Problem 3 · 2024 Math Kangaroo
Medium
Number Theory
divisibilityprimes
Which of the following numbers is two less than a multiple of ten, two more than a square number and two times a prime number?
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Answer: C — 38
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Hint 1 of 2
Test each option against all three conditions — the option ending in 8 is the first thing to check.
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Hint 2 of 2
A number two less than a multiple of ten ends in 8; then check it is two more than a square and twice a prime.
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Approach: check the three structure conditions
- Two less than a multiple of ten means the number ends in 8, leaving 78, 58 and 38.
- Two more than a square: 38 − 2 = 36 = 6² works (76 and 56 are not squares).
- Twice a prime: 38 = 2 × 19 and 19 is prime.
- So the number is 38.
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