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16 Sep 2014, 00:27
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Difficulty:
45%
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Question Stats:
69% (01:57) correct
31%
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If \(2^{98} = 256*m + n\), where \(m\) and \(n\) are integers and \(0 \le n \le 4\), what is the value of \(n\)?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
16 Sep 2014, 00:27
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Official Solution:
If \(2^{98} = 256*m + n\), where \(m\) and \(n\) are integers and \(0 \le n \le 4\), what is the value of \(n\)?
A. 0
B. 1
C. 2
D. 3
E. 4
Given:
\(2^{98} = 2^8 * m + n\).
Divide both sides by \(2^8\):
\(2^{90} = m + \frac{n}{2^8}\).
Since both \(2^{90}\) and \(m\) are integers, then \(\frac{n}{2^8}\) must also be an integer. Considering the constraint \(0 \le n \le 4\), this is only possible when \(n = 0\).
Answer: A
If \(2^{98} = 256*m + n\), where \(m\) and \(n\) are integers and \(0 \le n \le 4\), what is the value of \(n\)?
A. 0
B. 1
C. 2
D. 3
E. 4
Given:
\(2^{98} = 2^8 * m + n\).
Divide both sides by \(2^8\):
\(2^{90} = m + \frac{n}{2^8}\).
Since both \(2^{90}\) and \(m\) are integers, then \(\frac{n}{2^8}\) must also be an integer. Considering the constraint \(0 \le n \le 4\), this is only possible when \(n = 0\).
Answer: A
13 Feb 2017, 11:09
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Another way to approach this problem in terms of ODD and EVEN.
Given : \(2^{98}=256L+N\)
==> \(2^{98}=2^8L+N\) .Now , Left hand expression is EVEN and we know E+E or O+O only gives output as EVEN But since L is multiplied by 2^8 so ODD+ODD case is not possible.
Now , N can take only even values i.e. 0,2,4
If we Put N=2 then one 2 from N and L will cancel out from Right and Left side leaving below expression :
\(2^{97}=2^7L+1\)
But then Right side expression will give ODD value which is incorrect.Same is the case with N= 4 .
So only possible value is 0 . Ans A
Given : \(2^{98}=256L+N\)
==> \(2^{98}=2^8L+N\) .Now , Left hand expression is EVEN and we know E+E or O+O only gives output as EVEN But since L is multiplied by 2^8 so ODD+ODD case is not possible.
Now , N can take only even values i.e. 0,2,4
If we Put N=2 then one 2 from N and L will cancel out from Right and Left side leaving below expression :
\(2^{97}=2^7L+1\)
But then Right side expression will give ODD value which is incorrect.Same is the case with N= 4 .
So only possible value is 0 . Ans A
