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Bunuel
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For a positive integer m, [m] is defined to be the remainder when 7m 22 May 2023, 07:30
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73% (02:01) correct 27% (02:29) wrong based on 297 sessions

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For a positive integer m, [m] is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n + 1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
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A
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gmatophobia
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For a positive integer m, [m] is defined to be the remainder when 7m 22 May 2023, 13:54
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Bunuel
For a positive integer m, |m| is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n + 1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
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I. [3n + 1]

Remainder(\(\frac{7(3n + 1) }{ 3}\))

Remainder(\(\frac{7(3n) + (7) }{ 3}\))

Remainder = 1

II. [3n]

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder = 1

III. [3n] + 2

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder = 2

Hence, Only I (Option A)
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pragyanbhuyan999
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For a positive integer m, [m] is defined to be the remainder when 7m 19 Jun 2023, 07:30
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It should be n instead of m in the first line

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sanchitb23
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For a positive integer m, [m] is defined to be the remainder when 7m 20 Jun 2023, 13:31
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gmatophobia
Bunuel
For a positive integer m, |m| is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n + 1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

I. [3n + 1]

Remainder(\(\frac{7(3n + 1) }{ 3}\))

Remainder(\(\frac{7(3n) + (7) }{ 3}\))

Remainder = 1

II. [3n]

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder = 1

III. [3n] + 2

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder = 2

Hence, Only I (Option A)
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What is the difference between your solution of Case 1 and 2? Both Reminders are 1, Kindly elaborate the explanation

Bunuel , Please provide the Official Explanation of this Question
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ayushiii02
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For a positive integer m, [m] is defined to be the remainder when 7m 20 Jun 2023, 13:55
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I think case 2 should have zero as the remainder, hence only option A.

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imorenor
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For a positive integer m, [m] is defined to be the remainder when 7m 24 Jun 2023, 21:34
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gmatophobia
Bunuel
For a positive integer m, |m| is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n + 1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

I. [3n + 1]

Remainder(\(\frac{7(3n + 1) }{ 3}\))

Remainder(\(\frac{7(3n) + (7) }{ 3}\))

Remainder = 1

II. [3n]

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder = 1

III. [3n] + 2

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder = 2

Hence, Only I (Option A)
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Shouldn't it be the remainder of II equal to 0?? thanks!
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RohanNewDelhi
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For a positive integer m, [m] is defined to be the remainder when 7m 06 May 2026, 03:25
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guys do you feel wording of the question is wrong?
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Bunuel
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