Difference between revisions of "The positive three-digit integer N has a ones digit of 0. What is the probability that N is divisible by 4? Express your answer as a common fraction."
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An integer is divisible by 4 if and only if a number formed from the last two digits is divisible by 4. If the units digit is 0, all the numbers with even tens digits are divisible by 4 (00, 20, 40, 60, 80), and all the numbers with odd tens digits are not (10, 30, 50, 70, 90). Since there are the same number of even digits as odd digits, there is a <math>\boxed{1/2}</math> probability that <math>N</math> is divisible by 4. | An integer is divisible by 4 if and only if a number formed from the last two digits is divisible by 4. If the units digit is 0, all the numbers with even tens digits are divisible by 4 (00, 20, 40, 60, 80), and all the numbers with odd tens digits are not (10, 30, 50, 70, 90). Since there are the same number of even digits as odd digits, there is a <math>\boxed{1/2}</math> probability that <math>N</math> is divisible by 4. | ||
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Latest revision as of 12:48, 30 October 2024
An integer is divisible by 4 if and only if a number formed from the last two digits is divisible by 4. If the units digit is 0, all the numbers with even tens digits are divisible by 4 (00, 20, 40, 60, 80), and all the numbers with odd tens digits are not (10, 30, 50, 70, 90). Since there are the same number of even digits as odd digits, there is a 
probability that 
is divisible by 4.
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