Question

If "x" is a positive integer, is \(x>33\)?
I. x is an odd number.
II. The sum of the digits of x is 5.

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

Hint:

When testing Data Sufficiency statements, always be sure to test values on both sides of the "boundary" mentioned in the question. Here, the boundary is 33, so you must test values both greater than and less than (or equal to) 33.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This is a "Yes/No" Data Sufficiency question. We need to determine if the positive integer \(x\) is definitively greater than 33.
Step 2: Detailed Explanation:
Analyze Reconstructed Statement I: "x is an odd number."
This statement tells us x is odd.

Can \(x>33\)? Yes, for example, \(x = 35\).
Can \(x \leq 33\)? Yes, for example, \(x = 33\) or \(x = 31\).
Since we can get both "yes" and "no" answers, Statement I is not sufficient.
Analyze Reconstructed Statement II: "The sum of the digits of x is 5."
This statement gives us a set of possible values for x. Possible values for x: 5, 14, 23, 32, 41, 50, 104, 113, 122, 131, 140, 203, ...

Can \(x>33\)? Yes, for example, \(x = 41\).
Can \(x \leq 33\)? Yes, for example, \(x = 32\) or \(x = 23\).
Since we can get both "yes" and "no" answers, Statement II is not sufficient.
Analyze Statements I and II Together:
We need to find positive integers \(x\) that are odd AND have a digit sum of 5. Possible values for x:

From the list above, we select the odd numbers: 5, 23, 41, 104(no), 113, 131, 203, ...
The possible values are 5, 23, 41, 113, 131, 203, etc.
Now we check the question "is \(x>33\)?":

Can \(x>33\)? Yes, for example, \(x = 41\).
Can \(x \leq 33\)? Yes, for example, \(x = 23\) or \(x = 5\).
Even with both statements combined, we cannot determine a definitive answer. Therefore, the statements together are not sufficient.
Step 3: Final Answer:
Statements I and II together are not sufficient to answer the question. This corresponds to option (E).