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If x and y are positive integers, is the following cube root an integer?
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. Can you explain this answer?
Verified Answer
If x and y are positive integers, is the following cube root an intege...
Evaluate Statement (1) alone.
Substitute the value of x from Statement (1) into the equation and manipulate it algebraically.
Since the question says that y is a positive integer, you know that the cube root of y3, which equals y, will also be a positive integer. Statement (1) is SUFFICIENT.
Evaluate Statement (1) alone (Alternative Method).
For the cube root of a number to be an integer, that number must be an integer cubed. Consequently, the simplified version of this question is: "is x + y2 equal to an integer cubed?"
Statement (1) can be re-arranged as follows:
x = y3 - y2
y3 = x + y2
Since y is an integer, the cube root of y3, which equals y, will also be an integer.
Since y3 = x + y2, the cube root of x + y2 will also be an integer. Therefore, the following will always be an integer:
Statement (1) alone is SUFFICIENT.
Evaluate Statement (2) alone.
Statement (2) provides minimal information. The question can be written as: "is the following cube root an integer?"
If y = 4, x + y2 = 2 + 42 = 18 and the cube root of 18 is not an integer. However, if y = 5, x + y2 = 2 + 52 = 27 and the cube root of 27 is an integer. Statement (2) is NOT SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
Substitute the value of x from Statement (1) into the equation and manipulate it algebraically.
Since the question says that y is a positive integer, you know that the cube root of y3, which equals y, will also be a positive integer. Statement (1) is SUFFICIENT.
Evaluate Statement (1) alone (Alternative Method).
For the cube root of a number to be an integer, that number must be an integer cubed. Consequently, the simplified version of this question is: "is x + y2 equal to an integer cubed?"
Statement (1) can be re-arranged as follows:
x = y3 - y2
y3 = x + y2
Since y is an integer, the cube root of y3, which equals y, will also be an integer.
Since y3 = x + y2, the cube root of x + y2 will also be an integer. Therefore, the following will always be an integer:
Statement (1) alone is SUFFICIENT.
Evaluate Statement (2) alone.
Statement (2) provides minimal information. The question can be written as: "is the following cube root an integer?"
If y = 4, x + y2 = 2 + 42 = 18 and the cube root of 18 is not an integer. However, if y = 5, x + y2 = 2 + 52 = 27 and the cube root of 27 is an integer. Statement (2) is NOT SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
Most Upvoted Answer
If x and y are positive integers, is the following cube root an intege...
Evaluate Statement (1) alone.
Substitute the value of x from Statement (1) into the equation and manipulate it algebraically.
Since the question says that y is a positive integer, you know that the cube root of y3, which equals y, will also be a positive integer. Statement (1) is SUFFICIENT.
Evaluate Statement (1) alone (Alternative Method).
For the cube root of a number to be an integer, that number must be an integer cubed. Consequently, the simplified version of this question is: "is x + y2 equal to an integer cubed?"
Statement (1) can be re-arranged as follows:
x = y3 - y2
y3 = x + y2
Since y is an integer, the cube root of y3, which equals y, will also be an integer.
Since y3 = x + y2, the cube root of x + y2 will also be an integer. Therefore, the following will always be an integer:
Statement (1) alone is SUFFICIENT.
Evaluate Statement (2) alone.
Statement (2) provides minimal information. The question can be written as: "is the following cube root an integer?"
If y = 4, x + y2 = 2 + 42 = 18 and the cube root of 18 is not an integer. However, if y = 5, x + y2 = 2 + 52 = 27 and the cube root of 27 is an integer. Statement (2) is NOT SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
Substitute the value of x from Statement (1) into the equation and manipulate it algebraically.
Since the question says that y is a positive integer, you know that the cube root of y3, which equals y, will also be a positive integer. Statement (1) is SUFFICIENT.
Evaluate Statement (1) alone (Alternative Method).
For the cube root of a number to be an integer, that number must be an integer cubed. Consequently, the simplified version of this question is: "is x + y2 equal to an integer cubed?"
Statement (1) can be re-arranged as follows:
x = y3 - y2
y3 = x + y2
Since y is an integer, the cube root of y3, which equals y, will also be an integer.
Since y3 = x + y2, the cube root of x + y2 will also be an integer. Therefore, the following will always be an integer:
Statement (1) alone is SUFFICIENT.
Evaluate Statement (2) alone.
Statement (2) provides minimal information. The question can be written as: "is the following cube root an integer?"
If y = 4, x + y2 = 2 + 42 = 18 and the cube root of 18 is not an integer. However, if y = 5, x + y2 = 2 + 52 = 27 and the cube root of 27 is an integer. Statement (2) is NOT SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
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If x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. Can you explain this answer?
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If x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. 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 x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. 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 x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. Can you explain this answer?.
If x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. 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 x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. 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 x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. Can you explain this answer?.
Solutions for If x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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If x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. Can you explain this answer?, a detailed solution for If x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. Can you explain this answer? has been provided alongside types of If x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If x and y are positive integers, is the following cube root an integer?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
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