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Feb 19, 2015

#1
+17747
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The smallest 3-digit integer is 100, the largest is 999.

Divide 100 by 13; the quotient is 7 and the remainder is 9; this means that the first multiple of 13 that will be at least 100 is 8.

Divide 1000 by 13; the quotient is 76 and the remainder is 12; this means that the last multiple fo 13 that will be smaller than 1000 is 76.

We now need to count the number of numbers starting with 8 and ending with 76.

A short way to do this is to subtract 8 from 76 and add 1 -- 76 - 8 + 1 = 69. (Don't forget to add 1!)

There are 69 positive integer multiples of 13 whose answers have 3 digits.

Feb 20, 2015

#1
+17747
+5

The smallest 3-digit integer is 100, the largest is 999.

Divide 100 by 13; the quotient is 7 and the remainder is 9; this means that the first multiple of 13 that will be at least 100 is 8.

Divide 1000 by 13; the quotient is 76 and the remainder is 12; this means that the last multiple fo 13 that will be smaller than 1000 is 76.

We now need to count the number of numbers starting with 8 and ending with 76.

A short way to do this is to subtract 8 from 76 and add 1 -- 76 - 8 + 1 = 69. (Don't forget to add 1!)

There are 69 positive integer multiples of 13 whose answers have 3 digits.

geno3141 Feb 20, 2015