Since negative values of y squared will be positive anyway, let’s ignore the absolute values for a moment. If 3 < y < 7, then what’s the largest value that y could have? The highest value is NOT 6. There is nothing in this problem stating that y has to be a positive integer, so it could have any decimal or fraction value. Thus, y could be
How many numbers on the number line are between that last number and 7? An infinite number of them! That’s the mind-boggling nature of the continuous infinity of the number line.
It’s true that y could equal, say, 4. If y = 4, then
y2 + 5 = 16 + 5 = 21 < 50
That’s a value that would make column B bigger.
It’s also true that
48 < 49
Since both sides of that inequality are positive, we can take the square root of both sides.
That’s a legal value of y. If y = , then
y2 + 5 = 48 + 5 = 53 > 50
That’s a value that would make column A bigger.
Different valid choices of y give us different relationships between the columns. Thus, we do not have sufficient information to decide which column is bigger.
Answer = (D)
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