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# If (x - 3)^2 = 225, which of the following could be the

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If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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24 Feb 2013, 16:57
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66% (00:56) correct 34% (01:02) wrong based on 464 sessions

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If (x - 3)^2 = 225, which of the following could be the value of x + 3 ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have$$x - 3= 15$$so why the explanation says: $$x - 3 = 15$$ and $$x - 3 = -15$$ ?????

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Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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24 Feb 2013, 21:03
2
4
carcass wrote:
If $$(x - 3)^2 = 225$$, which of the following could be the value of $$x + 3$$ ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have$$x - 3= 15$$so why the explanation says: $$x - 3 = 15$$ and $$x - 3 = -15$$ ?????

Honestly carcass, that's a newbie mistake and you should not be making it!

$$(x - 3)^2 = 15^2$$

When you take the root, you get
|x-3| = 15
and hence you get x = 18 or -12

Alternatively,
$$(x - 3)^2 - 15^2 = 0$$
(x - 3 - 15)(x - 3 + 15) = 0
x = 18 or -12
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Joined: 16 Jan 2013
Posts: 22
Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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24 Feb 2013, 18:14
carcass wrote:
If $$(x - 3)^2 = 225$$, which of the following could be the value of $$x + 3$$ ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have$$x - 3= 15$$so why the explanation says: $$x - 3 = 15$$ and $$x - 3 = -15$$ ?????

both 18 and -12 satisfy the given equation

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Intern
Joined: 16 Jan 2013
Posts: 22
Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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24 Feb 2013, 18:23
jbisht wrote:
carcass wrote:
If $$(x - 3)^2 = 225$$, which of the following could be the value of $$x + 3$$ ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have$$x - 3= 15$$so why the explanation says: $$x - 3 = 15$$ and $$x - 3 = -15$$ ?????

both 18 and -12 satisfy the given equation

Posted from my mobile device

hence, x+3 is 21 or -9

Posted from my mobile device
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Posts: 3445
Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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24 Feb 2013, 19:01
dumb mistake

thanks
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Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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24 Feb 2013, 19:44
1
carcass wrote:
If $$(x - 3)^2 = 225$$, which of the following could be the value of $$x + 3$$ ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have$$x - 3= 15$$so why the explanation says: $$x - 3 = 15$$ and $$x - 3 = -15$$ ?????

Yes here are my two cents...

$$(x - 3)^2 = 225$$

Since squaring on both sides leaves +/- $$x - 3 = +/- 15$$
This gives two eqns..
$$x - 3 = 15$$
$$x - 3 = -15$$

So, x= 18 means x+3=15
or
x=-12 means x+3=-9
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Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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25 Feb 2013, 02:46
1
VeritasPrepKarishma wrote:
carcass wrote:
If $$(x - 3)^2 = 225$$, which of the following could be the value of $$x + 3$$ ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have$$x - 3= 15$$so why the explanation says: $$x - 3 = 15$$ and $$x - 3 = -15$$ ?????

Honestly carcass, that's a newbie mistake and you should not be making it!

$$(x - 3)^2 = 15^2$$

When you take the root, you get
|x-3| = 15
and hence you get x = 18 or -12

Alternatively,
$$(x - 3)^2 - 15^2 = 0$$
(x - 3 - 15)(x - 3 + 15) = 0
x = 18 or -12

No no .......you are perfectly right .

maybe tired maybe stressed..........I know but you are right. Thanks
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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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27 Feb 2014, 20:16
One more method (This is time consuming)

Writing the equation as

x^2 - 6x + 9 - 225 = 0

x^2 - 6x + 9 - 216 = 0

(x-18) . (x+12) = 0

x = 18 OR x = -12

x+3=15 or x+3 = -9
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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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23 Aug 2016, 06:58
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If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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Updated on: 03 Nov 2016, 06:13
x-3 = 15

or

x-3= -15

So x=18 or x=-12

x+3=21 or x+3=-9

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Originally posted by AnisMURR on 03 Nov 2016, 03:48.
Last edited by AnisMURR on 03 Nov 2016, 06:13, edited 1 time in total.
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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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03 Nov 2016, 04:05
How we can confirm which answer to be considered?

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If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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03 Nov 2016, 04:15
Pm091989 wrote:
How we can confirm which answer to be considered?

Sent from my Redmi Note 3 using GMAT Club Forum mobile app

(x-3)^2= 225
(x-3)^2= 15^2
(x-3)= +15 or -15
x=18 or -12
now the question asks which could be the value of x+3
if x=18 ==> x+3=21 (could be)
if x=-12==> x+3= -9 (could be)

only-9 is available as an option.
If both -9 and 21 were available as individual options then the question would be wrong.
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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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03 Nov 2016, 11:33
carcass wrote:
If (x - 3)^2 = 225, which of the following could be the value of x + 3 ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have$$x - 3= 15$$so why the explanation says: $$x - 3 = 15$$ and $$x - 3 = -15$$ ?????

$$\sqrt{(x - 3)^2} = \sqrt{225}$$

Or, $$( x - 3 ) =$$ + $$15$$

If x = +15

x - 3 = 15

Or, x = 18 so x + 3 = 21

If x - 3 = - 15

Or, x = -12 , so x + 3 = -9

Hence, answer will be (C) -9
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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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04 Nov 2016, 16:18
carcass wrote:
If (x - 3)^2 = 225, which of the following could be the value of x + 3 ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

We can start by taking the square root of both sides of the equation (x - 3)^2 = 225.

√(x - 3)^2 = √225

x - 3 = 15 or x - 3 = -15

Thus, x = 18 or -12.

So possible values of x + 3 are as follows:

18 + 3 = 21

-12 + 3 = -9

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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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04 Nov 2016, 22:28
carcass wrote:
If (x - 3)^2 = 225, which of the following could be the value of x + 3 ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

(x - 3)^2 = 225
i.e. x-3 = +15 or -15
i.e. x = +18 or -12
i.e. x+3 = +21 or -9

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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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