Solution:
The units digit of the expression \(7^X + 9^{X+3}\) will end with a zero, only when \(X\) is of the form \(4k\), i.e., a multiple of \(4\).
Step 1: Analyse Statement 1:\(2^X\) is odd.
• As per our conceptual knowledge, any even number when raised to a power will result in an even number only.
• However, this is not always true.
o Consider the example when an even number is raised to the power 0.
o It has been taught in our concept file that any number (except 0) when raised to the power 0, will yield 1 as the answer.
So, for 2X to be odd, X should be equal to 0.
Since 0 can be written in the form of 4k, where k =0,
Statement 1 alone is sufficient to answer the question.
Step 2: Analyse Statement 2:\((2X+2)\) is Even.
• \(2X\) is always even irrespective of the even-odd nature of \(X\).
o This is because \(X\) is multiplied by an even number (2), and from our conceptual knowledge we know that,
o Even * Even = Even
o Even * Odd = Even
• \(2\) is an even number
• Therefore, from this statement, the even-odd nature of X cannot be determined.
Since we do not know the exact even-odd nature of X,
Statement 2 alone is NOT sufficient to answer the question.
Hence, we can eliminate answer choice B.
Step 3: Combine both Statements:This step is not required since we already got a unique answer in step 3.
Correct Answer: Option A