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07 Apr 2021, 07:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:02) correct
24%
(01:28)
wrong
based on 74
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If m and n are integers and p = 13m + 25n, is p odd?
(1) One of m and n is odd.
(2) n is even.
(1) One of m and n is odd.
(2) n is even.
07 Apr 2021, 07:09
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Given: p = 13m + 25n, m and n are integers.
Is p odd?
First things first:
Odd * Odd = Odd and Odd + Even = Odd
Statement 1:
One of m and n is odd.
Case 1:
m is odd, n is even.
p = 13 * (odd number) + 25 * (even number) = Odd + Even = Odd.
Case 2:
m is even, n is odd.
p = 13 * (even number) + 25 * (odd number) = Even + Odd = Odd.
In both cases, p is odd.
As, one of m and n is odd, both cannot be odd.
Statement 1 is Sufficient.
Statement 2:
n is even.
Here, if m is even, p is even and if m is odd, p is odd.
We don't have much information on m.
Statement 2 is Not Sufficient.
So, correct answer is option A.
Is p odd?
First things first:
Odd * Odd = Odd and Odd + Even = Odd
Statement 1:
One of m and n is odd.
Case 1:
m is odd, n is even.
p = 13 * (odd number) + 25 * (even number) = Odd + Even = Odd.
Case 2:
m is even, n is odd.
p = 13 * (even number) + 25 * (odd number) = Even + Odd = Odd.
In both cases, p is odd.
As, one of m and n is odd, both cannot be odd.
Statement 1 is Sufficient.
Statement 2:
n is even.
Here, if m is even, p is even and if m is odd, p is odd.
We don't have much information on m.
Statement 2 is Not Sufficient.
So, correct answer is option A.
28 Sep 2021, 05:53
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Bunuel
Bunuel - S1 states that 'One of m and n is odd'. Does that automatically mean that the other is even?
