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Consider a 5 digit number, 3 a 25 b \overline{3a25b} for single digits non-negative integers a , b a,b .

If both values of a , b a,b are selected at random, what is the probability that the resultant number is divisible by 33 33 ?


The answer is 0.03.

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1 solution

Manish Mayank
Mar 31, 2015

For divisibility of 33 we should check the divisibity of 11 and 3. I think I need not to explain that for divisibility of 3 we should have ( a + b ) = 2 , 5 , 8 , 11 , 14 , 17 (a+b) = 2,5,8,11,14,17 Also for divisibility of 11 we need ( 3 + 2 + b ) ( a + 5 ) = 0 (3+2+b)-(a+5) = 0 (Since, the given numbers are not so large that we can get a multiple of 11 as difference) So we get, a + 5 = 5 + b a+5 = 5+b Or, a = b a=b Or, a + b = 2 a = 2 b a+b=2a=2b So a + b a+b is even. Hence only 2 , 8 , 14 2,8,14 are required 3 sums and there are only three sets of a a & b b . The number of ways in which a a & b b can be chosen are 10 × 10 = 100 10\times 10 = 100 Therefore required probability = 3 100 = 0.03 \frac{3}{100} = 0.03

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