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niitorious
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Post subject: Is sqrt((x-3)^2) = 3 - x?  Posted: Wed Jul 01, 2009 9:58 pm |
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Is sqrt((x-3)^2) = 3 - x?
1) x is not equal to 3
2) -x|x| > 0
I don't think I even understand what the question is asking. Is it possible to just cancel out the sqrt sign with the square? I thought you shouldn't do that because it leads to loss of information?
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abhinav_iitg
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Post subject: Re: difficult DS question Posted: Wed Jul 01, 2009 11:47 pm |
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niitorious wrote: Is sqrt((x-3)^2) = 3 - x?
1) x is not equal to 3
2) -x|x| > 0
I don't think I even understand what the question is asking. Is it possible to just cancel out the sqrt sign with the square? I thought you shouldn't do that because it leads to loss of information? If you remember the following rule then the rest is piece of cake: sqrt(x^2) = |x| as square root of a number is always positive. for above question it is |x-3|. now the question is when |x-3| = 3 - x clearly when x <= 3.
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RonPurewal
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Post subject: Re: difficult DS question Posted: Fri Jul 10, 2009 6:42 am |
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| ManhattanGMAT Staff |
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good post above. i'll elaborate on the following: abhinav_iitg wrote: now the question is when |x-3| = 3 - x
clearly when x <= 3. i don't know if i'd go as far as to say "clearly"; this is actually very difficult for most students of the gmat. takeaway: the absolute value will do one of two things to a quantity:
(a) LEAVE THE QUANTITY ALONE, if the quantity is POSITIVE;
(b) REVERSE THE SIGN of the quantity, if the quantity is NEGATIVE.if the quantity is exactly 0, then both of these result in the same number, so it doesn't matter which of them you call it. therefore: the expression |x - 3| will equal one of two expressions: LEFT ALONE as (x - 3), if x - 3 is POSITIVE -- i.e., if x is greater than 3; REVERSED to (3 - x) (which is the same as -x + 3), if x - 3 is NEGATIVE -- i.e., if x is less than 3; EITHER of these (since both equal 0) if x is exactly 3. therefore, we now have a rephrase of the question. REPHRASE:
is x ≤ 3 ?so, the answer is (b).
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RonPurewal
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Post subject: Re: difficult DS question Posted: Fri Jul 10, 2009 6:45 am |
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| ManhattanGMAT Staff |
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you can also solve this problem, perhaps more easily, by PLUGGING IN NUMBERS.
statement (1):
since 3 is clearly a pivotal number in this problem, try numbers that are greater than 3 and numbers that are less than 3.
try x = 0:
√((x - 3)^2) = 3
3 - x = 3
answer to prompt question = YES
try x = 5:
√((x - 3)^2) = 2
3 - x = -2
answer to prompt question = NO
insufficient.
--
statement (2)
this statement is an obnoxious way of stating that x is a negative number. (you still have to figure that out -- no way around it)
if you try plugging in a vast array of negative numbers - big, small, even, odd, etc. - you'll find that the equality in the prompt question holds for ALL of them.
sufficient.
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ashish.jere
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Post subject: Re: Is sqrt((x-3)^2) = 3 - x? Posted: Mon Jul 13, 2009 9:22 am |
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for (2) to be true, x has to be negative.
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RonPurewal
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Post subject: Re: Is sqrt((x-3)^2) = 3 - x? Posted: Tue Jul 21, 2009 5:11 pm |
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| ManhattanGMAT Staff |
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ashish.jere wrote: for (2) to be true, x has to be negative. true. this is what i said in the post directly above yours: Quote: statement (2)
this statement is an obnoxious way of stating that x is a negative number. did you see that post? if you did, are you trying to say something here in response, or was there something you didn't understand?
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tomslawsky
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Post subject: Re: Is sqrt((x-3)^2) = 3 - x? Posted: Mon Jul 27, 2009 10:20 pm |
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Ron,
I understand the mechanics of your answer until you made the leap to is X<=3. Can you please briefly elaborate? Thanx.
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RonPurewal
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Post subject: Re: Is sqrt((x-3)^2) = 3 - x? Posted: Fri Aug 07, 2009 7:33 am |
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see my comments as "editor:" in the previous post
-- ron
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tomslawsky
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Post subject: Re: Is sqrt((x-3)^2) = 3 - x? Posted: Fri Aug 07, 2009 9:17 am |
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I COMPLETELY missed the word "sqrt", now the question seems very simple. Man, my lack of READING the question can really kill me sometimes. Thank you guys!
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Ben Ku
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Post subject: Re: Is sqrt((x-3)^2) = 3 - x? Posted: Mon Aug 17, 2009 8:18 pm |
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Posts: 824
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Glad it was helpful!
_________________
Ben Ku
Instructor
ManhattanGMAT
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ishkaran88
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Post subject: Re: Is sqrt((x-3)^2) = 3 - x? Posted: Mon Jan 18, 2010 5:44 pm |
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Thanks to Manhattan Staff and Abhinav.
You cleared a major flaw in my approach!
Regards
Ishkaran
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zchampz
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Post subject: Re: difficult DS question Posted: Mon Jan 18, 2010 8:51 pm |
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RonPurewal wrote: god post above. i'll elaborate on the following: abhinav_iitg wrote: now the question is when |x-3| = 3 - x
clearly when x <= 3. i don't know if i'd go as far as to say "clearly"; this is actually very difficult for most students of the gmat. takeaway: the absolute value will do one of two things to a quantity:
(a) LEAVE THE QUANTITY ALONE, if the quantity is POSITIVE;
(b) REVERSE THE SIGN of the quantity, if the quantity is NEGATIVE.if the quantity is exactly 0, then both of these result in the same number, so it doesn't matter which of them you call it. therefore: the expression |x - 3| will equal one of two expressions: LEFT ALONE as (x - 3), if x - 3 is POSITIVE -- i.e., if x is greater than 3; REVERSED to (3 - x) (which is the same as -x + 3), if x - 3 is NEGATIVE -- i.e., if x is less than 3; EITHER of these (since both equal 0) if x is exactly 3. therefore, we now have a rephrase of the question. REPHRASE:
is x ≤ 3 ? I didn't get it ...how can we rephrase like this ....can you please elaborate?
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imanemekouar
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Post subject: Re: Is sqrt((x-3)^2) = 3 - x? Posted: Thu Jan 28, 2010 12:37 pm |
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Ron , what do you mean by this sentence.
if the quantity is exactly 0, then both of these result in the same number, so it doesn't matter which of them you call it.
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joshua.higgins
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Post subject: Re: Is sqrt((x-3)^2) = 3 - x? Posted: Mon Feb 08, 2010 1:39 pm |
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Am I missing something?
If you plug in these two numbers:
x=-1/2
x=-5
Statement 2:
-(-1/2)|-1/2|>0
1/4>0 True
-(-5)|-5|>0
25>0 True
Main question:
Is sqrt((x-3)^2) = 3 - x?
sqrt(((-1/2)-3)^2) = 3 - (-1/2)
3.5 = 2.5 (False)
sqrt(((-5)-3)^2) = 3 - (-5)
8=8 (True)
I generally tend to make pretty inane errors with things like this, which is totally possible here, but I've now done this like 5 times and I keep coming back to the same issue....
For this to work, wouldn't x need to be an integer? (which isn't specified)
What's the deal?
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RonPurewal
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Post subject: Re: Is sqrt((x-3)^2) = 3 - x? Posted: Mon Mar 08, 2010 7:50 am |
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| ManhattanGMAT Staff |
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@ joshua.higgins joshua.higgins wrote: sqrt(((-1/2)-3)^2) = 3 - (-1/2)
3.5 = 2.5 (False)
your mistake is on the right side here. remember that subtracting a negative is equivalent to adding a positive. therefore, 3 - (-1/2) is 3 + 1/2, or 3.5. so this is also "true".
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