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|x + y| = 10

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|x + y| = 10 [#permalink] New post   12 Aug 2018, 09:43
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\(|x + y| = 10\)

\(x ≥ 0\)

\(z < y – x\)

Quantity A
Quantity B
z
10


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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Romang67
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Re: |x + y| = 10 [#permalink] New post   13 Aug 2018, 06:27
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We can quickly check edge cases here:

|x+y| = 10 and x>=0

Let x = 0

Then y = 10

and z < 10 - 0

If x is any number bigger than 0, then y has to be less than 10 (by first constraint), and thus z is less than a number smaller than 10 minus a number bigger than 0, so z < 10.

So B.
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Re: |x + y| = 10 [#permalink] New post   31 Dec 2019, 07:51
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Official explanation

From z < y - x, the value of z depends on x and y. So, solve for x and y as much as possible. There are two cases for the absolute value equation: |x + y| = 10 means that (x + y) = ± 10. Consider these two cases separately

The positive case:

x + y = 10, so y = 10 - x. Substitute into z < y - x, getting z < (10 - x) - x, or z < 10 - 2x. Because x is at least zero, 10 - 2x 10. Putting the inequalities together, z < 10 - 2x 10. Thus, z < 10.


The negative case:

x + y = -10, so y = -10 - x. Substitute into z < y - x, getting z < (-10 - x) - x, or z < -10 - 2x. Because x is at least zero, -10 - 2x -10. Putting the inequalities together, z < -10 - 2x -10. Thus, z < -10.

In both cases, 10 is greater than z. The correct answer is (B).
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Re: |x + y| = 10 [#permalink] New post   19 Feb 2021, 01:27
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Hi,

You can try using a few possibilities.

x=0 y=+/-10
x=1 y=9 or -11

z<y-x
considering the first example,
10-0=10>0. Thus here z<10
Now, consider y=-11 x=1
-11-1=-12. Thus z<-12

Thus in both of the above case z is always less than 10

IMO B

Hope this helps!
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Re: |x + y| = 10 [#permalink] New post   22 May 2021, 01:56
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huda wrote:
Official explanation

From z < y - x, the value of z depends on x and y. So, solve for x and y as much as possible. There are two cases for the absolute value equation: |x + y| = 10 means that (x + y) = ± 10. Consider these two cases separately

The positive case:

x + y = 10, so y = 10 - x. Substitute into z < y - x, getting z < (10 - x) - x, or z < 10 - 2x. Because x is at least zero, 10 - 2x 10. Putting the inequalities together, z < 10 - 2x 10. Thus, z < 10.


The negative case:

x + y = -10, so y = -10 - x. Substitute into z < y - x, getting z < (-10 - x) - x, or z < -10 - 2x. Because x is at least zero, -10 - 2x -10. Putting the inequalities together, z < -10 - 2x -10. Thus, z < -10.

In both cases, 10 is greater than z. The correct answer is (B).

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Re: |x + y| = 10 [#permalink] New post   30 Jun 2023, 21:21
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Re: |x + y| = 10 [#permalink]
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