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(x - 1)^2 = 400 -> ?? Positive square root quesiton

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(x - 1)^2 = 400 -> ?? Positive square root quesiton

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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

The answer is C, -24.

I can do this simply by taking the square root of each side and obtaining:

x - 1 = +/- 20
x - 1 = 20 OR x - 1 = -20
Therefore, x=21, or x=-19

Then, (-19 - 5) = choice C, -24

However, I was under the impression that positive or even square roots on the GMAT are ALWAYS positive. So I got this one wrong b/c I took the square root of each side and obtained only one solution: (x - 1) = +20, therefore x = 21

Can someone explain to me why this OG problem is using +/- for an positive & even square root??

Thank you!

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Solution
If the question had been (x-1) = (400)^(1/2) then we would have taken just the positive square root of 400 that is 20 but since the question is (x-1)^2 = 400, we have to take both positive and negative roots.

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MFaulkner 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
Taking the square root of both sides, we have:

(x - 1)^2 = 400

√(x - 1)^2 = √400

This gives us:

|x - 1| = 20

This absolute value equation requires that we use two cases to determine all possible values of x.

Case 1. When (x-1) is positive:

x - 1 = 20

x = 21

Case 2. When (x-1) is negative:

-(x - 1) = 20

-x + 1 = 20

-x =19

x = -19

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

Answer: C

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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.

X-1 = -20
X = -19

We're asked for a possible value of X-5, so in this case (X-5) = -24.

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.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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MFaulkner wrote:
However, I was under the impression that positive or even square roots on the GMAT are ALWAYS positive. So I got this one wrong b/c I took the square root of each side and obtained only one solution: (x - 1) = +20, therefore x = 21

Can someone explain to me why this OG problem is using +/- for an positive & even square root??
To answer your actual question here:

When the GMAT given you a root *symbol*, as in √16, this represents just a positive number. This is understood to only have one value so that a question such as the following can have a single answer: https://www.beatthegmat.com/sqrt-80-t290557.html

If you're given that x^2 = 16, then you perform the operation of square rooting both sides; this is when you get a positive & negative solution.

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