# Becoming a GMAT Even-Odd Champion: Q1

## Question P1.2

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

1. N + KN = 915
2. P35 + 35P is Even

A

### Solution

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.

## 6 thoughts on “Becoming a GMAT Even-Odd Champion: Q1”

1. aniket says:

if the question is
If X = P*N^K + P where N and K are positive integers, is X divisible by 2?

then the ans is B.
Could you confirm my answer @egmat help

2. GMAT Test taker says:

sorry, but the question given in the PDF document was –>
If X = P*N^K + P where N and K are positive integers, is X divisible by 2?

My thoughts:
the expression reduces to X = P*(N^K+1). For X to be divisible by 2, it’s clear that P needs to be divisible by 2. So, in a way, question is asking us to evaluate “Is P even?”

If P is Even, then P is divisible by 2, hence X is divisible by 2
If P is Odd, then P is not divisible by 2, hence X is not divisible by 2.

Am i misinterpreting the question? OR did the question link from PDF navigate me to incorrect solution webpage?

The option 1 doesn’t even talk about P. it gives values of N + KN = 915. For me, it’s irrelevant info.

The Option 2 says P^35 + 35^P is Even; This is possible only if P is Odd.

so for me, option B is sufficient.

3. Sid says:

How do we know “P” is an integer ?

1. Juhi Gupta says:

Hi Sid,

The questions statement mentions that p, n, and k are positive integers.

Please let us know if you have any further questions.

1. Lynne says:

How do we know P is odd though??