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# If n is a positive integer and the units' digit of 7^n is divisible by

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Joined: 29 Jan 2015
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If n is a positive integer and the units' digit of 7^n is divisible by  [#permalink]

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24 Apr 2019, 01:21
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:24) correct 35% (00:51) wrong based on 23 sessions

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If n is a positive integer and the units' digit of 7^n is divisible by 3, which of the following must be true?

I. n is even.

II. n is odd.

III. n is divisible by 3.

(A) I only

(B) II only

(C) III only

(D) I and III

(E) None

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Re: If n is a positive integer and the units' digit of 7^n is divisible by  [#permalink]

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24 Apr 2019, 04:00
$$7^1 = 7$$
$$7^2 = 49$$. 9 divisible by 3.
$$7^3 = 343$$. 3 divisible by itself

I: false, since n can be 3 too.
II: false, since n can be 2 too.
III: false, since n can be 2 and is not divisible by 3.
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Re: If n is a positive integer and the units' digit of 7^n is divisible by  [#permalink]

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25 Apr 2019, 18:51
rohan2345 wrote:
If n is a positive integer and the units' digit of 7^n is divisible by 3, which of the following must be true?

I. n is even.

II. n is odd.

III. n is divisible by 3.

(A) I only

(B) II only

(C) III only

(D) I and III

(E) None

Since the pattern of units digits of 7^n is 7-9-3-1, we see that 7^2, 7^3, 7^6, 7^7, 7^10, 7^11, 7^14, 7^15, etc. all have units digits that is divisible by 3. We see that not all values of n are even, or odd, or divisible by 3. So none of the Roman numerals is true.

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Re: If n is a positive integer and the units' digit of 7^n is divisible by   [#permalink] 25 Apr 2019, 18:51
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