square of an integer

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Feb 10, 2010 10:31 am

For how many integers n, n / (20-n) is the square of an integer?

A) 0
B) 1
C) 2
D) 3
E) 4

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Wed Feb 10, 2010 11:51 am

shashank.ism wrote:For how many integers n, n / (20-n) is the square of an integer?

A) 0
B) 1
C) 2
D) 3
E) 4

IMO D

You only have to check from 19->10 for values of n. You will get is as square for 10 16 18.

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Harsha

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Thu Feb 11, 2010 8:30 am

shashank.ism wrote:For how many integers n, n / (20-n) is the square of an integer?

A) 0
B) 1
C) 2
D) 3
E) 4

n cannot be Less than 10 (20-n becomes greater than n if n is less than 10) and n cannot be greater than 20
squares less than 20 and greater than 10 - 16, 10 and 18
16/(20-16), 18/(20-18) and 10/(20-10) are squares

Hence D

Last edited by ajith on Thu Feb 11, 2010 11:34 am, edited 2 times in total.

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Thu Feb 11, 2010 8:42 am

ajith wrote:
shashank.ism wrote:For how many integers n, n / (20-n) is the square of an integer?

A) 0
B) 1
C) 2
D) 3
E) 4
n cannot be Less than 10 (20-n becomes greater than n if n is less than 10) and n cannot be greater than 20
squares less than 20 and greater than 10 - 16, 10 and 18
16/(20-4), 18/(20-18) and 10/(20-10) are squares

Hence D

I guess you meant 16/20-16 here rite?

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Thu Feb 11, 2010 11:33 am

papgust wrote:
I guess you meant 16/20-16 here rite?

Yes, I am sorry, Original post edited - not to mislead people.
Thanks papgust

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