7
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$\text{April} \times \text{May} - \text{June} = \text{December} - \text{January}$

$\text{September} \div \text{November} \times \text{December} = \text{March} \times \text{March}$

$\text{January} \times \text{February} \div (\text{February} + x ) = \text{April}$


These three equations follow a certain pattern. What month of the year fits in the spot marked $x$? Please provide a logical explanation as well.

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  • $\begingroup$ Are the mathematical operators as one would expect? i.e. Is '*' ordinary multiplication and '/' division as we commonly think of it? $\endgroup$ – Trenin Jun 13 '16 at 18:31
  • $\begingroup$ Yes, they are exactly what you use in maths. :) $\endgroup$ – user25136 Jun 13 '16 at 18:33
  • $\begingroup$ @LUNA was this found in an IQ-test or did you make it up? $\endgroup$ – Gordon Allocman Jun 13 '16 at 18:51
  • $\begingroup$ Oh, I've come up with it myself. Looks like I put in the "iq-test" tag. $\endgroup$ – user25136 Jun 13 '16 at 18:53
7
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The answer is

August

The math works as follows:

On the left side of the equation, the months represent the count of letters in their names (January = 7, February = 8, etc.).

On the right side of the equation, the months represent their location in the calendar (January = 1, February = 2, etc.).

To solve for the missing month, we have:

$ 7 \times 8 \div (8 + x) = 4$
$ 56 \div (8 + x) = 4$
$ 56 = 4(8 + x)$
$ 56 \div 4 = 8 + x$
$ 14 = 8 + x$
$ 14 - 8 = x$
$ x = 6$

The only month with

$6$ letters in its name is August, so that is the solution.

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  • $\begingroup$ Ah, Ninja'd. Oh well. $\endgroup$ – P... Jun 13 '16 at 18:59
3
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My guess:

August.

Reasoning:

The first two equations work if you replace months with the number of letters in their names on the left side of '=' and with their order in the year on the right side:

5 * 3 - 4 = 11 = 12 - 1
9 / 8 * 8 = 9 = 3 * 3
7 * 8 / (8 + _) = 4

6 is the number that fits in the gap, and August has six letters in its name.

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