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GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.- May 06
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07 Sep 2023, 16:14
Kudos
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I'm having a really hard time understanding why it's y-1 and not -1 - y
I get to the point of having -1 - √(y^2)
I don't understand how |y| = -y (can ever equal that), because the square root of y^2 is y, and if y is assumed negative then shouldn't you just leave it as y, why would you have to add a negative in front of it. Take y=-2, then -y=2 and subsequently not be negative? I'm just stuck on this logic
I get to the point of having -1 - √(y^2)
I don't understand how |y| = -y (can ever equal that), because the square root of y^2 is y, and if y is assumed negative then shouldn't you just leave it as y, why would you have to add a negative in front of it. Take y=-2, then -y=2 and subsequently not be negative? I'm just stuck on this logic
08 Sep 2023, 00:51
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epravetz
Firstly, \(\sqrt{y^2}=|y|\). This is because the square root function always returns non-negative values, and |y| ensures that the result is non-negative for all y.
For instance, consider y = -5:
\(\sqrt{(-5)^2} = \sqrt{25} = 5\), which is |-5|.
Next, when \(y \geq 0\), |y| is simply y. This is because y is already non-negative, so there's no need for adjustment.
For instance, if \(y = 3\):
\(|3| = 3\)
However, when \(y < 0\), |y| is -y to make it non-negative.
For example, for \(y = -2\):
\(|-2| = -(-2) = 2\)
Thus, this property ensures that the result of |y| is always non-negative, regardless of the original sign of y.
The above are basic properties of absolute values, so I suggest brushing up on fundamentals before solving hard questions on modulus:
10. Absolute Value
- Theory
Math: Absolute value (Modulus)
Absolute Value: Tips and hints
Properties of Absolute Values on the GMAT
Absolute modulus : A better understanding
GMAT Question Patterns: Abolute Value
The Reason Behind Absolute Value Questions on the GMAT
For more check Ultimate GMAT Quantitative Megathread
Hope it helps.
30 Oct 2023, 08:51
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Bunuel
Hello Bunuel
Really amazing question and explanation to understand the relation between absolute values and square roots.
The square root of y^2 will be |y|.
I just had one query here, how would we simplify the following expression:
Square root of (-y * y): would it be |y| only? Or square root of -x^2 ? Would it be |x| only?
Thank you Bunuel
