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Question 3

Is 3a + 2b + 5c even if 0<a<b<c and a, b and c are integers?

1. 9a+7c is not even
2. a³*(c-1)² is odd

Correct Answer

D

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In expression (3a + 2b + 5c), 2b is an Even term, and so will not impact the even-odd nature of the expression.

So, the expression will be even if (3a + 5c) is even.

Now, 3 and 5 are odd numbers. So in the product 3*a and 5*c respectively, 3 and 5 play no role in the even-odd nature of the product.

So, (3a + 5c) will be even if (a + c) is even.

And, (3a + 5c) is odd if (a + c) is odd.

With this understanding, let’s analyse the given statements.

 

Step 3: Analyze Statement 1

9a+7c is not even

–>  9a+7c is odd

–>  a + c is odd

 

Therefore, (3a + 5c) is odd.

 

Sufficient.

 

Step 4: Analyze Statement 2

a³*(c-1)² is odd

–>  a*(c-1) is odd

–>  a is odd and c – 1 is odd

–>  a + c – 1 is even

–>  a + c is odd

 

Therefore, (3a + 5c) is odd

Sufficient.

 

Step 5: Analyze Both Statements Together (if needed)

We get a unique answer in step 3 and step 4, so this step is not required

 

Answer: Option (D)