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Question 1 : The numbers 1, 2,..., 9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value. If the top left and the top right entries of the grid are 6 and 2, respectively, then the bottom middle entry is: [TITA]


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Explanatory Answer

Method of solving this CAT Question from Number Theory

Given that the numbers 1,2,.., 9 are arranged in a 3 × 3 square grid such that each number occurs once and the entries along each row, column and diagonals should add upto the same value.
So the total of all these should be \\frac{9 × 10}{2}) = 45 and since there are 3 rows and 3 columns \\frac{45}{3}) = 15
Hence each row or column or the diagonal would add upto 15.
CAT 2017 Question Paper Quants Slot 2 Number Theory
And it is also given that top left and top right entries of the grid are 6 and 2 respectively.
We have to find the bottom middle entry
Since in the first row 6 + 2 = 8 the middle value is 7, we know that from 1,.... 5 .... , 9, 5 is the middle number so 5 comes in the middle of the second row.
7 + 5 = 12 so the other number is 3.
CAT 2017 Question Paper Quants Slot 2 Number Theory
We know that each row ,column and each diagonal would add up to 15 and therefore we can fill the rest of the rows and columns.
Hence the bottom middle entry is found to be 3.

The question is "The numbers 1, 2,..., 9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value. If the top left and the top right entries of the grid are 6 and 2, respectively, then the bottom middle entry is: [TITA]"

Hence, the answer is 3

 

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