CAT 2017 Slot 2 — QA Question 1
The numbers 1,2, …, 9 are arranged in a 3 × 3 square grid in a such 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
Answer & solution
Answer: 3
Sum of all digits from 1 to 9 = 45
If entries along each of the rows, columns or diagonals adds upto the same number, it implies that the sum of each row, columns or diagonal will be 45 ÷ 3 = 15.
(âµ there are 3 rows and 3 columns we divide the total of the numbers 1 to 9 i.e. 45 by 3)
In the 1st row the top left cell contains the number 6 and the top right cell contains the number 2.
Therefore the middle element in the first row will be 15 – 6 – 2 = 7. Further elements of each row, columns or diagonal adds upto 15. Now this is only possible if the middle element in the entire grid i.e. the element corresponding to the 2nd row and 2nd column is the average of all 9 numbers i. e., 5. Now if the middle element is 5, then the bottom element in the 2nd column will be 15 – 7 – 5 or 3.
Hence, 3.