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Problem 635

AMC 10/12, early questions

Combinatorics Difficulty 3.8 Multiple choice CEMC Gauss (Grade 8) · Canada · 2020

Three spinners are shown. The spinners are used to determine the hundreds, tens and ones digits of a three-digit number.

How many possible three-digit numbers that can be formed in this way are divisible by 6?

Pick one

Official solution

Celyna spent $5.00 on candy A and$ 7.00 on candy B, or $12.00 in total.

The average price of all the candy that she purchased was $1.50 per 100 grams.

This means that if Celyna bought 100 grams of candy, she would have spent $1.50.

If she bought 200 grams of candy, she would have spent $2\times\$1.50=\$3.00$ .

How many grams of candy would Celyna need to buy to spend $12.00?

Since $8\times\$1.50=\$12.00$ (or $\$12.00\div\$1.50=8$ ), then she would need to buy a total of 800 grams of candy.
Celyna bought 300 grams of candy A, and so she must have purchased $800-300=500$ grams of candy B. The value of $x$ is 500.

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