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What is the remainder when the positive integer n is divided by 2?
(1)  When n is divided by 13, the remainder is 3
(2)  n + 2 is a multiple of  7
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 
  • c)
    BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 
  • d)
    EACH statement ALONE is sufficient. 
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
What is the remainder when the positive integer n is divided by 2?(1) ...
Steps 1 & 2: Understand Question and Draw Inferences
We need to find the remainder when the positive integer n is divided by 2
i.e., we need to find if n is even or odd.
If n is even, then the remainder is 0
If n is odd, then the remainder is 1.
Step 3: Analyze Statement 1
When n is divided by 13, the remainder is 3
  • n = 13k + 3
This is not sufficient. n is odd when k is even and even when k is odd. 
Step 4: Analyze Statement 2
n + 2 is a multiple of  7
  • n+2 = 7t
  • n = 7t -2  = 7(t-1) + 5
This statement is not sufficient. n is even when t-1 is odd and n is odd when t-1 is even
Step 5: Analyze Both Statements Together (if needed)
Inference from statement 1: n = 13k + 3
Inference from statement 2: n = 7t -2 =  7(t-1) + 5
 Inference from statement 1 and statement 2: 13k + 3 = 7(t-1) + 5
  • 13k – 7(t-1) = 2
  • 13k – 7(t-1) = even
We know:
Odd – Odd = Even
Even – Even = Even
So k and t-1 can be both even or both odd
Hence, we cannot find if k and t is even or odd, and therefore we cannot find if n is even or odd.
Statement 1 and Statement 2 together are not sufficient to answer the question.
 Answer: Option (E)
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What is the remainder when the positive integer n is divided by 2?(1) When n is divided by 13, the remainder is 3(2) n + 2 is a multiple of 7a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'E'. Can you explain this answer?
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What is the remainder when the positive integer n is divided by 2?(1) When n is divided by 13, the remainder is 3(2) n + 2 is a multiple of 7a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the remainder when the positive integer n is divided by 2?(1) When n is divided by 13, the remainder is 3(2) n + 2 is a multiple of 7a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the remainder when the positive integer n is divided by 2?(1) When n is divided by 13, the remainder is 3(2) n + 2 is a multiple of 7a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'E'. Can you explain this answer?.
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