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PrintSouth African Mathematics Olympiad Second Round
South Africa algebra
Problem
1. Joyce has a box with light bulbs, some blue and some red. She counts the bulbs and finds that 10 of the 40 are blue. What percentage of the bulbs are blue?
2. If is a perfect square, what is the smallest positive integer value for ?
2. If is a perfect square, what is the smallest positive integer value for ?
Solution
1. So, of the bulbs are blue.
2. The prime factorisation of is . In a perfect square, each prime factor has an even exponent, so we need one more power of and one more power of . The answer is .
2. The prime factorisation of is . In a perfect square, each prime factor has an even exponent, so we need one more power of and one more power of . The answer is .
Final answer
25%; 14
Techniques
FractionsFactorization techniques