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M20-30

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M20-30  [#permalink]

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New post 16 Sep 2014, 01:09
1
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:06) correct 33% (01:08) wrong based on 137 sessions

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Re M20-30  [#permalink]

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New post 16 Sep 2014, 01:09
Official Solution:


Is \(x \lt y\) ?



(1) \(x^3 \lt y^3\). Note that we can always take an odd root from both sides of an inequality (the same for raising both parts of an inequality to an odd power). Now, if we take 3rd root from \(x^3 \lt y^3\) we'll get \(x \lt y\). Sufficient.

(2) \((x+y)(x-y) \lt 0\). This statement tells that \(x^2-y^2 \lt 0\) or \(x^2 \lt y^2\), which is not sufficient to answer whether \(x \lt y\), consider \(x=1\) and \(y=2\) for an YES answer and \(x=1\) and \(y=-2\) for a NO answer.


Answer: A
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Re: M20-30  [#permalink]

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New post 25 Jul 2016, 10:42
I think this is a high-quality question and I agree with explanation.
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Re: M20-30  [#permalink]

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New post 11 May 2017, 12:36
Bunuel wrote:
Official Solution:


(1) \(x^3 \lt y^3\). Note that we can always take an odd root from both sides of an inequality (the same for raising both parts of an inequality to an odd power). Now, if we take 3rd root from \(x^3 \lt y^3\) we'll get \(x \lt y\). Sufficient.

(2) \((x+y)(x-y) \lt 0\). This statement tells that \(x^2-y^2 \lt 0\) or \(x^2 \lt y^2\), which is not sufficient to answer whether \(x \lt y\), consider \(x=1\) and \(y=2\) for an YES answer and \(x=1\) and \(y=-2\) for a NO answer.


Answer: A


Hi, why can we not consider that either (x+y)<0 or (x-y)<0? If we do this then we get X<-Y and X<Y. Thx
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Re: M20-30  [#permalink]

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New post 08 Jun 2017, 10:03
Hi,

Say x = -1/2 and y = -1/3 then this solution of your don't work.

In such case x to the power of 3 is greater than y to the power of 3, but x < y is false.
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Re: M20-30  [#permalink]

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New post 08 Jun 2017, 15:13
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Re: M20-30  [#permalink]

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New post 23 Aug 2017, 13:17
Bunuel wrote:
Official Solution:


(1) \(x^3 \lt y^3\). Note that we can always take an odd root from both sides of an inequality (the same for raising both parts of an inequality to an odd power). Now, if we take 3rd root from \(x^3 \lt y^3\) we'll get \(x \lt y\). Sufficient.

(2) \((x+y)(x-y) \lt 0\). This statement tells that \(x^2-y^2 \lt 0\) or \(x^2 \lt y^2\), which is not sufficient to answer whether \(x \lt y\), consider \(x=1\) and \(y=2\) for an YES answer and \(x=1\) and \(y=-2\) for a NO answer.


Answer: A


Hi Bunuel,

For 2, why can't I write -y<x<y ? Is it because we don't really know the sign of y?

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Re: M20-30  [#permalink]

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New post 23 Aug 2017, 13:35
sliceoflife wrote:
Bunuel wrote:
Official Solution:


(1) \(x^3 \lt y^3\). Note that we can always take an odd root from both sides of an inequality (the same for raising both parts of an inequality to an odd power). Now, if we take 3rd root from \(x^3 \lt y^3\) we'll get \(x \lt y\). Sufficient.

(2) \((x+y)(x-y) \lt 0\). This statement tells that \(x^2-y^2 \lt 0\) or \(x^2 \lt y^2\), which is not sufficient to answer whether \(x \lt y\), consider \(x=1\) and \(y=2\) for an YES answer and \(x=1\) and \(y=-2\) for a NO answer.


Answer: A


Hi Bunuel,

For 2, why can't I write -y<x<y ? Is it because we don't really know the sign of y?

Regards


\(x^2 \lt y^2\) means that |x| < |y|, so y is further from 0 than x is. We can have the following cases:


-----------0---x---y---
-------x---0-------y---
---y---x---0-----------
---y-------0---x------


As you can see, for the first two cases x < y and for the remaining two cases x > y.
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Re: M20-30  [#permalink]

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New post 24 Oct 2017, 02:51
+1 for A.
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Re: M20-30  [#permalink]

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New post 05 Dec 2017, 21:34
Hi brunel,
Cannt we take x=1 and y=1 in that case statement 1 fails??

Thanks
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Re: M20-30  [#permalink]

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New post 05 Dec 2017, 21:43
abhinashgc wrote:
Hi brunel,
Cannt we take x=1 and y=1 in that case statement 1 fails??

Thanks
Abhi


It's Bunuel, not brunel.

When testing numbers for DS, we should choose so that these numbers satisfy the statement we are examining. Does x = y = 1 satisfy x^3 < y^3?

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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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Re: M20-30  [#permalink]

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New post 06 Dec 2017, 11:46
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Re: M20-30  [#permalink]

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New post 10 Mar 2018, 16:25
another way to think of it is that statement 2 tells us that the absolute value of x is more than the absolute value of y. This means that x could be more or less than y, so (II) is insufficient. We don't need to test any cases for (II)

Good question but too easy to be a Q50/51 question. More like Q45-48. Would classify as medium
Re: M20-30 &nbs [#permalink] 10 Mar 2018, 16:25
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