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square of an integer

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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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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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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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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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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