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When a positive integer n is divided by 4, the remainder is 3. Which o
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22 Sep 2022, 12:16
22 Sep 2022, 12:16
Expert Reply
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A
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C
D
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Difficulty:
25%
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Question Stats:
73% (01:04) correct
28%
(01:25)
wrong
based on 80
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When a positive integer n is divided by 4, the remainder is 3. Which of the following could equal n for some integer t ?
A. 4t + 2
B. 4t
C. 4t – 1
D. 4t – 2
E. 4t – 3
A. 4t + 2
B. 4t
C. 4t – 1
D. 4t – 2
E. 4t – 3
Re: When a positive integer n is divided by 4, the remainder is 3. Which o
[#permalink]
22 Sep 2022, 21:41
22 Sep 2022, 21:41
Expert Reply
Bunuel wrote:
When a positive integer n is divided by 4, the remainder is 3. Which of the following could equal n for some integer t ?
A. 4t + 2
B. 4t
C. 4t – 1
D. 4t – 2
E. 4t – 3
A. 4t + 2
B. 4t
C. 4t – 1
D. 4t – 2
E. 4t – 3
The statement gives n=4t+3
When t is one less, that is t-1, then n becomes 4(t-1)+3 = 4t-4+3 = 4t-1
C
GMATWhiz Representative
Joined: 23 May 2022
Posts: 640
Given Kudos: 6
Location: India
GMAT 1: 760 Q51 V40 
Re: When a positive integer n is divided by 4, the remainder is 3. Which o
[#permalink]
23 Sep 2022, 00:37
23 Sep 2022, 00:37
Expert Reply
Bunuel wrote:
When a positive integer n is divided by 4, the remainder is 3. Which of the following could equal n for some integer t ?
A. 4t + 2
B. 4t
C. 4t – 1
D. 4t – 2
E. 4t – 3
A. 4t + 2
B. 4t
C. 4t – 1
D. 4t – 2
E. 4t – 3
Solution:
- It is given that when n is divided by 4, the remainder is 3
- This means we can say \(n=4\times Q+3\) where Q is any integer
\(⇒n=4Q+4-1\)
\(⇒4(Q+1)-1\)
\(⇒4t-1\) where \(t = Q+1\) is an integer
Hence the right answer is Option C
