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16 Sep 2014, 00:15
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16 Sep 2014, 00:16
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Official Solution:
Is \(x > y\)?
(1) \(|x| > |y|\).
This statement just implies that \(x\) is further from zero than \(y\). Yet, it doesn't provide enough information to determine if \(x > y\). For instance, consider the cases where \(x=2\), \(y=1\) and \(x=-2\), \(y=1\). Not sufficient.
(2) \(\frac{x}{y} > 0\).
This statement implies that \(x\) and \(y\) have the same sign, meaning they are both negative or both positive. However, it doesn't provide enough information to determine if \(x > y\). For instance, consider the cases where \(x=2\), \(y=1\) and \(x=-2\), \(y=-1\). Not sufficient.
(1)+(2) If, from statement (2), \(x\) and \(y\) are both negative, then from statement (1) we would conclude \(-x > -y\), which is equivalent to \(x < y\) (answer NO). However, if from (2) \(x\) and \(y\) are both positive, then from (1) we would conclude \(x > y\) (answer YES). Nevertheless, this is still insufficient.
Answer: E
Is \(x > y\)?
(1) \(|x| > |y|\).
This statement just implies that \(x\) is further from zero than \(y\). Yet, it doesn't provide enough information to determine if \(x > y\). For instance, consider the cases where \(x=2\), \(y=1\) and \(x=-2\), \(y=1\). Not sufficient.
(2) \(\frac{x}{y} > 0\).
This statement implies that \(x\) and \(y\) have the same sign, meaning they are both negative or both positive. However, it doesn't provide enough information to determine if \(x > y\). For instance, consider the cases where \(x=2\), \(y=1\) and \(x=-2\), \(y=-1\). Not sufficient.
(1)+(2) If, from statement (2), \(x\) and \(y\) are both negative, then from statement (1) we would conclude \(-x > -y\), which is equivalent to \(x < y\) (answer NO). However, if from (2) \(x\) and \(y\) are both positive, then from (1) we would conclude \(x > y\) (answer YES). Nevertheless, this is still insufficient.
Answer: E
06 Nov 2014, 07:31
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IntheHunt
Absolute value properties:
When \(x \le 0\) then \(|x|=-x\), or more generally when \(\text{some expression} \le 0\) then \(|\text{some expression}| = -(\text{some expression})\). For example: \(|-5|=5=-(-5)\);
When \(x \ge 0\) then \(|x|=x\), or more generally when \(\text{some expression} \ge 0\) then \(|\text{some expression}| = \text{some expression}\). For example: \(|5|=5\).
So, if both x and y are negative, then |x| = -x and |y| = - y.
Theory on Abolute Values: math-absolute-value-modulus-86462.html
Absolute value tips: absolute-value-tips-and-hints-175002.html
DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58
Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html
Absolute value tips: absolute-value-tips-and-hints-175002.html
DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58
Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html
