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For every positive even integer n, the function h(n)

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RonPurewal
 Post subject: Re: For every positive even integer n, the function h(n)
 Post Posted: Fri Dec 09, 2011 5:06 am 
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ManhattanGMAT Staff


Posts: 7146
varun.pendharkar wrote:
Hi ,

I agree with the analogy. But greater than 40 also includes numbers that are not greater than 50 and those numbers will not satisfy the condition.
Hence the question regarding choice E.

It is saying that if eqn X satisfies x> 15 it also satisfies x>10. I think that is incorrect assumption.

Please let me know your thoughts


irrelevant.

here's another example:
if N is a positive integer greater than 1, then N! is
(a) even
(b) odd

the answer here is (a), because all of these factorials are even.
your objection, in this case, would be like saying "But (a) is wrong because there are even numbers that aren't factorials!" that's not the point -- those would be irrelevant. the problem is just saying that all the factorials are even, not the other way around.

more generally, "all X's are Y's" does not imply, nor does it require, that all Y's also be X's.
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chandrahasreddy
 Post subject: Re: For every positive even integer n, the function h(n)
 Post Posted: Sun May 13, 2012 5:00 pm 
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Students


Posts: 5
Mgmat staff - Very good explanation. Thank you.

Can we generalize (sort off a takeaway ..):

For all positive integers of N, (N!+1) will have factors† > N.

The factors† of (N! + 1) will be above N

† - factors other than 1
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RonPurewal
 Post subject: Re: For every positive even integer n, the function h(n)
 Post Posted: Thu May 17, 2012 5:42 am 
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ManhattanGMAT Staff


Posts: 7146
chandrahasreddy wrote:
Mgmat staff - Very good explanation. Thank you.

Can we generalize (sort off a takeaway ..):

For all positive integers of N, (N!+1) will have factors† > N.

The factors† of (N! + 1) will be above N

† - factors other than 1


yes, except "factors" shouldn't be plural. it should be "at least one factor".
in some cases there will be only one such factor, e.g., 3! + 1 = 7, which only has one factor greater than 3 (namely, 7 itself).
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