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#### My friend claims there is a simpler way to solve this. Is there really a simpler way?

13 viewed last edited 2 years ago Anonymous
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My friend showed me this question. He claims it is easy to solve, but I am not seeing it. The solution I can think of is to find the values of the green circle, blue square and the red star and add them up. But, that requires solving equations. Is there a simpler method?  Vivekanand Vellanki
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I spent some time contemplating writing equations to solve, but I then realised there is a much simpler method.

There are 2 ways to add all the elements in a matrix:

1. Find the sum of each column and add up the column sums; or
2. Find the sum of each row and add up the row sums

Both of them lead to the same sum since each method is adding up each and every cell exactly once.

In this case, 15 + 13 + 19 (column sum) = ? + 19 + 14 (row sum). Hence, ? = 14. Mahesh Godavarti
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Yes, such questions usually require you to observe what they are asking for carefully. Note that what you want is the top row which (circle + square + triangle).

If you notice the columns and add the first two, you will see that 2*(circle + square + triangle) = 15 + 13 = 28.

Therefore, (circle + square + triangle) = 14