If the two-digit integers \(M\) and \(N\) are positive and have the same digits, but in reverse order, which of the following cannot be the sum of \(M\) and \(N?\)
A) 181
B) 165
C) 121
D) 99
E) 44
Answer: A
Source: Official Guide
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If the two-digit integers \(M\) and \(N\) are positive and have the same digits, but in reverse order, which of the foll
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If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following cannot be the sum of M and N
Let the unit's digit of M be m
So, its tens digit becomes m
Therefre, M can be written as M = 10m + m = 11m
Similarly, let the unit's digit of N be n
So, its tens digit becomes n
Therefre, N can be written as N = 10n + n = 11n
Now, M + N = 11m + 11n = 11 (m+n)
Therefore, all the options should be a multiple of 11.
Only 181 is not a multiple of 11 among the given options. Therefore, answer is option A.
Let the unit's digit of M be m
So, its tens digit becomes m
Therefre, M can be written as M = 10m + m = 11m
Similarly, let the unit's digit of N be n
So, its tens digit becomes n
Therefre, N can be written as N = 10n + n = 11n
Now, M + N = 11m + 11n = 11 (m+n)
Therefore, all the options should be a multiple of 11.
Only 181 is not a multiple of 11 among the given options. Therefore, answer is option A.
