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Is the solution debatable? What should be the right answer

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by utkalnayak » Wed Jan 21, 2015 4:33 pm
What is the value of x ?
1) √x^2 = 4
2) (√x)^2 = 4

OA B

The answer explained is that
[spoiler]option 1 can be simplified to x^2 = 16 or x = 4 or x = -4 hence this option is not sufficient[/spoiler]

However what if we try to rewrite the left side of the equation by changing the powers to fraction form and then try to equate, what is wrong in my approach ?
√x^2 = 4 or (x^2) ^ 1/2 or x ^ (2 * 1/2) or x ^ 1, in this case can I not conclude x = 4 ? thus option 1 is sufficient
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Source: — Data Sufficiency |

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by [email protected] » Wed Jan 21, 2015 5:28 pm
Hi utkalnayak,

GMAT questions are always carefully worded, so you have to "start" a problem with whatever you're given (in the format that you're given) and proceed from there, using the appropriate rules of math.

Here, with Fact 1 we start with √(x^2) = 4

Mathematically, PEMDAS rules state that x^2 must be dealt with FIRST. The square-root comes SECOND.

Since the square root of 16 = 4, we have to consider ALL possible values for x that can make that 16 occur. X can be either 4 or -4 given the starting information that we have. So Fact 1 is INSUFFICIENT (since the question asks for the value of x and we have 2 options).

In that same way, Fact 2 IS SUFFICIENT because here we have to deal with the square-root FIRST. X CANNOT be negative in Fact 2 - it can only be +4.

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by Brent@GMATPrepNow » Thu Jan 22, 2015 7:58 am
utkalnayak wrote:What is the value of x ?
1) √x² = 4
2) (√x)² = 4

OA B

Statement 1: √x² = 4
Once we recognize that we must square x first, we can use a technique I call the SOMETHING METHOD. It goes like this:
Statement 1 tells us that √SOMETHING = 4
So, that SOMETHING must equal 16.
In other words, x² = 16
This means that x = 4 OR x = -4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: We have a free video on the SOMETHING METHOD: https://www.gmatprepnow.com/module/gmat- ... ing?id=988

Statement 2: (√x)² = 4
Statement 2 tells us that (SOMETHING)² = 4
So, that SOMETHING must equal either 2 or -2.
In other words, √x = 2 or √x = -2
- If √x = 2, then x = 4
IMPORTANT: the √ notation refers to the POSITIVE square root of a number. So, √x CANNOT equal -2.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
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by Matt@VeritasPrep » Sun Jan 25, 2015 8:49 pm
One helpful note here: √(x²) = |x|, for any value of x. (Remember this: it's useful!)

Knowing that, we have

S1:: |x| = 4; NOT SUFFICIENT, as x = 4 or x = -4.
S2:: √x * √x = 4. In theory we could have √x = 2 or √x = -2, but on the GMAT square roots can NEVER be negative. So √x = -2 is impossible, and the only solution is √x = 2, or x = 4. SUFFICIENT!
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by Mseemab » Sat Mar 04, 2017 2:04 am
Dear Rich/ Brent,

Since squared root of x can also be written as x^1/2, so why does x^2 take precedence over square root of x? Also can you elaborate more on the PEMDAS point, as I was not able to see a relation between exponents and square root through this.

Thanks in advance.
[email protected] wrote:Hi utkalnayak,

GMAT questions are always carefully worded, so you have to "start" a problem with whatever you're given (in the format that you're given) and proceed from there, using the appropriate rules of math.

Here, with Fact 1 we start with √(x^2) = 4

Mathematically, PEMDAS rules state that x^2 must be dealt with FIRST. The square-root comes SECOND.

Since the square root of 16 = 4, we have to consider ALL possible values for x that can make that 16 occur. X can be either 4 or -4 given the starting information that we have. So Fact 1 is INSUFFICIENT (since the question asks for the value of x and we have 2 options).

In that same way, Fact 2 IS SUFFICIENT because here we have to deal with the square-root FIRST. X CANNOT be negative in Fact 2 - it can only be +4.

GMAT assassins aren't born, they're made,
Rich
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by DavidG@VeritasPrep » Sat Mar 04, 2017 5:08 am
Mseemab wrote:Dear Rich/ Brent,

Since squared root of x can also be written as x^1/2, so why does x^2 take precedence over square root of x? Also can you elaborate more on the PEMDAS point, as I was not able to see a relation between exponents and square root through this.

Thanks in advance.
[email protected] wrote:Hi utkalnayak,

GMAT questions are always carefully worded, so you have to "start" a problem with whatever you're given (in the format that you're given) and proceed from there, using the appropriate rules of math.

Here, with Fact 1 we start with √(x^2) = 4

Mathematically, PEMDAS rules state that x^2 must be dealt with FIRST. The square-root comes SECOND.

Since the square root of 16 = 4, we have to consider ALL possible values for x that can make that 16 occur. X can be either 4 or -4 given the starting information that we have. So Fact 1 is INSUFFICIENT (since the question asks for the value of x and we have 2 options).

In that same way, Fact 2 IS SUFFICIENT because here we have to deal with the square-root FIRST. X CANNOT be negative in Fact 2 - it can only be +4.

GMAT assassins aren't born, they're made,
Rich
The P in PEMDAS stands for parentheses. So if we see that the x² is inside the parentheses, √(x²), then x² must be dealt with first, as anything inside parentheses must be calculated first.
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by [email protected] » Sat Mar 04, 2017 11:23 am
Hi Mseemab,

If you want to refer to the square-root as "^(1/2)", then that's fine, but you still have to deal with the prompt that you're given - which is...

[(X^2)]^(1/2) = 4

The 'implied parentheses' around X^2 means that you have to deal with that math function first. In simple terms, BEFORE you square root that value, you have to consider ALL of the possible values of X, that when squared, equal 16... and there are 2 values: +4 and -4.

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