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Home › Non-Verbal Reasoning › Magic Squares

Magic Squares — Non-Verbal Reasoning Questions & Practice

Practise 269 Magic Squares questions from Non-Verbal Reasoning for competitive exams such as UPSC, Banking, SSC and Railway. Read the worked questions below, check every answer with an explanation, and track what you get wrong.

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Practice questions on Magic Squares — with answers

Try each question first, then open the answer. Explanations are included.

1. In a magic square, every row, column, and diagonal must sum to the same value. In a 3x3 magic square using numbers 1-9, what is the magic sum (the constant total for each row/column/diagonal)?

  1. A15
  2. B12
  3. C18
  4. D21
Show answer

Answer: A

The magic sum for a 3x3 magic square using numbers 1 through 9 is calculated as (sum of 1 to 9)/3 = 45/3 = 15.

2. A 3x3 magic square has 5 in the center. If the magic sum is 15, and the top row (excluding the center) has values 2 and 7 with a missing third number, what is that missing number?

  1. A6
  2. B5
  3. C4
  4. D8
Show answer

Answer: A

Since each row must sum to 15, the top row's missing number = 15 - 2 - 7 = 6.

3. In a magic triangle, the numbers at the corners and along each side must sum to the same total. If a triangle has corners 4, 5, and 6, and each side sums to 15, what is the sum of all three side totals combined (counting each corner once per side it belongs to)?

  1. A45
  2. B30
  3. C15
  4. D60
Show answer

Answer: A

With three sides each summing to 15, the combined total of all three side-sums is 3x15=45 (note that corner numbers are counted twice each in this combined total, once for each adjacent side).

4. In a number puzzle, numbers are placed at the vertices of a pentagon such that the sum of numbers on each side (two adjacent vertices) is constant at 10. If one vertex has 3, what is the value of its neighboring vertex?

  1. A7
  2. B3
  3. C5
  4. D10
Show answer

Answer: A

Since each side (pair of adjacent vertices) must sum to 10, if one vertex is 3, the adjacent vertex must be 10-3=7.

5. A 3x3 magic square is filled with numbers 1-9 such that the magic sum is 15. If the center is 5, what is the sum of the four corner numbers?

  1. A20
  2. B16
  3. C15
  4. D24
Show answer

Answer: A

In the standard 3x3 magic square with center 5, the four corners are 2, 4, 6, and 8 (in some order), which sum to 2+4+6+8=20.

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