Question : What are the values of R and M, respectively, if the given number is perfectly divisible by 16 and 11?
34R05030M6
Option 1: 4 and 6
Option 2: 7 and 5
Option 3: 5 and 5
Option 4: 5 and 7
Correct Answer: 5 and 5
Solution :
Any number that has 4 or greater than 4 digits is divisible by 16 if and only if the last 4 digits of the number are divisible by 16.
Last 4 digits = 30M6
$\frac{30M6}{16}$ should be a whole number.
So M = 5 because $\frac{3056}{16}$ = 191
Now the number is 34R0503056
A number is divisible by 11 if the difference of the sum of odd and even places is divisible by 11.
To be divisible by 11,
$\frac{[(3 + R + 5 + 3 + 5) - (4 + 0 + 0 + 0 + 6)]}{11}$ should be a whole number
$=\frac{16+R-10}{11}$
$=\frac{6+R}{11}$
Hence, R must be 5 so that (6 + R) is divisible by 11.
Hence, the correct answer is 5 and 5.
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