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arielle.bertman
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Post subject: Is the integer x divisible by 6?  Posted: Mon Aug 03, 2009 3:24 pm |
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Is the integer x divisible by 6?
(1) x + 3 is divisible by 3
(2) x + 3 is an odd number
I got this question right by creating a table with various numbers and testing values (x = 3, 6, 9, 12...), although this process was a bit time consuming and I was less than confident with my answer. I know these are common questions on the GMAT - was wondering if there is a faster way or more methodical way to solve using theory. If not, what are your suggestions for the best way to select values to test each condition?
Thanks so much for your help!
Arielle
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venkat_yj
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Post subject: Re: Is the integer x divisible by 6? Posted: Tue Aug 04, 2009 11:28 pm |
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Try this:
for x to be divisible by 6, it has to be divisible by factors of 6-> 3 and 2.
From (1), we can conclude that x is divisible by 3 (if x+3 is divisible by 3, it means x+3 is a multiple of 3 or x is a multiple of 3)
From (2), we can conclude that x is divisible by 2 (if x+3 is an odd number, x+2 has to be an even number, meaning x itself is even divisible by 2)
We need both conditions to conclusively say x is divisible by both 3 and 2. So answer should be C (now I hope thats the case :-)
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Ben Ku
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Post subject: Re: Is the integer x divisible by 6? Posted: Thu Aug 13, 2009 4:03 pm |
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Thanks, venkat_yj, for providing a clear and straightforward answer. I agree with the answer (C).
_________________
Ben Ku
Instructor
ManhattanGMAT
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cwhardie
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Post subject: Re: Is the integer x divisible by 6? Posted: Sat May 01, 2010 8:02 pm |
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Couldn't x also be zero?
0 +3 is divisible by 3 and
0 + 3 is an odd number
zero fit both categories but is not divisible by 6 so I thought the answer to this problem was E (stmts together were not sufficient)
Thanks in advance,
Carl
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abhyuday.c
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Post subject: Re: Is the integer x divisible by 6? Posted: Tue May 04, 2010 9:58 pm |
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I agree with cwhardie. What if x = 0?
Shoudn't the answer be E?
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debmalya.dutta
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Post subject: Re: Is the integer x divisible by 6? Posted: Tue May 04, 2010 10:32 pm |
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The answer should be E . 0 is an integer and hence it fits.
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sanyalpritish
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Post subject: Re: Is the integer x divisible by 6? Posted: Wed May 05, 2010 6:26 am |
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0 is divi by 6 ...
0 is multiple of all no.
0 is not a factor of any no.
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cwhardie
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Post subject: Re: Is the integer x divisible by 6? Posted: Wed May 05, 2010 8:55 am |
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Sanyalpritish,
I'm sorry but I don't understand the answer you posted. Could you explain it a little more?
Thanks
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sanyalpritish
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Post subject: Re: Is the integer x divisible by 6? Posted: Wed May 12, 2010 9:30 am |
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Well I meant that
0 is a factor of all Numbers (1,2,3.....)
[editor: this should say "multiple", not "factor".
a factor is the same thing as a divisor, so this statement, as written, contradicts the following one.]
0 is not a divisor of any number (1/0,2/0....)
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RonPurewal
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Post subject: Re: Is the integer x divisible by 6? Posted: Sun May 23, 2010 5:38 am |
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cwhardie wrote: Couldn't x also be zero?
0 +3 is divisible by 3 and
0 + 3 is an odd number
zero fit both categories but is not divisible by 6 so I thought the answer to this problem was E (stmts together were not sufficient)
Thanks in advance,
Carl actually, zero is divisible by 6. in fact, * zero is divisible by any positive integer * zero is a multiple of any positive integer the above are facts -- which, given this problem, it's apparently important that you know -- but this really doesn't seem to be the sort of thing that the gmat would test. (on EVERY other official question that i have seen, the test has absolutely gone out of its way to exclude "tricky" cases such as this one.) to all posters: has anybody seen this actual problem on the software? are we sure that the problem statement doesn't say "POSITIVE integer", not just "integer"?
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askhoman4
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Post subject: Re: Is the integer x divisible by 6? Posted: Sat Jul 03, 2010 7:26 am |
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RonPurewal wrote: to all posters:
has anybody seen this actual problem on the software? are we sure that the problem statement doesn't say "POSITIVE integer", not just "integer"? Hi Ron, Yes, I can confirm that the problem says "integer", not "positive integer". It came up in GMAT Prep1.
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mschwrtz
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Post subject: Re: Is the integer x divisible by 6? Posted: Mon Jul 12, 2010 11:45 pm |
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Notice that the apparently tricky case 0 isn't really a tricky case at all. It gives the same answer as every other legal value of x.
Well, that might be a bit strong. The way that 0 could trick you here is if it occurred to you to test 0, but you didn't know its properties.
You're smart to consider that 0 works differently than other numbers in lots of circumstances, but Ron is right (as usual) that the GMAT won't generally exploit special properties of 0 in questions like this one.
Students will sometimes ask "But isn't 0 divisible by __?" I will answer "Yeah, but that doesn't change the answer."
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