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If x and y are positive integers, is the product x
y even?
1)5x - 4y is even
2)6x + 7y is even
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 'C'. Can you explain this answer?
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Verified Answer
If x and y are positive integers, is the product x... morey even?1)5x ...
1) 4y will always be even. Then we have 5x−even=even ,
For this to be the case, 5x must be even. Since 5 can't be even, then x must be even. Thus the product xy will be even. Sufficient.
2) 6x will always be even. Then we have even+7y=even.
2) 6x will always be even. Then we have even+7y=even.
Thus 7y is even, and y is even, and xy is even. Sufficient.
Most Upvoted Answer
If x and y are positive integers, is the product x... morey even?1)5x ...
Even + Even = Even
Even - Even = Even
Even * Even = Even
Even * Odd = Even
Number 1 says 5x - 4y is even, according to the above stated rules, the 2 intergers involved must be even to give an even number, you can see that it is correct.
We can see that at least either x or y is even, and the product of an even number and an odd must give an even.
Also number 2 says the multiplication gives even.
The rules gives the answer, any one of the 2 options answers the question.
Even - Even = Even
Even * Even = Even
Even * Odd = Even
Number 1 says 5x - 4y is even, according to the above stated rules, the 2 intergers involved must be even to give an even number, you can see that it is correct.
We can see that at least either x or y is even, and the product of an even number and an odd must give an even.
Also number 2 says the multiplication gives even.
The rules gives the answer, any one of the 2 options answers the question.
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Community Answer
If x and y are positive integers, is the product x... morey even?1)5x ...
To determine if the product xy is even, we need to consider the parity (evenness or oddness) of both x and y.
Statement 1: 5x - 4y is even
Statement 1 tells us that 5x - 4y is even. To analyze the parity of xy, we need to consider the possible parities of x and y separately.
- If both x and y are even, then 5x - 4y will be even, and hence xy will be even.
- If both x and y are odd, then 5x - 4y will be odd, and hence xy will be odd.
- If x is even and y is odd, then 5x - 4y can be either even or odd, depending on the specific values of x and y. Therefore, we cannot determine the parity of xy.
Since we cannot determine the parity of xy from statement 1 alone, statement 1 is not sufficient to answer the question.
Statement 2: 6x + 7y is even
Statement 2 tells us that 6x + 7y is even. Again, we need to analyze the possible parities of x and y separately.
- If both x and y are even, then 6x + 7y will be even, and hence xy will be even.
- If both x and y are odd, then 6x + 7y will be even, and hence xy will be even.
- If x is even and y is odd, then 6x + 7y can be either even or odd, depending on the specific values of x and y. Therefore, we cannot determine the parity of xy.
Since we cannot determine the parity of xy from statement 2 alone, statement 2 is also not sufficient to answer the question.
Combining both statements:
By combining the two statements, we have the information that both 5x - 4y and 6x + 7y are even. This gives us additional information about the parities of x and y.
- If both x and y are even, then both 5x - 4y and 6x + 7y will be even, and hence xy will be even.
- If both x and y are odd, then both 5x - 4y and 6x + 7y will be even, and hence xy will be even.
- If x is even and y is odd, then 5x - 4y will be even and 6x + 7y will be odd, resulting in a product xy that could be either even or odd. Therefore, we still cannot determine the parity of xy.
Thus, combining both statements allows us to determine the parity of xy when both x and y are even or when both x and y are odd. Therefore, each statement can individually answer the question, and the correct answer is option C.
Statement 1: 5x - 4y is even
Statement 1 tells us that 5x - 4y is even. To analyze the parity of xy, we need to consider the possible parities of x and y separately.
- If both x and y are even, then 5x - 4y will be even, and hence xy will be even.
- If both x and y are odd, then 5x - 4y will be odd, and hence xy will be odd.
- If x is even and y is odd, then 5x - 4y can be either even or odd, depending on the specific values of x and y. Therefore, we cannot determine the parity of xy.
Since we cannot determine the parity of xy from statement 1 alone, statement 1 is not sufficient to answer the question.
Statement 2: 6x + 7y is even
Statement 2 tells us that 6x + 7y is even. Again, we need to analyze the possible parities of x and y separately.
- If both x and y are even, then 6x + 7y will be even, and hence xy will be even.
- If both x and y are odd, then 6x + 7y will be even, and hence xy will be even.
- If x is even and y is odd, then 6x + 7y can be either even or odd, depending on the specific values of x and y. Therefore, we cannot determine the parity of xy.
Since we cannot determine the parity of xy from statement 2 alone, statement 2 is also not sufficient to answer the question.
Combining both statements:
By combining the two statements, we have the information that both 5x - 4y and 6x + 7y are even. This gives us additional information about the parities of x and y.
- If both x and y are even, then both 5x - 4y and 6x + 7y will be even, and hence xy will be even.
- If both x and y are odd, then both 5x - 4y and 6x + 7y will be even, and hence xy will be even.
- If x is even and y is odd, then 5x - 4y will be even and 6x + 7y will be odd, resulting in a product xy that could be either even or odd. Therefore, we still cannot determine the parity of xy.
Thus, combining both statements allows us to determine the parity of xy when both x and y are even or when both x and y are odd. Therefore, each statement can individually answer the question, and the correct answer is option C.
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If x and y are positive integers, is the product x... morey even?1)5x - 4y is even2)6x + 7y is evena)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'C'. Can you explain this answer?
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