If X = P*NK + P where P, N and K are positive integers, is X odd?
- N + KN = 915
- P35 + 35P is Even
Steps 1 & 2: Understand Question and Draw Inferences
X = P*NK + P
–> X = P(1 + NK)
X will be odd only if P is odd and (1+NK) is odd
NK will have the same Even-odd nature as N (Power doesn’t change the even- odd nature of an expression)
–> (1+N) needs to be odd
–> N needs to be even
So, X will be odd only if P is odd and N is even.
So, let’s now look at the given statements to ascertain the Even-Odd nature of P and N.
Step 3: Analyze Statement 1
N + KN = 915
–> N(1+K) = 915, which is an odd number
–> The product of 2 numbers is odd only if both the numbers are themselves odd.
–> N is odd
Since we know that N is not even, we can say for sure that X will not be odd.
Therefore, Statement 1 is Sufficient.
Step 4: Analyze Statement 2
P35 + 35P is even
–> P + 35 is even (Power doesn’t change the even- odd nature of an expression)
–> P is odd
But, we don’t know if N is even or odd. Thus, Statement 2 is not sufficient
Step 5: Analyze Both Statements Together (if needed)
We’ve already arrived at a unique answer in Step 3. Therefore, this step is not required.
Answer: Option (A)