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"35. Place the numbers 13,14,15,16, and 18 in the circles to make the sum across equal to the sum vertically. A. 15 B. 14 and 18 C. 15 and 18 D. 13 and 18 Which numbers can be placed in the center circle?

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Full solution

Q.
  1. Identify Total Sum: Identify the total sum of all numbers and the required sum for each line.\newlineGiven numbers: 13,14,15,16,1813, 14, 15, 16, 18.\newlineTotal sum of numbers = 13+14+15+16+18=7613 + 14 + 15 + 16 + 18 = 76.\newlineSince there are 44 lines (22 horizontal, 22 vertical) sharing these numbers, each line should sum to 76/4=1976 / 4 = 19.
  2. Calculate Required Sum: Assume a number for the center circle and check sums.\newlineLet's assume 1515 is in the center.\newlineThen, the pairs (13,16)(13, 16) and (14,18)(14, 18) can be used to complete the lines.\newlineCheck sums: 13+16=2913 + 16 = 29, 14+18=3214 + 18 = 32; these don't work because each pair exceeds 1919 when added to 1515.

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