A < 1 min read

Question 2

If P and Q are positive integers, is the product 3P^Q divisible by 2?

1. 6Q³ + 2 is an even number
2. P + 8Q² is a prime number

Correct Answer

B

Solution

Steps 1 & 2: Understand Question and Draw Inferences

3P^Q is divisible by 2, if:

• 3P^Q is even

–>  P^Q is even (Odd term 3 plays no role in the even-odd nature of product 3P^Q)

–>  P is even (Power doesn’t impact the even-odd nature of a term)

 

So, to answer the question we need to find if P is even

 

Step 3: Analyze Statement 1

6Q³ + 2 is an even number

Not Sufficient. We do not know if P is even or odd

 

Step 4: Analyze Statement 2

P + 8Q² is a prime number

All the prime numbers except 2 are odd

–>  As Q ≠0, P + 8Q²> 2      (Given: Q is a positive integer => Q >0)

–>  P + 8Q² is always odd

8Q² is always even

–>  P must be odd                                                                                  (Odd + Even = Odd)

Sufficient.

 

Step 5: Analyze Both Statements Together (if needed)

We get a unique answer in step 4, so this step is not required

 

Answer: Option (B)