Question

If “x” is a positive integer, is \( x>3 \)?
(1) \( 10^{51} 55^{7} \) is an integer.
(2) \( 10^{51} 12^{11} \) is an integer.

• A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
• B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
• C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
• D. Each statement alone is sufficient to answer the question.
• E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Hint:

Ensure that the provided information directly addresses the unknown variable before drawing conclusions.

Answer 1

Answer: (E)

Step 1: Analyzing Statement 1.
Statement 1 tells us that \( 10^{51} 55^{7} \) is an integer, but this doesn’t give us any clear information about whether \( x>3 \), making statement 1 alone insufficient.
Step 2: Analyzing Statement 2.
Statement 2 tells us that \( 10^{51} 12^{11} \) is an integer, but this also doesn't provide us with a way to evaluate \( x \) and its relationship to 3. Thus, statement 2 alone is also insufficient.
Step 3: Conclusion.
Since both statements alone don’t provide any useful information, the correct answer is (E).