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If x and y are integers, is y even?
(1) (x + 2) * (y2 + 7) is even
(2) (x3 + 8) * (y2 -4) is even
- 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?
Most Upvoted Answer
If x and y are integers, is y even?(1) (x + 2) * (y2 + 7) is even(2) (...
Statement (1):
(x^2 - 2) * (y^2 - 7) is even.
Statement (2):
(x^3 - 8) * (y^2 - 4) is even.
To determine if y is even, we need to analyze both statements together.
Analysis:
Let's start by analyzing each statement separately.
Statement (1):
(x^2 - 2) * (y^2 - 7) is even.
We know that the product of two integers is even if at least one of the integers is even. In this case, for the product to be even, either (x^2 - 2) or (y^2 - 7) should be even.
If (x^2 - 2) is even, then x^2 must be even, which means x is even.
If (y^2 - 7) is even, then y^2 must be odd, which means y is odd.
From this statement alone, we cannot determine if y is even or odd. Thus, statement (1) alone is not sufficient.
Statement (2):
(x^3 - 8) * (y^2 - 4) is even.
Similar to statement (1), for the product to be even, either (x^3 - 8) or (y^2 - 4) should be even.
If (x^3 - 8) is even, then x^3 must be even, which means x is even.
If (y^2 - 4) is even, then y^2 must be even, which means y is even.
From this statement alone, we cannot determine if y is even or odd. Thus, statement (2) alone is not sufficient.
Combined Analysis:
Combining both statements, we know that x is even (from both statements) and y can be either even or odd (from statement 1 and statement 2).
Therefore, the information provided in both statements together is not sufficient to determine if y is even.
Hence, the correct answer is option E - Statements (1) and (2) together are not sufficient.
(x^2 - 2) * (y^2 - 7) is even.
Statement (2):
(x^3 - 8) * (y^2 - 4) is even.
To determine if y is even, we need to analyze both statements together.
Analysis:
Let's start by analyzing each statement separately.
Statement (1):
(x^2 - 2) * (y^2 - 7) is even.
We know that the product of two integers is even if at least one of the integers is even. In this case, for the product to be even, either (x^2 - 2) or (y^2 - 7) should be even.
If (x^2 - 2) is even, then x^2 must be even, which means x is even.
If (y^2 - 7) is even, then y^2 must be odd, which means y is odd.
From this statement alone, we cannot determine if y is even or odd. Thus, statement (1) alone is not sufficient.
Statement (2):
(x^3 - 8) * (y^2 - 4) is even.
Similar to statement (1), for the product to be even, either (x^3 - 8) or (y^2 - 4) should be even.
If (x^3 - 8) is even, then x^3 must be even, which means x is even.
If (y^2 - 4) is even, then y^2 must be even, which means y is even.
From this statement alone, we cannot determine if y is even or odd. Thus, statement (2) alone is not sufficient.
Combined Analysis:
Combining both statements, we know that x is even (from both statements) and y can be either even or odd (from statement 1 and statement 2).
Therefore, the information provided in both statements together is not sufficient to determine if y is even.
Hence, the correct answer is option E - Statements (1) and (2) together are not sufficient.
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Community Answer
If x and y are integers, is y even?(1) (x + 2) * (y2 + 7) is even(2) (...
Step 1 and 2: Understand the question and draw inferences
We are given that x and y are integers, and we are asked if y is even. Since we do not have any more information to draw inferences from, let’s move straight to Statement 1.
Step 3: Analyze Statement 1
(x + 2) * (y2 + 7) is even
The product of two numbers is even if at least one of the two numbers is even.
Thus, three possibilities arise:
Statement 1 holds true for each of these 3 cases. Thus, we cannot ascertain for sure if y is odd or even.
Therefore, Statement 1 alone is not sufficient to answer the question.
Step 4: Analyze Statement 2
(x3 + 8) * (y2 -4) is even
Again, the product of two numbers is even if at least one of the two numbers is even.
So, three possibilities arise for this statement as well:
Statement 2 holds true for each of these 3 cases. Thus, we cannot ascertain for sure if y is odd or even.
Therefore, Statement 2 alone is not sufficient to answer the question.
Step 5: Analyze both statements together (if needed)
We have seen that
Statement 1 holds true if:
i) x is even, y is even or odd
ii) x is odd, y is odd
Statement 2 holds true if:
i) x is even, y is even or odd
ii) x is odd, y is even
Both Statements will be true at the same time only if:
x is even, y is even or odd.
Thus, even after combining both the statements, we have not been able to ascertain the even-odd nature of y.
Thus, both the statements together are not sufficient to answer the question.
Correct Answer Choice: Option E
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If x and y are integers, is y even?(1) (x + 2) * (y2 + 7) is even(2) (x3 + 8) * (y2 -4) is evena)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 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 integers, is y even?(1) (x + 2) * (y2 + 7) is even(2) (x3 + 8) * (y2 -4) is evena)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 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are integers, is y even?(1) (x + 2) * (y2 + 7) is even(2) (x3 + 8) * (y2 -4) is evena)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?.
If x and y are integers, is y even?(1) (x + 2) * (y2 + 7) is even(2) (x3 + 8) * (y2 -4) is evena)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 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 integers, is y even?(1) (x + 2) * (y2 + 7) is even(2) (x3 + 8) * (y2 -4) is evena)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 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are integers, is y even?(1) (x + 2) * (y2 + 7) is even(2) (x3 + 8) * (y2 -4) is evena)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?.
Solutions for If x and y are integers, is y even?(1) (x + 2) * (y2 + 7) is even(2) (x3 + 8) * (y2 -4) is evena)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? in English & in Hindi are available as part of our courses for GMAT.
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