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If m and n are nonzero integers, is mn an integer?
(1) nm is positive.
(2) nm is an integer.
(1) nm is positive.
(2) nm is an integer.
- 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;
- 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 are needed.
Correct answer is option 'E'. Can you explain this answer?
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Most Upvoted Answer
If m and n are nonzero integers, is mn an integer?(1) nm is positive.(...
We need to determine if m^n is an integer, given that m and n are nonzero integers. Notice that m^n is an integer if n is positive OR if n is negative and m is either 1 or -1.
Statement One Alone:
If n = 2 and m = 4, then mn = 42 = 16 is an integer. However, if n = -2 and m = 4, then m^n = 4(-2) = 1/16 is not an integer. Statement one alone is not sufficient.
Statement Two Alone:
If n = 2 and m = 4, then mn = 42 = 16 is an integer. However, if n = -2 and m = 4, then m^n = 4(-2) = 1/16 is not an integer. Statement two alone is not sufficient.
Statements One and Two Together:
With the two statements, nm is a positive integer. We can use the same examples for statement one and statement two to see that both statements together are not sufficient.
Statement One Alone:
If n = 2 and m = 4, then mn = 42 = 16 is an integer. However, if n = -2 and m = 4, then m^n = 4(-2) = 1/16 is not an integer. Statement one alone is not sufficient.
Statement Two Alone:
If n = 2 and m = 4, then mn = 42 = 16 is an integer. However, if n = -2 and m = 4, then m^n = 4(-2) = 1/16 is not an integer. Statement two alone is not sufficient.
Statements One and Two Together:
With the two statements, nm is a positive integer. We can use the same examples for statement one and statement two to see that both statements together are not sufficient.
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If m and n are nonzero integers, is mn an integer?(1) nm is positive.(...
Statement 1:
nm is positive.
If nm is positive, it means that n and m have the same sign. If both n and m are positive or both are negative, then their product mn will be positive. If one of them is positive and the other is negative, then their product mn will be negative. In both cases, mn will be an integer.
Therefore, statement 1 alone is sufficient to answer the question.
Statement 2:
nm is an integer.
If nm is an integer, it implies that n and m have no fractional or decimal parts. However, this information alone does not provide any information about the sign of n and m. Therefore, we cannot determine whether mn is an integer or not based on statement 2 alone.
Therefore, statement 2 alone is not sufficient to answer the question.
Combined statements:
From statement 1, we know that nm is positive. This means that n and m have the same sign, either both positive or both negative.
From statement 2, we know that nm is an integer. This means that n and m have no fractional or decimal parts.
Combining these two statements, we can conclude that n and m are both nonzero integers with the same sign (either both positive or both negative), and they have no fractional or decimal parts. Therefore, their product mn will be an integer.
Therefore, both statements together are sufficient to answer the question.
Hence, the correct answer is option (C).
nm is positive.
If nm is positive, it means that n and m have the same sign. If both n and m are positive or both are negative, then their product mn will be positive. If one of them is positive and the other is negative, then their product mn will be negative. In both cases, mn will be an integer.
Therefore, statement 1 alone is sufficient to answer the question.
Statement 2:
nm is an integer.
If nm is an integer, it implies that n and m have no fractional or decimal parts. However, this information alone does not provide any information about the sign of n and m. Therefore, we cannot determine whether mn is an integer or not based on statement 2 alone.
Therefore, statement 2 alone is not sufficient to answer the question.
Combined statements:
From statement 1, we know that nm is positive. This means that n and m have the same sign, either both positive or both negative.
From statement 2, we know that nm is an integer. This means that n and m have no fractional or decimal parts.
Combining these two statements, we can conclude that n and m are both nonzero integers with the same sign (either both positive or both negative), and they have no fractional or decimal parts. Therefore, their product mn will be an integer.
Therefore, both statements together are sufficient to answer the question.
Hence, the correct answer is option (C).
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If m and n are nonzero integers, is mn an integer?(1) nm is positive.(2) nm is an integer.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;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 are needed.Correct answer is option 'E'. Can you explain this answer?
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If m and n are nonzero integers, is mn an integer?(1) nm is positive.(2) nm is an integer.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;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 are needed.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 If m and n are nonzero integers, is mn an integer?(1) nm is positive.(2) nm is an integer.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;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 are needed.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 If m and n are nonzero integers, is mn an integer?(1) nm is positive.(2) nm is an integer.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;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 are needed.Correct answer is option 'E'. Can you explain this answer?.
If m and n are nonzero integers, is mn an integer?(1) nm is positive.(2) nm is an integer.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;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 are needed.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 If m and n are nonzero integers, is mn an integer?(1) nm is positive.(2) nm is an integer.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;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 are needed.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 If m and n are nonzero integers, is mn an integer?(1) nm is positive.(2) nm is an integer.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;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 are needed.Correct answer is option 'E'. Can you explain this answer?.
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