Which one will replace the question mark ?

2023

Which one will replace the question mark ?

  1. A.

    6

  2. B.

    7

  3. C.

    8

  4. D.

    9

Attempted by 3 students.

Show answer & explanation

Correct answer: B

Concept:

In this cross-figure number series, the four corner numbers combine by a fixed rule to give the center number. Testing the two complete figures shows the rule: the center equals half the sum of the four corner numbers. Once confirmed, the same rule applies to the incomplete figure to find the missing corner.

Application:

  1. First figure: corners are 10, 9, 7, 14. Sum = 10 + 9 + 7 + 14 = 40. Half of 40 = 20, which matches the given center value of 20.

  2. Second figure: corners are 11, 16, 13, 10. Sum = 11 + 16 + 13 + 10 = 50. Half of 50 = 25, which matches the given center value of 25 — confirming the rule holds across figures.

  3. Third figure: corners are 15, ?, 10, 12, with center 22. So the corner sum must be 2 × 22 = 44. The three known corners add to 15 + 10 + 12 = 37, so the missing corner is 44 − 37 = 7.

Cross-check:

Substituting 7 back: corners 15, 7, 10, 12 sum to 44, and half of 44 is 22 — exactly the given center. The value 7 is confirmed.

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