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# 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??

1. Rahul says:

Hi Lynne,

I presume you are hinting at the following: From Statement (1) we have deduced N to be odd, however, there is no mention of P. In that case, how can we be so certain that X is divisible by 2?

Explanation:
For X to be divisible by 2, we know that X must be even. Consequently, for X to be even, either P must be even or (N+1) must be even.
Note, this is the minimum satisfying condition. If we can establish with certainty that one of the terms (and not necessarily both) is even, it doesn’t matter if the other terms are even or odd.

Let’s take cases to understand this better:

Case 1: P = 2 (E), N = 2 (E); X = 4 (E)
Case 2: P = 2 (E), N = 3 (O); X = 6 (E)
Case 3: P = 3 (O), N = 2 (E); X = 6 (E)
Case 4: P = 3 (O), N = 3 (O); X = 9 (O)

Observe that for X to be even (Cases 1-3), the only necessary condition is for one of the terms to be even.

From Statement (1), since we already know that N is odd, (N+1) will always be even. Hence, irrespective of what P is, X will always be even and we can be certain that X will be divisible by 2.

Hope this clarifies. Payal Tandon
Co-founder, e-GMAT
Welcome to e-GMAT Support!
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