Math Circles

Math Circles

By Ngo Minh

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The difference between 2 numbers is equal to one-half of their sum. What is the ratio of the first to the second number?

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The 5-digit number 9a65b is divisible by 36, where a and b are digits. Find sum of all possible values of those 5-digit numbers

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A scalene triangle has side lengths which are all prime numbers. What is the smallest possible perimeter it could have?

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Julia is buying a new laptop. She pays $260 of her own money, and her dad, sister, and brother are helping her with the rest of the sum. Her sister gave her 1/8 of the price of the laptop. Her brother gave her 1/4 of the price, and her dad gave her 1/2 of the price of the laptop. What is the price ($) of the new laptop?

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Consider the diagram on the right. What is the sum of the seven marked angles in degrees?