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mukund.jagadish
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Post subject: If x does not equal 0, then square root of x^2/x =  Posted: Sun Jan 24, 2010 10:27 am |
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Source: GMAT Prep Test 1
If x does not equal 0, then square root of x^2/x =
a. -1
b. 0
c. 1
d. x
e. |x|/x
OA: E
Please advise, thanks.
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ryan.m.doyle
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Post subject: Re: If x does not equal 0, then square root of x^2/x = Posted: Tue Feb 02, 2010 11:56 pm |
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mukund.jagadish wrote: Source: GMAT Prep Test 1
If x does not equal 0, then square root of x^2/x =
a. -1
b. 0
c. 1
d. x
e. |x|/x
OA: E
Please advise, thanks. I saw this explanation on another board Stuart Kovinsky - The key to this question is recognizing that the sqrt symbol literally translates as "the positive square root of". So, if you saw a question that asks: What's the sqrt(25), the answer would be ONLY +5. Since we translate the notation in this manner, we know that, no matter the sign of x, sqrt(x^2) is always going to be positive. In other words, the numerator in the expression will be the absolute value of x. So, we end up with: |x|/x ... choose (5) http://www.beatthegmat.com/if-x-0-then- ... 14328.html
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mschwrtz
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Post subject: Re: If x does not equal 0, then square root of x^2/x = Posted: Fri Apr 16, 2010 4:48 pm |
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Posts: 506
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Just to clarify, the expression originally posted as "square root of x^2/x" should read "[square root of (x^2)]/x." If we read it as square root of [(x^2)/x], then none of the listed answers is correct. In fact, it would be even better to write, say, "[radical (x^2)]/x," to emphasize that the radical sign indicates the primary (positive) square root.
But--bottom line--Ryan and SK are correct: radical (x^2)=|x|.
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eduardo_holsch
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Post subject: Re: If x does not equal 0, then square root of x^2/x = Posted: Wed Oct 12, 2011 7:33 pm |
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Hello, I think I understand the explanation, but I still have one question... and my thinking is as follows:
If we have (square root of x^2)/x, couldn't we square the whole fraction to get x^2/x^2... and this would equal 1 (regardless of the value of "x")?
Thanks in advance!
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RonPurewal
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Post subject: Re: If x does not equal 0, then square root of x^2/x = Posted: Sat Oct 15, 2011 3:03 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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eduardo_holsch wrote: Hello, I think I understand the explanation, but I still have one question... and my thinking is as follows:
If we have (square root of x^2)/x, couldn't we square the whole fraction to get x^2/x^2... and this would equal 1 (regardless of the value of "x")?
Thanks in advance! you could, but that wouldn't tell you anything. analogously, squaring -1/1 and squaring 1/1 will both give you 1/1, but that certainly doesn't mean that -1/1 and 1/1 are the same.
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mirzank
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Post subject: Re: If x does not equal 0, then square root of x^2/x = Posted: Tue Dec 20, 2011 5:46 pm |
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ryan.m.doyle wrote: mukund.jagadish wrote: Source: GMAT Prep Test 1
If x does not equal 0, then square root of x^2/x =
a. -1
b. 0
c. 1
d. x
e. |x|/x
OA: E
Please advise, thanks. I saw this explanation on another board Stuart Kovinsky - The key to this question is recognizing that the sqrt symbol literally translates as "the positive square root of". So, if you saw a question that asks: What's the sqrt(25), the answer would be ONLY +5. Since we translate the notation in this manner, we know that, no matter the sign of x, sqrt(x^2) is always going to be positive. In other words, the numerator in the expression will be the absolute value of x. So, we end up with: |x|/x ... choose (5) http://www.beatthegmat.com/if-x-0-then- ... 14328.htmlNeed to clarify something here. Why are we only choosing the positive square root? For Gmat purposes, isn't it INSUFFICIENT to get to an answer that contains a square root since you don't know if its the positive or the negative root, unless explicitly told in question stem if we are looking at greater than 0 or less than 0? So if we get to squareroot 25, it would be insufficient for a DS question unless say we are dealing with geometry or another question type that automatically excludes negative numbers. Please clarify. As for my solution, i thought it should be 1. Since if we assume that the variable is negative, then it gets cancelled out by the x in the denominator (which would now be negative), but if its positive, then the denominator is still positive and we still end up with 1.
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RonPurewal
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Post subject: Re: If x does not equal 0, then square root of x^2/x = Posted: Tue Dec 27, 2011 5:48 pm |
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| ManhattanGMAT Staff |
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mirzank wrote: Need to clarify something here. Why are we only choosing the positive square root? For Gmat purposes, isn't it INSUFFICIENT to get to an answer that contains a square root since you don't know if its the positive or the negative root, unless explicitly told in question stem if we are looking at greater than 0 or less than 0? "the square root" (and the "√" symbol) are universally described across all of mathematics -- not just the gmat -- as representing the non-negative root. this is done so that notations are unambiguous; if this convention were not in place, then it would actually be impossible to write the positive square root of a number. for instance, if you wanted to write the length of the diagonal of a square with side length 1, but "√2" meant either positive or negative, then how would you write that length? you wouldn't be able to. fortunately, "√2" means only the positive square root of 2, so we are good.
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