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12 May 2015, 04:21
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E
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Difficulty:
15%
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Question Stats:
80% (01:15) correct
20%
(01:10)
wrong
based on 473
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On the number line shown above, the tick marks are equally spaced. Which of the following statements about the numbers x, y, and z must be true?
I. xyz < 0
II. x + z = y
III. z(y - x) > 0
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
Attachment:
2015-05-12_1519.png
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18 May 2015, 06:21
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Bunuel
Based on the number line shown, we can determine that \(x\) is negative, while \(y\) and \(z\) are positive. Additionally, since the tick marks are equally spaced, the distance between \(x\) and 0 is the same as the distance between \(y\) and 0, and the distance between \(z\) and 0 is twice that distance. For instance, we can assume \(x = -1\), \(y = 1\), and \(z = 2\).
I. \(xyz < 0\)
Given that \(x\) is negative and both \(y\) and \(z\) are positive, this statement must be true.
II. \(x + z = y\)
Using the example values of \(x = -1\), \(y = 1\), and \(z = 2\), we can confirm that this statement must also be true.
III. \(z(y - x) > 0\)
Similarly, with the example values of \(x = -1\), \(y = 1\), and \(z = 2\), we can confirm that this statement must be true as well.
Answer: E
General Discussion
As the numbers are equally spaced one can see that
x = -y ; y = y and z = 2y
Now statement I is always true as xyz is nothing but -(y * y *2y) which is always negative. So I must be true.
Statement II x + z = -y + 2y = y ; So x+z =y So Statement II must be true.
Statement III : z(y-x) = 2y(y - -y) = 2(2y) which is always positive. Hence III must be true.
So I, II & III must be true.
Answer E
Ambarish
x = -y ; y = y and z = 2y
Now statement I is always true as xyz is nothing but -(y * y *2y) which is always negative. So I must be true.
Statement II x + z = -y + 2y = y ; So x+z =y So Statement II must be true.
Statement III : z(y-x) = 2y(y - -y) = 2(2y) which is always positive. Hence III must be true.
So I, II & III must be true.
Answer E
Ambarish
