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M01-25

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M01-25  [#permalink]

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New post 15 Sep 2014, 23:15
1
5
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

65% (00:44) correct 35% (00:35) wrong based on 170 sessions

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Re M01-25  [#permalink]

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New post 15 Sep 2014, 23:16
2
Official Solution:


(1) \(|x| \gt |y|\). This statement just tells us that \(x\) is further from zero than \(y\), which is not sufficient to say whether \(x \gt y\). Consider: \(x=2\), \(y=1\) and \(x=-2\), \(y=1\). Not sufficient.

(2) \(\frac{x}{y} \gt 0\). This statement tells us that \(x\) and \(y\) have the same sign, either both are negative or both are positive. Not sufficient.

(1)+(2) If from (2) \(x\) and \(y\) are both negative then from (1) we would have \(-x \gt -y\) which is the same as \(x \lt y\) (answer NO). But if from (2) \(x\) and \(y\) are both positive then from (1) we would have \(x \gt y\) (answer YES). Not sufficient.


Answer: E
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Re: M01-25  [#permalink]

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New post 05 Nov 2014, 14:57
Quick question:

From (1)+(2) If from (2) x and y are both negative then from (1) shouldn't we have |-x|> |-y| which will give us x>y. So won't it be sufficient with both statements?
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Re: M01-25  [#permalink]

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New post 06 Nov 2014, 06:31
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1
IntheHunt wrote:
Quick question:

From (1)+(2) If from (2) x and y are both negative then from (1) shouldn't we have |-x|> |-y| which will give us x>y. So won't it be sufficient with both statements?


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

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Re: M01-25  [#permalink]

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New post 24 Feb 2015, 10:54
IntheHunt wrote:
Quick question:

From (1)+(2) If from (2) x and y are both negative then from (1) shouldn't we have |-x|> |-y| which will give us x>y. So won't it be sufficient with both statements?


I thought the same at first.

Another way to look at it:

If |x| > |y|, test values for x and y both being positive, as well as x and y both being negative.

If negative:

|-2| > |-1|

This would mean that y (which is -1) is greater than x (which is -2).

If positive:

|2| > |1|

This would mean that x (which is 2) is greater than y (which is 1).

Therefore, the answer is E.
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Re: M01-25  [#permalink]

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New post 27 Mar 2016, 01:55
Bunuel wrote:
Official Solution:


(1) \(|x| \gt |y|\). This statement just tells us that \(x\) is further from zero than \(y\), which is not sufficient to say whether \(x \gt y\). Consider: \(x=2\), \(y=1\) and \(x=-2\), \(y=1\). Not sufficient.

(2) \(\frac{x}{y} \gt 0\). This statement tells us that \(x\) and \(y\) have the same sign, either both are negative or both are positive. Not sufficient.

(1)+(2) If from (2) \(x\) and \(y\) are both negative then from (1) we would have \(-x \gt -y\) which is the same as \(x \lt y\) (answer NO). But if from (2) \(x\) and \(y\) are both positive then from (1) we would have \(x \gt y\) (answer YES). Not sufficient.


Answer: E


Hi Bunuel,

I am slightly confused. In 1 we say X is further than Y from zero (which is highlighted in the attached PNG file - hopefully that is the correct representation).
In 2 we say that X and Y are the same sign.

So together, wouldn't it be that -X < -Y (i.e. further to the left of the number line and further than Y from zero) and X > Y (i.e. further than Y from zero to the right)?

Thanks
>> !!!

You do not have the required permissions to view the files attached to this post.

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Re: M01-25  [#permalink]

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New post 27 Mar 2016, 02:00
zizzi wrote:
Bunuel wrote:
Official Solution:


(1) \(|x| \gt |y|\). This statement just tells us that \(x\) is further from zero than \(y\), which is not sufficient to say whether \(x \gt y\). Consider: \(x=2\), \(y=1\) and \(x=-2\), \(y=1\). Not sufficient.

(2) \(\frac{x}{y} \gt 0\). This statement tells us that \(x\) and \(y\) have the same sign, either both are negative or both are positive. Not sufficient.

(1)+(2) If from (2) \(x\) and \(y\) are both negative then from (1) we would have \(-x \gt -y\) which is the same as \(x \lt y\) (answer NO). But if from (2) \(x\) and \(y\) are both positive then from (1) we would have \(x \gt y\) (answer YES). Not sufficient.


Answer: E


Hi Bunuel,

I am slightly confused. In 1 we say X is further than Y from zero (which is highlighted in the attached PNG file - hopefully that is the correct representation).
In 2 we say that X and Y are the same sign.

So together, wouldn't it be that -X < -Y (i.e. further to the left of the number line and further than Y from zero) and X > Y (i.e. further than Y from zero to the right)?

Thanks


|x| > |y| means that x is further from zero than y: x from y NOT -x from -y.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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M01-25  [#permalink]

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New post Updated on: 01 Sep 2018, 19:10
Hi Bunuel

Ok let me try again :) (edited this question)
Here is my question -
From Statement 2, can i not say x>0 ?

Thanks
Rahul

Originally posted by itsrahulmohan on 31 Aug 2018, 16:41.
Last edited by itsrahulmohan on 01 Sep 2018, 19:10, edited 1 time in total.
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Re: M01-25  [#permalink]

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New post 31 Aug 2018, 20:56
My 2 cents.

Statement 2 tells us that both x & Y are of the same sign. they could both be +ve or both be -ve.
Statement 1 tells us that the magnitude of X is greater than Y.

on combining Statement 1 and Statement 2

Case 1:Both x & y are +ve.(this is the one you took as example)
We open the modulus.
X>Y. the answer to our question is Yes.

Case 2: Both x & y are -ve.

ON opening the modulus, we get
-X>-Y
multiplying by -1 on both sides
X<Y. The answer to our question is No

Here, we get two different answers to our questions. Hence E is correct.

itsrahulmohan wrote:
Hi Bunuel

From Statement 2, can i not say x>0 and tie this with statement no.1 to confirm x and y are both positive, therefore answer C?
cos positive 3 is greater than positive 2 as per statement 1

Thanks
Rahul

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Re: M01-25 &nbs [#permalink] 31 Aug 2018, 20:56
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