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13 Jun 2022, 01:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
25% (02:17) correct
75%
(02:02)
wrong
based on 51
sessions
History
Date
Time
Result
Not Attempted Yet
For how many integers n is \(\frac {n}{20-n}\) the square of an integer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 10
Are You Up For the Challenge: 700 Level Questions
(A) 1
(B) 2
(C) 3
(D) 4
(E) 10
Are You Up For the Challenge: 700 Level Questions
13 Jun 2022, 02:18
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Starting with
n/(20-n)=0 => n=0
n/(20-n)=1 => n=10
n/(20-n)=4 => n=16
n/(20-n)=9 => n=18
We can see n=19 won't work.
n=20 is undefined.
Starting from n=21, n/(20-n) is negative and cannot be a square.
(I was not that smart in answering this question, though. I tried
n/(20-n)=16
n/(20-n)=25
n/(20-n)=36
and give up without feeling very confident. )
Now we know that (D) is the answer.
n/(20-n)=0 => n=0
n/(20-n)=1 => n=10
n/(20-n)=4 => n=16
n/(20-n)=9 => n=18
We can see n=19 won't work.
n=20 is undefined.
Starting from n=21, n/(20-n) is negative and cannot be a square.
(I was not that smart in answering this question, though. I tried
n/(20-n)=16
n/(20-n)=25
n/(20-n)=36
and give up without feeling very confident. )
Now we know that (D) is the answer.
13 Jun 2022, 05:50
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Bookmarks
N can be 2, 4, 10, 16, 18 and 20 too (since 0^2=0). And thus, (E) can be the only possible answer.
