Question: What is the sum of two natural numbers?<br>Statement-I:<br>LCM of the two numbers is 144.<br>Statement-II:<br>One of the numbers is 72.

Consider the following for the next ten (10) items that follow :<br>Mark option (a) if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.<br>Mark option (b) if the question can be answered by using either statement alone.<br>Mark option (c) if the question can be answered by using both the statements together, but cannot be answered using either statement alone.<br>Mark option (d) if the question cannot be answered even by using both the statements together.

  1. A. The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
  2. B. The question can be answered by using either statement alone
  3. C. The question can be answered by using both the statements together, but cannot be answered using either statement alone
  4. D. The question cannot be answered even by using both the statements together ✓

Correct Answer: D. The question cannot be answered even by using both the statements together

Explanation

Statement-I simply gives LCM = 144. Not sufficient. Statement-II gives one number = 72. Not sufficient. Combining them, \text{LCM}(72, y) = 144. The number y must have 2^4=16 as a factor and a power of 3 up to 3^2. Thus y can be 16, 48, or 144. Since there are multiple possible values for y, their sum is not unique. Not sufficient even together.

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