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02 Oct 2024, 12:18
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (00:58) correct
0% (00:00) wrong based on 1 sessions
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N = \(824^x\), where x is a positive integer.
Quantity A
The number of possible values of the units digit of N
Quantity B
4
Quantity A
The number of possible values of the units digit of N
Quantity B
4
03 Mar 2025, 10:54
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OE
Note that the units digit of a product of positive integers is equal to the units digit of the product of the units digits of those integers. In particular, since \(824^x\) is a product of x integers, each of which is 824, it follows that the units digit of \(824^x\) is equal to the units digit of \(4^x\). Also, the units digit of \(4^x\) is equal to the units digit of the product (4)(units digit of \(4^{x-1}\)).
The following table shows the units digit of \(4^x\) for some values of x, beginning with x = 2.
From the table, you can see that the units digit of \(4^x\) alternates, and will continue to alternate, between 4 and 6. Therefore, Quantity A, the number of possible values of the units digit of \(824^x\), is 2. Since Quantity B is 4, the correct answer is Choice B.
Note that the units digit of a product of positive integers is equal to the units digit of the product of the units digits of those integers. In particular, since \(824^x\) is a product of x integers, each of which is 824, it follows that the units digit of \(824^x\) is equal to the units digit of \(4^x\). Also, the units digit of \(4^x\) is equal to the units digit of the product (4)(units digit of \(4^{x-1}\)).
The following table shows the units digit of \(4^x\) for some values of x, beginning with x = 2.
From the table, you can see that the units digit of \(4^x\) alternates, and will continue to alternate, between 4 and 6. Therefore, Quantity A, the number of possible values of the units digit of \(824^x\), is 2. Since Quantity B is 4, the correct answer is Choice B.
