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If x, y, z and w are positive integers, is x odd?
(1) 7x + 8y + 4z + 5w is odd
(2) 3x + 2y + 8z + 2w is even
(2) 3x + 2y + 8z + 2w is even
- 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 x, y, z and w are positive integers, is x odd?(1) 7x + 8y + 4z + 5w...
NOTE. addition OF EVEN NO. RESULTS IN AN EVEN NO.
In statement 1. 7x+8y+4z+5w is odd here, which means the values of 8y,4z are even as multiple of 8 and 4 are even and the addition of these 5 terms results in an odd no.
it concludes that either 7x is odd or 5w is odd
as any no. multiplied by 7 is either even or odd Same is the case with 5w , so we can say that the whole complete value of the term depends upon the value of 5w (being odd or even)
In Statement 2. 3x+2y+8z+2w is even .
here terms , 2y,8z,2w are even as any no. multiplied by 2 and 8 or results in an even no.
So, if the whole expression is even 3x neends to be even which means x is even and multiple of 3x is also even
Result . X is an even no. hence Option B is correct
In statement 1. 7x+8y+4z+5w is odd here, which means the values of 8y,4z are even as multiple of 8 and 4 are even and the addition of these 5 terms results in an odd no.
it concludes that either 7x is odd or 5w is odd
as any no. multiplied by 7 is either even or odd Same is the case with 5w , so we can say that the whole complete value of the term depends upon the value of 5w (being odd or even)
In Statement 2. 3x+2y+8z+2w is even .
here terms , 2y,8z,2w are even as any no. multiplied by 2 and 8 or results in an even no.
So, if the whole expression is even 3x neends to be even which means x is even and multiple of 3x is also even
Result . X is an even no. hence Option B is correct
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Community Answer
If x, y, z and w are positive integers, is x odd?(1) 7x + 8y + 4z + 5w...
Solution:
To determine whether x is odd, we need to analyze the information provided in each statement.
Statement 1: 7x + 8y + 4z + 5w is odd.
To determine whether this expression is odd, we need to examine the individual terms.
- The term 7x is odd since it is the product of an odd number (7) and any integer, x.
- The term 8y is even since it is the product of an even number (8) and any integer, y.
- The term 4z is even since it is the product of an even number (4) and any integer, z.
- The term 5w is odd since it is the product of an odd number (5) and any integer, w.
Since the sum of odd and even terms is always odd, we can conclude that the expression 7x + 8y + 4z + 5w is odd.
However, this information is not sufficient to determine whether x is odd or even. For example, if x = 2, then the expression becomes 14 + 8y + 4z + 5w, which is still odd. But if x = 4, then the expression becomes 28 + 8y + 4z + 5w, which is even. Therefore, statement 1 alone is not sufficient to answer the question.
Statement 2: 3x + 2y + 8z + 2w is even.
To determine whether this expression is even, we need to examine the individual terms.
- The term 3x is odd since it is the product of an odd number (3) and any integer, x.
- The term 2y is even since it is the product of an even number (2) and any integer, y.
- The term 8z is even since it is the product of an even number (8) and any integer, z.
- The term 2w is even since it is the product of an even number (2) and any integer, w.
Since the sum of odd and even terms is always even, we can conclude that the expression 3x + 2y + 8z + 2w is even.
However, this information is also not sufficient to determine whether x is odd or even. For example, if x = 2, then the expression becomes 6 + 2y + 8z + 2w, which is even. But if x = 4, then the expression becomes 12 + 2y + 8z + 2w, which is also even. Therefore, statement 2 alone is not sufficient to answer the question.
Combining the statements:
By combining the information from both statements, we have:
7x + 8y + 4z + 5w is odd
3x + 2y + 8z + 2w is even
Since the sum of two odd numbers is always even, we can conclude that x must be odd. Therefore, both statements together are sufficient to answer the question.
Thus, the correct answer is option (c) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is
To determine whether x is odd, we need to analyze the information provided in each statement.
Statement 1: 7x + 8y + 4z + 5w is odd.
To determine whether this expression is odd, we need to examine the individual terms.
- The term 7x is odd since it is the product of an odd number (7) and any integer, x.
- The term 8y is even since it is the product of an even number (8) and any integer, y.
- The term 4z is even since it is the product of an even number (4) and any integer, z.
- The term 5w is odd since it is the product of an odd number (5) and any integer, w.
Since the sum of odd and even terms is always odd, we can conclude that the expression 7x + 8y + 4z + 5w is odd.
However, this information is not sufficient to determine whether x is odd or even. For example, if x = 2, then the expression becomes 14 + 8y + 4z + 5w, which is still odd. But if x = 4, then the expression becomes 28 + 8y + 4z + 5w, which is even. Therefore, statement 1 alone is not sufficient to answer the question.
Statement 2: 3x + 2y + 8z + 2w is even.
To determine whether this expression is even, we need to examine the individual terms.
- The term 3x is odd since it is the product of an odd number (3) and any integer, x.
- The term 2y is even since it is the product of an even number (2) and any integer, y.
- The term 8z is even since it is the product of an even number (8) and any integer, z.
- The term 2w is even since it is the product of an even number (2) and any integer, w.
Since the sum of odd and even terms is always even, we can conclude that the expression 3x + 2y + 8z + 2w is even.
However, this information is also not sufficient to determine whether x is odd or even. For example, if x = 2, then the expression becomes 6 + 2y + 8z + 2w, which is even. But if x = 4, then the expression becomes 12 + 2y + 8z + 2w, which is also even. Therefore, statement 2 alone is not sufficient to answer the question.
Combining the statements:
By combining the information from both statements, we have:
7x + 8y + 4z + 5w is odd
3x + 2y + 8z + 2w is even
Since the sum of two odd numbers is always even, we can conclude that x must be odd. Therefore, both statements together are sufficient to answer the question.
Thus, the correct answer is option (c) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is
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If x, y, z and w are positive integers, is x odd?(1) 7x + 8y + 4z + 5w is odd(2) 3x + 2y + 8z + 2w is evena)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? 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, y, z and w are positive integers, is x odd?(1) 7x + 8y + 4z + 5w is odd(2) 3x + 2y + 8z + 2w is evena)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? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x, y, z and w are positive integers, is x odd?(1) 7x + 8y + 4z + 5w is odd(2) 3x + 2y + 8z + 2w is evena)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?.
If x, y, z and w are positive integers, is x odd?(1) 7x + 8y + 4z + 5w is odd(2) 3x + 2y + 8z + 2w is evena)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? 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, y, z and w are positive integers, is x odd?(1) 7x + 8y + 4z + 5w is odd(2) 3x + 2y + 8z + 2w is evena)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? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x, y, z and w are positive integers, is x odd?(1) 7x + 8y + 4z + 5w is odd(2) 3x + 2y + 8z + 2w is evena)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?.
Solutions for If x, y, z and w are positive integers, is x odd?(1) 7x + 8y + 4z + 5w is odd(2) 3x + 2y + 8z + 2w is evena)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? in English & in Hindi are available as part of our courses for GMAT.
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