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If (x - 1)^2 = 400 which of the following could be the value

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If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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If (x - 1)^2 = 400, which of the following could be the value of x - 5?

(A) 15
(B) 14
(C) -24
(D) -25
(E) -26
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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 13 May 2014, 09:36
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Hi,

this is an interesting problem regarding the GMAT Club Math Book. I studied it and on page 15 it says:

When the GMAT provides the square root sign for an even root, the only accepted answer is the positive root. That is, NOT +5 or -5. In contrast, the equation x^2 has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.

Due to this fact (which of course does not include this particular situation, because it's talking about the "sign"), I didn’t consider the negative root.
Maybe a phrase, which could be improved on the next issue :).

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If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 30 Jul 2014, 08:33
holdem wrote:
Hi,

this is an interesting problem regarding the GMAT Club Math Book. I studied it and on page 15 it says:

When the GMAT provides the square root sign for an even root, the only accepted answer is the positive root. That is, NOT +5 or -5. In contrast, the equation x^2 has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.

Due to this fact (which of course does not include this particular situation, because it's talking about the "sign"), I didn’t consider the negative root.
Maybe a phrase, which could be improved on the next issue :).

That statement from the book still holds good, it says "when GMAT provides the square root sign" whereas in this problem you were explicitly calculating the square root of 400 rather than GMAT providing \(\sqrt{400}\).
Hope that helps.

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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 08 Dec 2014, 22:04
Bunuel wrote:
Walkabout wrote:
If (x - 1)^2 = 400, which of the following could be the value of x - 5?

(A) 15
(B) 14
(C) -24
(D) -25
(E) -26


\((x - 1)^2 = 400\) --> \(x-1=20\) or \(x-1=-20\) --> \(x-5=20-4=16\) or \(x-5=-20-4=-24\).

Answer: C.


Hi there, where did the -4 come from? i.e.
\(x-5=20-4=16\) or \(x-5=-20-4=-24\)

Thanks.

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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 09 Dec 2014, 01:15
ColdSushi wrote:
Bunuel wrote:
Walkabout wrote:
If (x - 1)^2 = 400, which of the following could be the value of x - 5?

(A) 15
(B) 14
(C) -24
(D) -25
(E) -26


\((x - 1)^2 = 400\) --> \(x-1=20\) or \(x-1=-20\) --> \(x-5=20-4=16\) or \(x-5=-20-4=-24\).

Answer: C.


Hi there, where did the -4 come from? i.e.
\(x-5=20-4=16\) or \(x-5=-20-4=-24\)

Thanks.


hi, remember we have calculated the value of x-1=20 or -20. ------------1)
x-5 = (x-1)-4 now from 1, put the value of x-1 as 20 or -20
= 20-4 =16
or x-5 = (x-1)-4 = -20-4 = -24

i hope it helps.

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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 09 Dec 2014, 03:24
Hi there, where did the -4 come from? i.e.
\(x-5=20-4=16\) or \(x-5=-20-4=-24\)

Thanks.[/quote]

hi, remember we have calculated the value of x-1=20 or -20. ------------1)
x-5 = (x-1)-4 now from 1, put the value of x-1 as 20 or -20
= 20-4 =16
or x-5 = (x-1)-4 = -20-4 = -24

i hope it helps.[/quote]

Yep great - understand now. Appreciate your help!

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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 06 Jan 2015, 07:58
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Could we also solve this like this:

(x-1)^2 = (x-1)(x-1)?

I tried like this at first, but didn't end up well.. Unless I miscalculated sth somewhere.

Thank you.

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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 06 Jan 2015, 10:17
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Hi All,

GMAT writers often provide little 'hints' in the wording of the question that can help you to avoid some of the work.

Here, notice the phrase "...which of the following COULD be the value...." That's an interesting way to phrase a question - it's NOT asking "...what IS the value...." - it's asking "what COULD be the value...."

This implies that there's MORE than 1 answer AND that the 'obvious' answer is not the one that's going to be listed.

With (X-1)^2 = 400

I know there are two solutions (because of the 'squared sign')...

(X-1) COULD = 20 or -20

From the wording of the prompt though, it's likely that the "-20 option" is the one that we supposed to be going after, since that's the less obvious solution. Obviously, there's nothing wrong with being thorough and finding BOTH answers, but the question didn't ASK for that, so you have to be mindful about how much extra work you might be doing (and how much extra time you might be spending) on a given question, especially if you have a pacing problem.

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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 06 Jan 2015, 10:28
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Hi pacifist85,

While you could convert the equation into a Quadratic, I don't think that you'll find that method to be particularly fast nor easy....

(X-1)^2 = 400
(X-1)(X-1) = 400

X^2 - 2X + 1 = 400

X^2 - 2X - 399 = 0
(X - 21)(X + 19) = 0

X = 21 or -19

Now, contrast the above with the following....

(something)^2 = 400
(something) = +20 or -20

(X - 1) = 20
or
(X - 1) = -20

X = 21 or -19

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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 08 Jan 2015, 01:41
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\((x - 1)^2 = 400\)

\(x - 1 = \pm 20\)

\(x = 1 \pm 20 = 21 OR -19\)

x - 5 = 21-5 = 16 OR -19-5 = -24

Answer = C
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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 08 Jan 2015, 04:47
Here is an another approach

20^2 =400
thus (x-1)^2 = 20^2
(x-1)^2 - 20^2 = 0
now we know that a^2-b^2 = (a-b)(a+b)
here x-1 =a and 20=b

thus we have
(x-1-20)(x-1+20)=0
(x-21)(x+19)=0
x=21 or x=-19

thus x-5=21-5 =16 or -19-5 =-24

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If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 07 Jul 2016, 08:33
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Bunuel wrote:
Walkabout wrote:
If (x - 1)^2 = 400, which of the following could be the value of x - 5?

(A) 15
(B) 14
(C) -24
(D) -25
(E) -26


This is an interesting question because our initial instincts tell us to square x -1 by the FOIL method. However, an easier method is to instead take the square root of both sides of the equation.

(x - 1)^2 = 400

√(x - 1)^2 = √400

This gives us:

|x – 1| = 20

Because there is an expression inside the absolute value sign, we must consider that the entire expression, and not just the variable, can be either positive or negative. We’ll need to solve the equation twice.

Solve for x-1 as positive:

|x – 1| = 20

x – 1 = 20

x = 21

Solve for x-1 as negative:

|x – 1| = 20

-(x – 1) = 20

-x + 1 = 20

-x =19

x = -19

Thus, x – 5 can equal either 21 – 5 = 16 or -19 – 5 = -24.

Answer is C.
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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 08 Apr 2017, 01:35
Taking the root of both sides is definitely a better approach. Finding the roots of the quadratics can drive one insane! :roll:

\({ \left( x-1 \right) }^{ 2 }=400\\ \sqrt { { \left( x-1 \right) }^{ 2 } } =\sqrt { 400 } \\ \left| x-1 \right| =20\\ +\left( x-1 \right) =20\quad \leftrightarrow \quad -\left( x-1 \right) =20\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad or\\ { \left( x-1 \right) }^{ 2 }=400\\ \left( x-1 \right) \left( x-1 \right) =400\)
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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 08 Apr 2017, 07:02
Walkabout wrote:
If (x - 1)^2 = 400, which of the following could be the value of x - 5?

(A) 15
(B) 14
(C) -24
(D) -25
(E) -26


\((x - 1 ) =\) + \(20\)

If\(x - 1 = +20\) ; \(x = 21 ; So, x - 5 = 16\)

If \(x - 1 = -20\) ; \(x = -19; So, x - 5 = -24\)

Thus, answer must be (C) -24
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Re: If (x - 1)^2 = 400 which of the following could be the value [#permalink]

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New post 19 Aug 2017, 04:36
(x-1)^2= 400
(x-1)^2= (20)^2

(x-1)^2 -(20)^2= 0

Use identity a^2-b^2= (a+b)*(a-b)

(x-1+20)(x-1-20)=0
(x+19) (x-21)=0

Equate the factorized form to zero.

x= -19 or x= 21

Plug in (x-5) and check the options.


If I took (-20)^2

(x-1)^2 - (-20)^2= 0

(x-1-20)* (x-1+20)= 0

(x-21) (x+19)= 0

x= 21 or x= -19


Same answer.

This identity: a^2-b^2= (a+b)(a-b) comes in handy in many questions.
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Re: If (x - 1)^2 = 400 which of the following could be the value   [#permalink] 19 Aug 2017, 04:36
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