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Re: If x and y are numbers such that x < - 10 and y > 6, which of the [#permalink]

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20 May 2015, 14:26

1

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Tried solving the question by substituting values for x and y. Suppose if we sub. x = -11 and y = 7, and solve the three equations, It's found that statements (i) and (iii) satisfy. Hence D.

Be careful now, normally once you have an answer that is true, it doesn't mean that it will be true for all the values of x and y. Here im pretty confident because i took the smallest (integer) numbers for x and y and the result is 36 which is a difference of 4 to 32. Even if you plug in smaller fractional numbers the statement will still be true.

First representing the points x and y on the number line: x < -10 and y > 6.

Then, since the expressions talk about |x+4|, |x-4|, |y+4| and |y-4|, representing these distances on the number line as well.

|x+4| represents the distance of x from -4 on the number line |x-4| represents the distance of x from 4 |y+4| represents the distance of y from -4 |y-4| represents the distance of y from 4

Adding all these we get Expression 1. Therefore, is true always.

II. |x – 4| + |y + 4| - | x + 4| - | y – 4| < 0 From the diagram, we can see that |x – 4| - |x + 4| = 8 And, |y + 4| - | y – 4| = 8 Adding the 2 equations, we get:

|x – 4| + |y + 4| - | x + 4| - | y – 4| = 16

So, expression 2 is NOT TRUE.

III. |x + 4| + |y + 4| - |x – 4| - |y – 4| = 0

From the diagram, we can see that |x + 4| - |x – 4| = -8 And, |y + 4| - | y – 4| = 8 Adding the 2 equations, we get:

The key to answering this question within 2 minutes is: the ability to represent |x+4|, |x-4|, |y+4|, |y-4| on the number line. Do make sure that you are comfortable with this visual sense of absolute value.

The key to answering this question within 2 minutes is: the ability to represent |x+4|, |x-4|, |y+4|, |y-4| on the number line. Do make sure that you are comfortable with this visual sense of absolute value.

Best Regards

Japinder

To be honest, I feel more comfortable with plugging in. Just to set up the number line as you did in your example takes me too much time. And I don't feel comfortable with the number line, I assume that the error probability is bigger in my case by visualising the number line than plugging in.
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Re: If x and y are numbers such that x < - 10 and y > 6, which of the [#permalink]

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15 Oct 2017, 09:40

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