PUNE MCA Exam 2015 Question Paper with answers for online practice

Concept:The question asks for the range that always contains the result of a missing statement. Based on common MCA problems, the result is often a large count, such as the number of integers less than 1,000,000 divisible by 2, 3, or 5, which equals 733,334.Explanation:Using inclusion–exclusion, the count of numbers ≤ 1,000,000 divisible by 2, 3, or 5 is computed as:Let $A$ = multiples of 2, $B$ = multiples of 3, $C$ = multiples of 5.$|A| = 500{,}000$, $|B| = 333{,}333$, $|C| = 200{,}000$.$|A \cap B| = 166{,}666$, $|A \cap C| = 100{,}000$, $|B \cap C| = 66{,}666$.$|A \cap B \cap C| = 33{,}333$.Total = $500{,}000 + 333{,}333 + 200{,}000 - (166{,}666 + 100{,}000 + 66{,}666) + 33{,}333 = 733{,}334$.This value is greater than 700,000.Thus, it always belongs to the range “greater than 700,000”.Answer:$\boxed{\text{D. greater than 700000}}$