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Data Sufficiency on the GMAT is not just about solving equations. It is about thinking like a detective, weighing information, and deciding whether the data is enough to answer the question. Sometimes the answer is yes, sometimes the answer is no, and sometimes neither statement works alone, but they work when combined. What matters most is clarity in approach. Take the simple question, “Is X even?” On the surface it looks harmless, but once you begin testing cases, you see how quickly the possibilities branch out. These are the moments where you must train yourself to handle uncertainty with calmness. Learning to welcome a “no” as a valid answer is a big step in mastering this section. Structured practice with a GMAT preparation course and reinforcement through GMAT mock tests ensures that your mind learns to test, combine, and eliminate options with confidene.
Data Sufficiency questions often take a simple-sounding problem and turn it into a test of logic, patience, and precision. The question “Is X even?” may appear straightforward, but when examined under the GMAT framework, it becomes a lesson in how to think systematically.
A: Statement 1 alone is sufficient, but statement 2 alone is not.
B: Statement 2 alone is sufficient, but statement 1 alone is not.
C: Both statements together are sufficient, but neither alone is sufficient.
D: Each statement alone is sufficient.
E: Even both statements together are not sufficient.
Statement 1 tells us that 8Y is even, and the overall sum is odd. Since 8Y will always be even, the odd sum means 5X must be odd. Therefore, X is odd. The answer is no, X is not even. Statement 1 alone is sufficient.
Statement 2 does not mention X at all, so it cannot be sufficient.
Thus, the correct answer is A.
Statement 1 says 5X + 7Y is odd. This means one term is even and the other odd. That does not give certainty about X. Statement 1 is not sufficient.
Statement 2 says 6X + 5Y is even. Since 6X is always even, 5Y must also be even, meaning Y is even. However, this gives no conclusion about X. Statement 2 alone is not sufficient.
When combining, Y is even, so 7Y is even. For 5X + 7Y to be odd, 5X must be odd, so X is odd. The answer is no, X is not even.
The correct choice is C.
An alternative approach is to add both statements: 11X + 12Y is odd. Since 12Y is always even, 11X must be odd, which again means X is odd.
Statement 1 says 7X + 9Y is even. That means both are even or both are odd. Not sufficient.
Statement 2 says 10X + 15Y is odd. Since 10X is always even, 15Y must be odd, meaning Y is odd. Alone, this still does not settle X.
On combining, if Y is odd, then from statement 1 both must be odd. Hence X is odd. Once again, the answer is no, X is not even.
The correct choice is C.
Another way is to add the two statements: 17X + 24Y is odd. Since 24Y is even, 17X must be odd, which proves X is odd.
The answers across the three questions are A, C, and C. The real learning is not just in finding these answers but in observing how “no” is as valid and powerful as “yes.” Data Sufficiency trains you to test boundaries, combine insights, and remain open to every possibility until a unique conclusion emerges. This is what makes DS both frustrating and beautiful. By practicing consistently and nurturing this mindset, you not only master question types but also sharpen the calm, analytical reasoning that the GMAT values most. These habits carry forward, strengthening the way you approach both the test and challenges beyond. For deeper conceptual clarity, exploring a structured GMAT preparation course can anchor your learning and give direction to your practice.
The journey through even and odd examples shows that Data Sufficiency is not about chasing the comfort of “yes.” It is about embracing certainty, whether it comes as yes or no. The real test is in your ability to stay calm, examine every path, and accept the truth revealed by logic. This discipline teaches more than problem solving; it builds the patience to question, the courage to accept unexpected answers, and the maturity to see clarity as the true goal. These qualities not only define GMAT success but also strengthen the decision-making valued in the MBA admissions process and in leadership beyond.
