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A number is divided by 13 and leaves a remainder of 7. If the same number is divided by 26, what will be the remainder?
7
13
20
Cannot be determined
7
Check if the second divisor is a multiple of the first; if it is a multiple, the remainder is indeterminate without knowing the quotient parity.
A number N when divided by 13 leaves a remainder of 7.
N=13q+7
Check if the second divisor is a multiple of the first; if it is a multiple, the remainder is indeterminate without knowing the quotient parity.
Blindly assuming the remainder stays 7 or using the factor rule backward.
Division Algorithm Representation
Express the given statement mathematically using the division algorithm where q is the quotient: N=13q+7.
N=13q+7
Testing Divisibility by 26
We need to find the remainder when N is divided by 26. Substitute 13q+7 and analyze for different values of q.
N=13q+7
Case Analysis based on Quotient Parity
If q is even (q=2k), then N=26k+7 (remainder is 7). If q is odd (q=2k+1), then N=26k+20 (remainder is 20).
N=26k+7┬аor┬а26k+20
Final Conclusion
Since the remainder can be either 7 or 20 depending on the quotient, a unique remainder cannot be determined.
Remainder┬атИИ{7,20}
D is correct because the remainder can be either 7 or 20 depending on whether the quotient is even or odd, meaning it cannot be uniquely determined.
Always check if the new divisor is a factor (where remainder rules apply directly) or a multiple of the original divisor.
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