When 10 000 is divided by 13, the remainder is 3. Which one of the following numbers also gives a remainder of 3 when divided by 13?
CEMC Gauss (Grade 8), 2013
Pick one
Solution
Each time Daniel reaches into the jar, he removes half of the coins that are in the jar.
Since he removes half of the coins, then the other half of the coins remain in the jar.
We summarize Daniel’s progress in the table below.
| Number of Times Coins are Removed | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Number of Coins Remaining in the Jar | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
For exactly 1 coin to remain in the jar, Daniel must reach in and remove coins from the jar 6 times.
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