalink]

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14 Jul 2018, 18:33
Bunuel wrote:
If (x+2)^2 = 225, which of the following could be the value of x−2?

A. 15
B. 13
C. -13
D. -17
E. -19

Taking the square root of both sides we have:

|x+2| = 15

Because this is an absolute value equation, we must consider 2 different cases to find all possible values of x.

Case 1.Solving for when (x + 2) is positive, we have:

x + 2 = 15

x = 13

Case 2. Solving for when (x + 2) is negative we have:

-(x + 2) = 15

-x - 2 = 15

-x = 17

x = -17

Thus, (x - 2) is either 11 or -19.

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Re: If (x+2)^2 = 225, which of the following could be the value of x−2? &nbs [#permalink] 14 Jul 2018, 18:33
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