Complete the series. 9 = 4, 21 = 9, 22 = 9, 24 = 10, 8 = 5, 7 = 5, 99 = 10, 100 = 7, 16 = ?
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7
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8
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9
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10
The pattern counts the number of letters in the English word for each number. For example: 9 is 'nine' (4 letters), 21 is 'twenty one' (9 letters), and 16 is 'sixteen' (7 letters). Notice that 100 being 7 suggests 'hundred' only, which is consistent with counting letters in the number word.
To solve this series, let's analyze the patterns in the given equations:
9 = 4: 9 is the square of 3, and 4 is the square of 2. 21 = 9: 21 is the square of 4 + 1, and 9 is the square of 3. 22 = 9: 22 is the square of 4 + 2, and 9 is the square of 3. 24 = 10: 24 is the square of 4 + 4, and 10 is the square of 4. 8 = 5: 8 is the square of 2 + 2, and 5 is the square of 2. 7 = 5: 7 is the square of 2 + 1, and 5 is the square of 2. 99 = 10: 99 is the square of 9 + 0, and 10 is the square of 3. 100 = 7: 100 is the square of 10 + 0, and 7 is the square of 2.
From the given patterns, we can observe that the left side of the equation is always the square of a specific number, while the right side of the equation is the square of a different number.
Applying the same pattern to the equation 16 = ?, we can find that 16 is the square of 4 + 0. Therefore, the square root of 16 is 4.
So, the correct answer is A) 7.