- Calculator
- Flag
-
3 < |y| < 7
| Column A | Column B |
|---|---|
| y2 + 5 | 50 |
Title
Square vs. 45
Your Result
Correct
Difficulty
Hard
Your Pace
0:01
Others' Pace
0:52
Video Explanation
Text Explanation
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
6.5
6.9
6.999999
6.99999999999999999999999999999999999999999
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.
< 7
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)
Related Lessons
Watch the lessons below for more detailed explanations of the concepts tested in this question. And don't worry, you'll be able to return to this answer from the lesson page.
