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Problem 225

Number theory Difficulty 1.6 Multiple choice CEMC Gauss (Grade 8) · Canada · 2012

The digits 2, 4, 6 and 8 are each used once to create two 2-digit numbers. What is the smallest possible difference between the two 2-digit numbers?

Pick one

Official solution

Solution 1

Since the ratio of boys to girls is $8:5$ , then for every 5 girls there are 8 boys.

That is, the number of girls at Gauss Public School is $\frac{5}{8}$ of the number of boys.

Since the number of boys at the school is 128, the number of girls is $\frac{5}{8}\times128=\frac{640}{8}=80$ .
The number of students at the school is the number of boys added to the number of girls or $128+80=208$ .

Solution 2

Since the ratio of boys to girls is $8:5$ , then for every 8 boys there are $8+5=13$ students.

That is, the number of students at Gauss Public School is $\frac{13}{8}$ of the number of boys.
Since the number of boys at the school is 128, the number of students is $\frac{13}{8}\times128=\frac{1664}{8}=208$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.