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If z is an integer greater than 1, is z even?
(1) 2z is not a factor of 8
(2) 3z/4 is a factor of 6
- 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 'B'. Can you explain this answer?
Most Upvoted Answer
If z is an integer greater than 1, is z even?(1) 2z is not a factor of...
Statement (1): 2z is not a factor of 8
This statement tells us that 2z does not divide evenly into 8. In other words, if we divide 8 by 2z, we will have a remainder.
To determine whether z is even or odd, we need to consider the possible values of z. If z is odd, then 2z will also be odd, and we would not be able to divide 8 by 2z without a remainder. However, if z is even, then 2z will also be even, and 8 will be divisible by 2z without a remainder.
Therefore, if 2z is not a factor of 8, it implies that z is odd, because if z were even, 2z would be a factor of 8.
Statement (2): 3z/4 is a factor of 6
This statement tells us that 3z/4 is a factor of 6. In other words, 6 is divisible by 3z/4 without a remainder.
To determine whether z is even or odd, we need to consider the possible values of z. If z is odd, then 3z/4 will also be odd, and 6 would not be divisible by 3z/4 without a remainder. However, if z is even, then 3z/4 will also be even, and 6 will be divisible by 3z/4 without a remainder.
Therefore, if 3z/4 is a factor of 6, it implies that z is even, because if z were odd, 3z/4 would not be a factor of 6.
Combined statements:
From statement (1), we know that if 2z is not a factor of 8, z must be odd.
From statement (2), we know that if 3z/4 is a factor of 6, z must be even.
Since the two statements provide contradictory information about the parity of z, we cannot determine whether z is even or odd. Therefore, neither statement alone is sufficient to answer the question.
Therefore, the correct answer is option B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
This statement tells us that 2z does not divide evenly into 8. In other words, if we divide 8 by 2z, we will have a remainder.
To determine whether z is even or odd, we need to consider the possible values of z. If z is odd, then 2z will also be odd, and we would not be able to divide 8 by 2z without a remainder. However, if z is even, then 2z will also be even, and 8 will be divisible by 2z without a remainder.
Therefore, if 2z is not a factor of 8, it implies that z is odd, because if z were even, 2z would be a factor of 8.
Statement (2): 3z/4 is a factor of 6
This statement tells us that 3z/4 is a factor of 6. In other words, 6 is divisible by 3z/4 without a remainder.
To determine whether z is even or odd, we need to consider the possible values of z. If z is odd, then 3z/4 will also be odd, and 6 would not be divisible by 3z/4 without a remainder. However, if z is even, then 3z/4 will also be even, and 6 will be divisible by 3z/4 without a remainder.
Therefore, if 3z/4 is a factor of 6, it implies that z is even, because if z were odd, 3z/4 would not be a factor of 6.
Combined statements:
From statement (1), we know that if 2z is not a factor of 8, z must be odd.
From statement (2), we know that if 3z/4 is a factor of 6, z must be even.
Since the two statements provide contradictory information about the parity of z, we cannot determine whether z is even or odd. Therefore, neither statement alone is sufficient to answer the question.
Therefore, the correct answer is option B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
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Community Answer
If z is an integer greater than 1, is z even?(1) 2z is not a factor of...
Steps 1 & 2: Understand Question and Draw Inferences
Given: Integer z > 1
To find: Is z even?
Step 3: Analyze Statement 1 independently
- 2z is not a factor of 8
- Factors of 8: {1, 2, 4, 8}
- This means, 2z is not equal to 1, 2, 4, 8
- z is not equal to ½ or 1(anyways not possible since z is an integer greater than 1)
- And, z is not 2 or 4
- But z can be equal to 8 or 10 or 12 etc.
- That is, z can still be an even number.
Thus, Statement 1 is not sufficient to answer the question
Step 4: Analyze Statement 2 independently
- 3z/4 is a factor of 6
- Factors of 6: {1, 2, 3, 6}
- This means 3z/4 is an integer and is equal to one of these 4 numbers.
- Since 3z/4 is an integer, z must be divisible by 4.
- Therefore, z is indeed even.
Statement 2 is sufficient to answer the question
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in Step 4, this step is not required
Answer: Option B
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If z is an integer greater than 1, is z even?(1) 2z is not a factor of 8(2) 3z/4 is a factor of 6a)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 askedd)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 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If z is an integer greater than 1, is z even?(1) 2z is not a factor of 8(2) 3z/4 is a factor of 6a)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 askedd)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 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If z is an integer greater than 1, is z even?(1) 2z is not a factor of 8(2) 3z/4 is a factor of 6a)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 askedd)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 'B'. Can you explain this answer?.
If z is an integer greater than 1, is z even?(1) 2z is not a factor of 8(2) 3z/4 is a factor of 6a)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 askedd)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 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If z is an integer greater than 1, is z even?(1) 2z is not a factor of 8(2) 3z/4 is a factor of 6a)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 askedd)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 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If z is an integer greater than 1, is z even?(1) 2z is not a factor of 8(2) 3z/4 is a factor of 6a)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 askedd)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 'B'. Can you explain this answer?.
Solutions for If z is an integer greater than 1, is z even?(1) 2z is not a factor of 8(2) 3z/4 is a factor of 6a)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 askedd)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 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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