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12 Nov 2004, 08:03
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How many 3 digit integers between 310 and 400, exclusive, are divisible by 3 when the tens digits and the hundred's digit are switched?
a)3 b)19 c)22 d)30 e)90
a)3 b)19 c)22 d)30 e)90
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12 Nov 2004, 08:43
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Good question. My answer: 30.
The second part of this is irrelevant, because a number who's digits add up to a multiple of three is divisible by 3, and switching the tens and hundreds place of a number keeps the same digits, so the new number is also divisible by three. Basically, it will be true of all numbers.
So the real question is how many numbers from 311 to 399 are divisible by three? Start with 312, since that's the first, and end with 399, since that's the last. The process is simple:
399-312 = 87
87/3 = 29
29 + 1 = 30
If you're not familiar with that, the way to find out how many numbers fit your category in a list of numbers is always just this: subtract, divide, add 1.
The second part of this is irrelevant, because a number who's digits add up to a multiple of three is divisible by 3, and switching the tens and hundreds place of a number keeps the same digits, so the new number is also divisible by three. Basically, it will be true of all numbers.
So the real question is how many numbers from 311 to 399 are divisible by three? Start with 312, since that's the first, and end with 399, since that's the last. The process is simple:
399-312 = 87
87/3 = 29
29 + 1 = 30
If you're not familiar with that, the way to find out how many numbers fit your category in a list of numbers is always just this: subtract, divide, add 1.
