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Twenty consecutive numbers are chosen. All numbers that are divisible by five are discarded. What is the units digit of the product of the remaining numbers?

User Xrdty
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1 Answer

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To find the units digit of the product of the remaining numbers, we need to understand the pattern of units digits when multiplying consecutive numbers. The units digit of a product depends on the units digits of the multiplied numbers. For example, if we multiply two numbers with units digits of 3 and 4, the units digit of their product will be 2 (3 * 4 = 12).

Since we are discarding all numbers divisible by five, we need to consider the units digits of the remaining numbers. If the units digit of a number is not divisible by 5, it means it is one of the following: 1, 2, 3, 4, 6, 7, 8, or 9.

Let's consider the sequence of units digits when multiplying consecutive numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, ...

Notice that the units digits repeat in cycles of four: 1, 2, 3, 4. Therefore, the units digit of the product of any 20 consecutive numbers will be the same as the units digit of the product of the first four consecutive numbers: 1 * 2 * 3 * 4 = 24. Therefore, the units digit of the product of the remaining numbers is 4.

Final answer is The units digit of the product of the remaining numbers is 4.

User Ravi Koradia
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