A < 1 min read

Question P1.2

 

If X = P*N^K + P where P, N and K are positive integers, is X odd?

1. N + KN = 915
2. P³⁵ + 35^P is Even

Correct Answer

A

Solution

Steps 1 & 2: Understand Question and Draw Inferences

X = P*N^K + P

–>  X = P(1 + N^K)

X will be odd only if P is odd and (1+N^K) is odd

N^K 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 + 35^P 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)