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20 Jun 2015, 10:17
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If in the number line shown above, the tick marks are equally spaced, which of the following 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
20 Jun 2015, 10:17
Kudos
Bookmarks
Official Solution:
If in the number line shown above, the tick marks are equally spaced, which of the following 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
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
If in the number line shown above, the tick marks are equally spaced, which of the following 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
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
15 Jan 2017, 05:59
Kudos
Bookmarks
Hi,
Should we assume that the positive numbers go from zero to right and the negatives from zero to left?
In my opinion it is not clear the direction in which numbers increase. For example, 1, 0, -1, -2 could be possible and then statement 1 wouldn't be true.
Thank you!
Should we assume that the positive numbers go from zero to right and the negatives from zero to left?
In my opinion it is not clear the direction in which numbers increase. For example, 1, 0, -1, -2 could be possible and then statement 1 wouldn't be true.
Thank you!
