Alice the number theorist knows the rule for testing if a numbernis divisible by 3: n is divisible by 3 if and only if the sum of the digits ofnis divisible by 3.

When Alice visits Mars, she finds that the Martians have six hands, and six fingers on eachhand, so that they count in base 36. In base 36, Alice’s divisibility test doesn’t work for testing divisibility by d= 3. But it does work for one of the d listed below. Which one?

a. 4
b. 7
c. 10
d. 11
e. 15

e. 15

Explanation:

Alice is conducting a test which is to find that a number is divisible by 3 only if the sum of the digits is divisible by 3. The sum will be divisible by 3 but the digits may not be divisible by 3. In the case of Martians the number 36 is divisible by 3 but the sum is not divisible by 3. Same will be the case with 15. The number 15 is divisible by 3 but the sum may not be divisible by 3 and therefore the test will not work.

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