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An ordered pair of digits (a,b) is such that 4a5, b72 is a multiple of 66. Find a + b .

 Sep 16, 2021
 #1
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a + b = 12.

 Sep 16, 2021
 #2
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The prime factors of 66 are 2.3.11, so 4a5b72 must be divisible by these factors.

 Clearly it is divisible by 2.

For it to be divisible by 3 we must have a+b as a multiple of 3.

Try the simplest:  a = 0, b = 3:   405372/66 = 6142.

 

Assuming the sum of a and b is unique, then a+b = 3

 Sep 16, 2021
edited by Alan  Sep 16, 2021

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