is SQRT(x-3)^2 = 3-x?
1) x is not equal to 3
(2)-x/x/ >0
1) if SQRT(x-3)^2 = 3-x, then x=3 otherwise it does not have any solution. i think A is correct answer; but answer is B
why...
many thanks
GMAT Forum
4 postsPage 1 of 1
- allenliuwx
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
i swear i've written up a fairly detailed thread on this problem, and that it's not showing up just because the forum hates me today.
FACT: √(expression^2) = |expression|
you should know this. in words: if you square a quantity, and then take the square root of the resulting square, then you get the absolute value of the original expression.
this happens because squaring makes the quantity "go positive", and, once that happens, the quantity will still be positive once you have taken its square root.
therefore, the problem is asking you the following:
is |x - 3| = 3 - x ?
the problem is NOT asking you whether (x - 3) equals (3 - x). if you're claiming (as you are) that the answer is only "yes" for x = 3, then this is probably your thought process.
hint: they won't usually make your life that easy.
in general, if you think that you can just cancel something in an absolutely trivial way, then you are almost certainly wrong. these test writers like to chuckle to themselves about how awfully clever the problems are; remember that.
the quantity |x - 3| will be just x - 3, so long as x - 3 is positive or 0. this happens when x > 3.
the quantity |x - 3| will return 3 - x, the opposite of x - 3, if x - 3 is negative or 0. this happens when x < 3.
therefore, the question can be rephrased even further:
is x < 3 ?
therefore #1 is insufficient.
statement #2 is just a weird way of telling you that x is negative. since all negative numbers are < 3, this statement is sufficient.
by the way, using your (incorrect) reasoning, you should still have concluded that statement #2 is sufficient, because, if x is negative, then you know that it isn't 3. since your (mis)interpretation of the question prompt was "is x = 3?", this would have been sufficient anyway, so you should have concluded that the answer is (d).
just to reiterate, the actual solution to the problem is (b).
FACT: √(expression^2) = |expression|
you should know this. in words: if you square a quantity, and then take the square root of the resulting square, then you get the absolute value of the original expression.
this happens because squaring makes the quantity "go positive", and, once that happens, the quantity will still be positive once you have taken its square root.
therefore, the problem is asking you the following:
is |x - 3| = 3 - x ?
the problem is NOT asking you whether (x - 3) equals (3 - x). if you're claiming (as you are) that the answer is only "yes" for x = 3, then this is probably your thought process.
hint: they won't usually make your life that easy.
in general, if you think that you can just cancel something in an absolutely trivial way, then you are almost certainly wrong. these test writers like to chuckle to themselves about how awfully clever the problems are; remember that.
the quantity |x - 3| will be just x - 3, so long as x - 3 is positive or 0. this happens when x > 3.
the quantity |x - 3| will return 3 - x, the opposite of x - 3, if x - 3 is negative or 0. this happens when x < 3.
therefore, the question can be rephrased even further:
is x < 3 ?
therefore #1 is insufficient.
statement #2 is just a weird way of telling you that x is negative. since all negative numbers are < 3, this statement is sufficient.
by the way, using your (incorrect) reasoning, you should still have concluded that statement #2 is sufficient, because, if x is negative, then you know that it isn't 3. since your (mis)interpretation of the question prompt was "is x = 3?", this would have been sufficient anyway, so you should have concluded that the answer is (d).
just to reiterate, the actual solution to the problem is (b).
- davidl.fernandez
- Students
- Posts: 1
- Joined: Sat Mar 07, 2009 2:01 pm
Re: prep-math: is SQRT(x-3)^2 = 3-x?
I encountered this question and I was able to deduce that the GMAT thought that as Ron posted that the square root of a quantity squared is positive. I don't buy this and it's a poor question at best. It might be *convention* (I doubt it) but it cannot be derived mathematically.
According to the GMAT all the following below are correct.
1) Square root of (25) which can be +/- 5
2) Square root of ((-5)^2) which is + 5
3) Square root of (5^2) which is + 5
This implies for that for the SAME INPUT (25) the square root gives DIFFERENT OUTPUTS. In one case it acts as a function and has a bijection between input (25) and output (+5) and in the other case it is not a function at all and maps to to two different outputs (+,- 5). Two cases for the SAME INPUT? That's not math, that's a clumsy test-maker. Math doesn't care if you are given (-5)^2 or 25, they are equal and when you input the same input into a certain mapping the output should be defined the same way for the same input.
It might be conventional to do this but, but it's poor convention and worthless to test someone on.
According to the GMAT all the following below are correct.
1) Square root of (25) which can be +/- 5
2) Square root of ((-5)^2) which is + 5
3) Square root of (5^2) which is + 5
This implies for that for the SAME INPUT (25) the square root gives DIFFERENT OUTPUTS. In one case it acts as a function and has a bijection between input (25) and output (+5) and in the other case it is not a function at all and maps to to two different outputs (+,- 5). Two cases for the SAME INPUT? That's not math, that's a clumsy test-maker. Math doesn't care if you are given (-5)^2 or 25, they are equal and when you input the same input into a certain mapping the output should be defined the same way for the same input.
It might be conventional to do this but, but it's poor convention and worthless to test someone on.
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
Re: prep-math: is SQRT(x-3)^2 = 3-x?
According to the GMAT all the following below are correct.
1) Square root of (25) which can be +/- 5
2) Square root of ((-5)^2) which is + 5
3) Square root of (5^2) which is + 5
no, #1 is incorrect. i don't know where you got the idea that "√" can represent either a positive or negative square root, but it's totally, completely, and unarguably wrong.
√25 is positive 5.
period.
end of story.
fact.
and, √(anything else) is always the positive square root (unless "anything else" happens to be 0, in which case it's also 0).
DO NOT ARGUE WITH THIS. THIS IS CORRECT, AND, IF YOU DISPUTE IT, YOU ARE WRONG.
the reason i'm "yelling" is that, on another forum on which i moderate, we had users keep trying to justify their views that "√blah" can be negative.
it can't.
--
the source of confusion may be with the EQUATION x^2 = 25, which genuinely has two solutions (5 and -5).
notice that this is an EQUATION that you HAVE TO SOLVE.
more to the point, notice that it doesn't contain the "√" sign... anywhere. if it did, then that sign would, as always, automatically be taken to mean the positive square root.
4 posts Page 1 of 1