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If m, n, and p are integers, is m n odd??
(1) m =
(1) m =
p^2 + 4p + 4
(2) n = p^2 + 2m + 1
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 'B'. Can you explain this answer?
Most Upvoted Answer
If m, n, and p are integers, is m n odd??(1) m =... more p^2 + 4p + ...
**Statement 1:** m = p^2 + 4p + 4
**Statement 2:** n = p^2 + 2m + 1
To determine if m - n is odd, we need to determine the parity (whether it's odd or even) of both m and n.
**Analyzing Statement 1:**
We are given that m = p^2 + 4p + 4.
Since p is an integer, p^2 is always non-negative.
Adding 4p and 4 to a non-negative number will always result in an even number.
Therefore, m is always even.
**Analyzing Statement 2:**
We are given that n = p^2 + 2m + 1.
From Statement 1, we know that m is always even.
Adding an even number (2m) to any number will not change its parity, since even + even = even.
Therefore, n has the same parity as p^2 + 1.
To determine the parity of p^2 + 1, we can consider the possible parities of p.
- If p is even, then p^2 is even, and adding 1 to an even number results in an odd number.
- If p is odd, then p^2 is odd, and adding 1 to an odd number results in an even number.
Therefore, n can be either odd or even, depending on the parity of p.
**Combining the Statements:**
From Statement 1, we know that m is always even.
From Statement 2, we know that n can be either odd or even, depending on the parity of p.
Since the parities of m and n are independent of each other, we cannot determine whether m - n is odd or even based on the given information.
Therefore, both statements are required to answer the question.
Hence, the correct answer is option B.
**Statement 2:** n = p^2 + 2m + 1
To determine if m - n is odd, we need to determine the parity (whether it's odd or even) of both m and n.
**Analyzing Statement 1:**
We are given that m = p^2 + 4p + 4.
Since p is an integer, p^2 is always non-negative.
Adding 4p and 4 to a non-negative number will always result in an even number.
Therefore, m is always even.
**Analyzing Statement 2:**
We are given that n = p^2 + 2m + 1.
From Statement 1, we know that m is always even.
Adding an even number (2m) to any number will not change its parity, since even + even = even.
Therefore, n has the same parity as p^2 + 1.
To determine the parity of p^2 + 1, we can consider the possible parities of p.
- If p is even, then p^2 is even, and adding 1 to an even number results in an odd number.
- If p is odd, then p^2 is odd, and adding 1 to an odd number results in an even number.
Therefore, n can be either odd or even, depending on the parity of p.
**Combining the Statements:**
From Statement 1, we know that m is always even.
From Statement 2, we know that n can be either odd or even, depending on the parity of p.
Since the parities of m and n are independent of each other, we cannot determine whether m - n is odd or even based on the given information.
Therefore, both statements are required to answer the question.
Hence, the correct answer is option B.
Community Answer
If m, n, and p are integers, is m n odd??(1) m =... more p^2 + 4p + ...
It's a product of mn .
m is having 2 in 4p and 4
n is having 2 2m
we can say m is alwys even and n is alwys even .
alone we cant find it out as mn is even or odd.
together we can find it out, its alwys even and it can't be odd.
so we can conclude mn is not odd .
m is having 2 in 4p and 4
n is having 2 2m
we can say m is alwys even and n is alwys even .
alone we cant find it out as mn is even or odd.
together we can find it out, its alwys even and it can't be odd.
so we can conclude mn is not odd .
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If m, n, and p are integers, is m n odd??(1) m =... more p^2 + 4p + 4(2) n = p^2 + 2m + 1a)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 'B'. Can you explain this answer?
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