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For non-negative integers x, y, and z, is xz odd?
1) xz = odd
2) x = 2y
- a)Exactly one of the statements can answer the question
- b)Both statements are required to answer the question
- c)Each statement can answer the question individually
- d)More information is required as the information provided is insufficient to answer the question
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
For non-negative integers x, y, and z, is xz odd?1) xz = odd2) x = 2ya...
(1) The product xz is odd.
=> x, z are odd => xz odd => SUF
=> x, z are odd => xz odd => SUF
(2) x = 2y
=> x is even => xz even => SUF
Most Upvoted Answer
For non-negative integers x, y, and z, is xz odd?1) xz = odd2) x = 2ya...
Statement 1: xz = odd
This statement tells us that the product of x and z is odd. In order for a product to be odd, both x and z must be odd. If either x or z is even, then the product will be even. Therefore, we can conclude that both x and z are odd.
Statement 2: x = 2y
This statement tells us that x is even because it is equal to 2 multiplied by y. If x is even, then the product xz will also be even, regardless of the value of z. Therefore, we cannot determine whether xz is odd or not based on this statement alone.
Combining the Statements:
From statement 1, we know that both x and z are odd. From statement 2, we know that x is even. This is a contradiction because a number cannot be both even and odd at the same time. Therefore, the two statements are contradictory and cannot both be true.
Conclusion:
From the above analysis, we can conclude that statement 1 alone is sufficient to answer the question. If x and z are both odd, then the product xz will also be odd. Therefore, the answer is option A - exactly one of the statements can answer the question.
This statement tells us that the product of x and z is odd. In order for a product to be odd, both x and z must be odd. If either x or z is even, then the product will be even. Therefore, we can conclude that both x and z are odd.
Statement 2: x = 2y
This statement tells us that x is even because it is equal to 2 multiplied by y. If x is even, then the product xz will also be even, regardless of the value of z. Therefore, we cannot determine whether xz is odd or not based on this statement alone.
Combining the Statements:
From statement 1, we know that both x and z are odd. From statement 2, we know that x is even. This is a contradiction because a number cannot be both even and odd at the same time. Therefore, the two statements are contradictory and cannot both be true.
Conclusion:
From the above analysis, we can conclude that statement 1 alone is sufficient to answer the question. If x and z are both odd, then the product xz will also be odd. Therefore, the answer is option A - exactly one of the statements can answer the question.
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