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|x + y| = 10
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12 Aug 2018, 09:43
12 Aug 2018, 09:43
Expert Reply
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Question Stats:
68% (01:50) correct
31% (06:56) wrong based on 216 sessions
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\(|x + y| = 10\)
\(x ≥ 0\)
\(z < y – x\)
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.
Kudos for R.A.E
\(x ≥ 0\)
\(z < y – x\)
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.
Kudos for R.A.E
Re: |x + y| = 10
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13 Aug 2018, 06:27
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.
|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.
Re: |x + y| = 10
[#permalink]
31 Dec 2019, 07:51
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).
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).
