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

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

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New post 04 Aug 2017, 09:17
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

78% (01:10) correct 22% (01:36) wrong based on 189 sessions

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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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New post 04 Aug 2017, 10:10
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

Answer is E
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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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New post 04 Aug 2017, 10:59
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.

\(x + 2 = -15\)

\(x = -15 - 2 => -17\)

\(x - 2 => -17 - 2 = -19\)

Answer (E)...
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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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New post 05 Aug 2017, 11:20
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

Answer E
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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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New post 10 Jul 2018, 15:34
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

Answer E


How did the number 15 come about?
sorry, I started a study for the GMAt today
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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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New post 10 Jul 2018, 20:20
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

Answer E


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

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New post 14 Jul 2018, 19:33
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.

Answer: E
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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, 19:33
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