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If 77*n is divisible by 3, 7, and 77 for a positive integer n, which

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Bunuel
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If 77*n is divisible by 3, 7, and 77 for a positive integer n, which [#permalink] New post   31 Jan 2023, 07:21
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If 77*n is divisible by 3, 7, and 77 for a positive integer n, which of the following is also divisible by 3, 7, and 77?

A. 77n + 231
B. 11n + 231
C. 77n + 321
D. 7n + 231
E. 11n
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Re: If 77*n is divisible by 3, 7, and 77 for a positive integer n, which [#permalink] New post   31 Jan 2023, 08:26
Bunuel wrote:
If 77*n is divisible by 3, 7, and 77 for a positive integer n, which of the following is also divisible by 3, 7, and 77?

A. 77n + 231
B. 11n + 231
C. 77n + 321
D. 7n + 231
E. 11n

Let n be 3...

77*n = 77*3 = 231

Now, since 231 is divisible by 3, 7, and 77 , 231+231 must be divisible by 3, 7, and 77 , Answer must be (A) 77n + 231
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Re: If 77*n is divisible by 3, 7, and 77 for a positive integer n, which [#permalink] New post   31 Jan 2023, 18:50
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Bunuel wrote:
If 77*n is divisible by 3, 7, and 77 for a positive integer n, which of the following is also divisible by 3, 7, and 77?

A. 77n + 231
B. 11n + 231
C. 77n + 321
D. 7n + 231
E. 11n


Since 77 has factors of 77 and 7, but not 3, we see that n must be a multiple of 3.

So, since 77n is a multiple of 3, 7, and 11, and since 321 is also a multiple of 3, 7, and 11, the correct answer is 77n + 231.

Answer: A
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Re: If 77*n is divisible by 3, 7, and 77 for a positive integer n, which [#permalink] New post   31 Jan 2023, 19:21
Bunuel wrote:
If 77*n is divisible by 3, 7, and 77 for a positive integer n, which of the following is also divisible by 3, 7, and 77?

A. 77n + 231
B. 11n + 231
C. 77n + 321
D. 7n + 231
E. 11n



We need to find the LCM (lowest common Multiple) of 3,7,77

77n is already divided by the three numbers

We need to find the lowest common multiple that can be divided by all three

so LCM is 231

Option (A) perfectly fits and is our answer
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Re: If 77*n is divisible by 3, 7, and 77 for a positive integer n, which [#permalink]
31 Jan 2023, 19:21
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