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Is the square of positive integer Z divisible by 9?
       (1)  The sum of the digits of Z3 is divisible by 9
       (2)  3Z4 + 16 leaves a remainder of 7 when divided by 9
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  • d)
    EACH statement ALONE is sufficient to answer the question asked.
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Is the square of positive integer Z divisible by 9? (1) The sum of t...
Steps 1 & 2: Understand Question and Draw Inferences
Given: Positive integer Z
To find:
  • Is Z2 divisible by 9?
    • 9 = 32
  • So, Z2 will be divisible by 32 if
    • Z is divisible by 3
  Step 3: Analyze Statement 1 independently
  • The sum of the digits of Z3 is divisible by 9
  • This means, Z3 is divisible by 9
    • 9 = 32
  • So, 3 is a prime factor of Z3
  • Therefore, 3 is a prime factor of Z as well
Hence, Z is indeed divisible by 3
Statement 1 is sufficient to answer the question.
 
Step 4: Analyze Statement 2 independently
  • 3Z4 + 16 leaves a remainder of 7 when divided by 9
    • So, we can write: 3Z4 + 16 = 9k + 7, where k is some integer
  • 3Z4 = 9k + (7 – 16) = 9k – 9 = 9(k-1)
  • This simplifies to: Z4  = 3(k-1)
  • Z4 is divisible by 3
  • In other words, 3 is a prime factor of Z4
  • Therefore 3 is a prime factor of Z as well.
So, Z is indeed divisible by 3
Statement 2 alone is sufficient to answer the question.
Step 5: Analyze Both Statements Together (if needed)
Since we’ve arrived at a unique answer in each of Steps 3 and 4, this step is not required
Answer: Option D
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Is the square of positive integer Z divisible by 9? (1) The sum of the digits of Z3 is divisible by 9 (2) 3Z4 + 16 leaves a remainder of 7 when divided by 9a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?
Question Description
Is the square of positive integer Z divisible by 9? (1) The sum of the digits of Z3 is divisible by 9 (2) 3Z4 + 16 leaves a remainder of 7 when divided by 9a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. 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 Is the square of positive integer Z divisible by 9? (1) The sum of the digits of Z3 is divisible by 9 (2) 3Z4 + 16 leaves a remainder of 7 when divided by 9a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is the square of positive integer Z divisible by 9? (1) The sum of the digits of Z3 is divisible by 9 (2) 3Z4 + 16 leaves a remainder of 7 when divided by 9a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?.
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