if n is a integer and n²

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figs: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Mon Mar 30, 2009 9:00 am; Thanked: 2 times

by figs » Tue Apr 07, 2009 10:23 am

if n is a integer and n² is divisible by 50, then the largest positive integer that must divide n is

A. 2
B. 4
C. 5
D. 10
E. 25

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moutar: Senior | Next Rank: 100 Posts; Posts: 92; Joined: Wed Mar 25, 2009 12:13 pm; Thanked: 10 times

by moutar » Tue Apr 07, 2009 10:34 am

50 = 2*5^2

n^2 is divisible by 50 implies that it is divisible by 2^2*5^2 (100)

Therefore n is divisible by 10. D.

Ergh. Thats a horrible explanation.

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scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Tue Apr 07, 2009 10:40 am

given n²/50=an inetger
=> n²/2*5²=an integer

n² must have 2² and 5² (squares have even powers and given that n is an integer)
=> n must have 2 and 5 ie n must be atleast 10
if n is atleast 10, the greatest divisor can be 10. (the number itself is its greatest divisor)

hence, D

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mjjking: Master | Next Rank: 500 Posts; Posts: 353; Joined: Sat Jan 20, 2007 1:29 am; Location: Italy; Thanked: 7 times; GMAT Score:720

by mjjking » Tue Apr 07, 2009 10:56 am

It's like the following:

if n^3 is divisible by 240, then what can be the minimum highest factor of n?

You see that 240 = 2^4x3x5

Hence, n must contain at least all these numbers in equal manner:

n n n
2 2 2
3 - -
2 - -
5 - -

From this we can imply that n includes at least a 3, a 5 and 2 2s, hence 60 is a factor of n.

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figs: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Mon Mar 30, 2009 9:00 am; Thanked: 2 times

by figs » Wed Apr 08, 2009 12:11 am

OA: D

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