2024 · Q68
A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option.
Question: There are three different weights. All the weights are integers and their sum is a prime number. What are the weights?
Statement IOne of the weights is twice the another weight
Statement IIOne of the weights is thrice the another weight Which one of the following is correct in respect of the above Question and the Statements?
Elementary MathematicsNumber System
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question cannot be answered even by using both the Statements together
Explanation
With both statements, sorting the weights a<b<c and assigning the ×2 and ×3 pairs, the only consistent structure is {a, 3a/2, 3a} with a even: {2k, 3k, 6k}. Prime sum 11k forces k = 1, i.e. weights {2,3,6} uniquely (verified by exhaustive search). Neither statement alone suffices, but together they do — option C.