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02 Oct 2023, 00:00
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D
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Difficulty:
25%
(medium)
Question Stats:
73% (01:22) correct
27%
(01:41)
wrong
based on 49
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What is the remainder when the positive integer N is divided by 2?
(1) If \(N^2\) is divided by 2, the remainder is 1.
(2) If N is divided by 4, the remainder is 3.
(1) If \(N^2\) is divided by 2, the remainder is 1.
(2) If N is divided by 4, the remainder is 3.
Data Insights (DI) Butler 2023-24 [Click here for Details]
03 Oct 2023, 10:49
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Could someone explain the 2nd one n/4 rem is 3 how will it let us know the rem when N/2?
03 Oct 2023, 12:00
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Sajjad1994
From the question stem, we get :
N is a positive Integer.
We have to find the value of rem(N/2).
Consider first stem :
(1) If \(N^2\) is divided by 2, the remainder is 1.
\(REM[\frac{{n^2}}{2}]\) = 1
Take a few examples :
n = 2 ;\(n^2\) = 4 ; rem = 0.
n = 3 ; \(n^2\) = 9 ; rem = 1.
So we can safely say that N is odd.
From this we can conclude that \(REM[\frac{{n}}{2}]\) will also be 1.
Cancel B,C,E.
(2) If N is divided by 4, the remainder is 3.
Now independently consider stem 2 :
\(REM[\frac{{n}}{4}]\) = 3
From this think of a few basic numbers, and you will conclude that it is possible only when N is of the kind 7,11,15 etc or simply of the kind 7 + (n-1)4 where n = {1,2,3,4,......n}
Note 7 be odd, while (n-1)*4 will always be even. even + odd = odd.
From this we can conclude that N will be Odd and thus \(REM[\frac{{n}}{2}]\) will also be 1.
Cancel A.
IMO D.
