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 : $\frac{128}{18} , \frac{162}{18} , \frac{198}{18}, \frac{306}{18}$ $7+9+11+17 = 44$