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Absolute Values

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Absolute Values  [#permalink]

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New post 20 Mar 2017, 08:18
hi Guys,

I wanted to know why in the attached screen shot the answer is x*2 = X*2

thanks
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Re: Absolute Values  [#permalink]

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New post 22 Mar 2017, 12:50
jamescarey86 wrote:
hi Guys,

I wanted to know why in the attached screen shot the answer is x*2 = X*2

thanks


\(\frac{x}{|y|} = -1\) is equivalent to \(x = -|y|\) or \(-x = |y|\).
It is also equivalent to \((-x)^2 = |y|^2 = y^2\), and so we have \(x^2 = y^2\).
Hence, D is the correct answer.

We have used a property as follows.
- \(|x| = a\) is equivalent to \(x^2 = a^2\).
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Re: Absolute Values  [#permalink]

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New post 23 Sep 2019, 20:23
I always forget the properties of absolute values and so I always go by the basics. Any value inside mods can come out as +ve or -ve.

x / |y| can be either x/y or x/-y.

so,
x/y = -1
Which means x = -y

or

x/-y = -1 which can be written as x/y = 1 and ultimately, x = y.

Now looking at x = -y and x = y, the only way to make them equal is by squaring both the equations. -y square will be positive and equal to the square of y. Hence answer is D.
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Re: Absolute Values  [#permalink]

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New post 24 Sep 2019, 14:04
Hi All,

We're told that X/|Y| = -1. We're asked which of the following MUST be true (which really means "which of the following is ALWAYS true no matter how many different examples you come up with?"). This question can be solved by TESTing VALUES.

For a fraction to equal -1, the numerator and denominator must be OPPOSITE values: for example, -2 and +2. In this fraction, the denominator is an Absolute Value, so there's no way for the denominator to be negative. Thus, the numerator MUST be negative. Based on that deduction, there are now 2 possibilities:

1) X is negative and Y is positive
2) X is negative and Y is negative (and that negative value will be made positive by the Absolute Value function).

So, which of the 5 answers is ALWAYS true (both when X = -2, Y = +2 AND when X = -2 and Y = -2)? Only one...

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Re: Absolute Values   [#permalink] 24 Sep 2019, 14:04
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