One Solution
The answer seems to be July 10, based on the number of syllables in the month names, times 5.
Jan-u-ar-y is 4 x 5 = 20
A-pril is 2 x 5 = 10
May is 1 x 5 = 5
No-vem-ber is 3 x 15 = 15
Ju-ly is 2 x 5 = 10
A Different Solution (requires alternating criteria)
Based on consonant : Each consonant or each vowel pair is worth 5 points.
Alternating every quarter from vowels to consonants. So it's July 15.
January has 4 consonants --------> 20
February has 5 consonants -> 25
march has 4 consonants -> 20
April has 2 vowels -------------> 10
May has 1 vowel ----------------> 5
June has 2 vowels -> 10
July has 3 consonants -----------> 15
August has 3 consonants -> 15
September has 6 consonants -> 30
October has 3 vowels -----------> 15
November has 3 vowels -> 15
December has 3 vowels -> 15
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