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Suppose that |x| < |y + 2| < |z|. Suppose further that y >
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07 Aug 2017, 12:16
07 Aug 2017, 12:16
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Question Stats:
37% (02:05) correct
62% (02:26) wrong based on 228 sessions
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Suppose that \(|x| < |y + 2| < |z|\). Suppose further that \(y > 0\) and that \(xz > 0\). Which of the following could be true ?
Indicate all statements that apply
❑ \(0 < y < x < z\)
❑ \(0 < x < y < z\)
❑ \(x < z < 0 < y\)
❑ \(0 < y + 1.5 < x < z\)
❑ \(z < x < 0 < y\)
ShowHide Answer
Official Answer
A,B,D,E
Re: Suppose that |x| < |y + 2| < |z|. Suppose further that y >
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15 Sep 2018, 06:39
15 Sep 2018, 06:39
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Carcass wrote:
Suppose that \(|x| < |y + 2| < |z|\). Suppose further that \(y > 0\) and that \(xz > 0\). Which of the following could be true ?
Indicate all statements that apply
❑ \(0 < y < x < z\)
❑ \(0 < x < y < z\)
❑ \(x < z < 0 < y\)
❑ \(0 < y + 1.5 < x < z\)
❑ \(z < x < 0 < y\)
Show: :: OA
A,B,D,E
Given y > 0 and xz > 0)
Therefore : y must be positive,
Either x and z are both positive or they are both negative
If x and z are positive,
then y > x or y < x
Let us take two possibilities such as:
1. x = 1, y = 3, z = 6,
2. y = 2, x = 3, z = 6.
Then we can see that Option A and Option B are true
For option C,
It cannot be true because If x and z are both negative, then x must be greater than z, since |z| > |x|.
Option D
It can be true if we consider fraction let say,
y = 1, x = 2.5, and z = 4. (As nothing is mentioned for the quantities to be integer, it can be fraction as well)
Option E
Similarly if x and z are both negative,
x = -1, y = 2, and z = -4 such that |z| > |x|, y > 0
so z < x
General Discussion
Re: Suppose that |x| < |y + 2| < |z|. Suppose further that y >
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08 Jul 2018, 08:02
08 Jul 2018, 08:02
Carcass wrote:
Suppose that |x| < |y + 2| < |z|. Suppose further that y > 0 and that xz > 0. Which of the following could be true ?
Indicate all statements that apply
❑ 0 < y < x < z
❑ 0 < x < y < z
❑ x < z < 0 < y
❑ 0 < y + 1.5 < x < z
❑ z < x < 0 < y
Show: :: OA
A,B,D,E
Hello Carcass, i am a little not sure about the solutions, could you please just show us your strategy?
