Xavier Aptitude Test 2022 Paper

The number of oranges, apples, guavas, and pears $=126,162,198,$ and $306$.
Each box must contain an equal number of fruits with only one type of fruit. The additional condition provided is that there should be a minimum number of boxes in total.
The distribution is possible in multiple ways in such a way that distribution in each box is placed in such that each box contains a certain number of fruits n which is a factor for all the four given number of fruits :
Arrangement of 1 fruit of one kind in a basket. 2 is a factor of $126,162,198,$ and $306$. So we can place 2 fruits of a particular kind in a basket.
Since we were asked for the minimum number of boxes this is possible when a maximum number of fruits of a kind are placed in a box. Hence each box must contain the Highest common factor for the four numbers :
The prime factorization for the four numbers :
$126:2.7.9$, $162:2.9.9$ , $198:2.9.11$ , $306=2.9.17$
The HCF is $18.$
The number of boxes required for each :
$\frac{128}{18},\frac{162}{18},\frac{198}{18},\frac{306}{18}$
$7+9+11+17=44$