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22 Oct 2020, 03:51
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:44) correct
24%
(02:17)
wrong
based on 63
sessions
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Date
Time
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Not Attempted Yet
How many numbers, which are squares of prime numbers have sum of factors equal to 57?
(A) One
(B) Two
(C) Three
(D) Seven
(E) Nine
(A) One
(B) Two
(C) Three
(D) Seven
(E) Nine
22 Oct 2020, 04:06
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Sajjad1994
If the prime number is p, then its square will be \(p^2\).
number of factors of \(p^2\) will be (2+1) or 3, and they are \(1, p, p^2\).
Given that \(1+p+p^2=57..........p+p^2=56............p(p+1)=56\)
So product of two consecutive number is 56, and there can be only one such value.
\(p(p+1)=56=7*8\)
p=7..ONLY 1 value
A
22 Oct 2020, 04:22
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IMO, it's A
When the prime number is 7, the number is 49
And the sum of the factors is 1+7+49=57
Any other square of prime number would be greater or smaller than 57.
Posted from my mobile device
When the prime number is 7, the number is 49
And the sum of the factors is 1+7+49=57
Any other square of prime number would be greater or smaller than 57.
Posted from my mobile device
