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jj97cornell
Joined: 29 Dec 2011
Last visit: 30 Aug 2012
Posts: 2
Given Kudos: 6
Concentration: Finance
Schools: Yale '14 (II)
GMAT 1: 710 Q48 V38
GMAT 2: 720 Q49 V40
GPA: 3.3
03 Feb 2012, 14:32
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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65% (02:16) correct
35%
(02:13)
wrong
based on 2450
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On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?
(1) xyz < 0
(2) xy < 0
(1) xyz < 0
(2) xy < 0
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03 Feb 2012, 16:21
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jj97cornell
On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?
The distance between x and y is greater than the distance between \(x\) and \(z\), means that we can have one of the following four scenarios:
A. y--------z--x (YES case);
B. x--z--------y (YES case);
C. y--------x--z (NO case);
D. z--x--------y (NO case)'
The question asks whether we have scenarios A or B (\(z\) lies between \(x\) and \(y\)).
(1) \(xyz <0\) --> either all three are negative or any two are positive and the third one is negative. If we place zero between \(y\) and \(z\) in case A (making \(y\) negative and \(x\), \(z\) positive), then the answer would be YES but if we place zero between \(y\) and \(x\) in case C, then the answer would be NO. Not sufficient.
(2) \(xy<0\) --> \(x\) and \(y\) have opposite signs. The same here: We can place zero between \(y\) and \(x\) in case A and the answer would be YES but we can also place zero between \(y\) and \(x\) in case C and the answer would be NO. Not sufficient.
(1)+(2) Both case A (answer YES) and case C (answer NO) satisfy the statements. Not sufficient.
A. y----0----z--x (YES case) --> \(xyz<0\) and \(xy<0\);
C. y----0----x--z (NO case) --> \(xyz<0\) and \(xy<0\).
Answer: E.
Hope it's clear.
1. Statement 1 tells us that \(xyz<0\)
Which basically means that either all 3 are negative or one of them is negative. We can draw two scenarios of a number line where z is between \(x\) and \(y\) and where \(z\) is on the right of \(x\) and \(y\) on the left of \(x\) and maintain the condition that all three are negative. Hence Insufficient.
2. Statement 2 tells us that \(xy<0\)
Which basically means that either \(x\) is negative or \(y\) is negative. No statement about \(z\) so obviously insufficient.
Now together we know that if either \(x\) or \(y\) are negative, and one of them is positive, \(z\) has to be positive. So again we draw two scenarios on the number line and we find that two cases are possible, one where \(z\) is in the middle and one where it is not. Hence both statements combined are insufficient as well.
Answer. E .. I am attaching a diagram to illustrate.
[img]
Which basically means that either all 3 are negative or one of them is negative. We can draw two scenarios of a number line where z is between \(x\) and \(y\) and where \(z\) is on the right of \(x\) and \(y\) on the left of \(x\) and maintain the condition that all three are negative. Hence Insufficient.
2. Statement 2 tells us that \(xy<0\)
Which basically means that either \(x\) is negative or \(y\) is negative. No statement about \(z\) so obviously insufficient.
Now together we know that if either \(x\) or \(y\) are negative, and one of them is positive, \(z\) has to be positive. So again we draw two scenarios on the number line and we find that two cases are possible, one where \(z\) is in the middle and one where it is not. Hence both statements combined are insufficient as well.
Answer. E .. I am attaching a diagram to illustrate.
[img]
Attachment:
Number%20Line.jpg
[/img] Attachments
Number Line.jpg [ 105.17 KiB | Viewed 135394 times ]
