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Question
Consider this calendar. Select the numbers 4,5,6,11,12,13,18,19,20 such that they form a square. The sum of the selected numbers of the square, is ____ times the middle number of the square.
Consider this calendar. Select the numbers 4,5,6,11,12,13,18,19,20 such that they form a square. The sum of the selected numbers of the square, is ____ times the middle number of the square.
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Solution
The correct option is D 9
Sum of the selected numbers
= 4 + 5 + 6 + 11 + 12 + 13 + 18 + 19 + 20
= 144
If the central number is x, we can fill in the other numbers in the way displayed above.
Sum of these numbers would be
= x - 8 + x - 7 + x -6 + x -1 + x + x +1 + x +6 + x + 7 + x + 8
= 9x
Hence, sum of all the 9 numbers = 9 times the middle number of the square
9
Sum of the selected numbers
= 4 + 5 + 6 + 11 + 12 + 13 + 18 + 19 + 20
= 144
If the central number is x, we can fill in the other numbers in the way displayed above.
Sum of these numbers would be
= x - 8 + x - 7 + x -6 + x -1 + x + x +1 + x +6 + x + 7 + x + 8
= 9x
Hence, sum of all the 9 numbers = 9 times the middle number of the square
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