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Amos counts out loud by six beginning with $0.$ Sarah counts out loud by three also beginning with $0.$ Between $0$ and $100$ inclusive, how many of the numbers do both Sarah and Amos say out loud?

 Feb 8, 2024

Best Answer 

 #1
avatar+1632 
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Both Sarah and Amos say 0.

Sarah says all multiples of 3, and Amos says all multiples of 6 (under 100), because 6 is a multiple of 3 (3 x 2), then all the numbers Amos says, Sarah will say too. So now the problem becomes how many multiples of 6 are under 100? 

The largest multiple of 6 under 100 is 96 (6 x 16), and the smallest would be 6 (6 x 1). 6 x 1 to 6 x 16 would yield 16 multiples.

So Amos says a multiple of 6 sixteen times, not including 0. Hence, 1 + 16 = 17 numbers that both Sarah and Amos say out loud.

 Feb 9, 2024
 #1
avatar+1632 
+2
Best Answer

Both Sarah and Amos say 0.

Sarah says all multiples of 3, and Amos says all multiples of 6 (under 100), because 6 is a multiple of 3 (3 x 2), then all the numbers Amos says, Sarah will say too. So now the problem becomes how many multiples of 6 are under 100? 

The largest multiple of 6 under 100 is 96 (6 x 16), and the smallest would be 6 (6 x 1). 6 x 1 to 6 x 16 would yield 16 multiples.

So Amos says a multiple of 6 sixteen times, not including 0. Hence, 1 + 16 = 17 numbers that both Sarah and Amos say out loud.

proyaop Feb 9, 2024

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