Problem 5 · 2020 Math Kangaroo
Easy
Algebra & Patterns
arithmetic-sequence
Eli drew a board on the floor with nine squares and wrote a number in each one, starting from 1 and adding 3 each time, until the board was full. Three of the numbers she wrote are shown in the picture. Which number below could be the one in the colored box?
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Answer: E — 22
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Hint 1 of 3
Skip-count out loud: start at 1 and keep adding 3 until you have written nine numbers.
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Hint 2 of 3
The colored box must hold one of the numbers Eli actually wrote, so check which answer choice shows up in your skip-count.
Still stuck? Show hint 3 →
Hint 3 of 3
Notice that some choices never appear in the count-by-3 list at all.
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Approach: write out Eli's count-by-3 list and see which choice fits
- Eli starts at 1 and keeps adding 3, so the nine numbers she writes are 1, 4, 7, 10, 13, 16, 19, 22, 25.
- Look at the choices: 14, 17 and 20 are never on this list, and 10 is already shown in another box, so they cannot sit in the colored box.
- The only choice left that Eli really wrote is 22, so the colored box holds 22, which is choice E.
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