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# M20-30

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Math Expert
Joined: 02 Sep 2009
Posts: 50626

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16 Sep 2014, 00:09
1
1
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:08) correct 34% (01:10) wrong based on 152 sessions

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Is $$x \lt y$$ ?

(1) $$x^3 \lt y^3$$

(2) $$(x + y)(x - y) \lt 0$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50626

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16 Sep 2014, 00:09
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.

_________________
Intern
Joined: 09 Sep 2015
Posts: 5
GMAT 1: 630 Q46 V31
GPA: 3.53
WE: Education (Education)

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25 Jul 2016, 09:42
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 12 Jan 2013
Posts: 2

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11 May 2017, 11:36
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.

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
Intern
Joined: 22 May 2017
Posts: 4

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08 Jun 2017, 09:03
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.
Math Expert
Joined: 02 Sep 2009
Posts: 50626

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08 Jun 2017, 14:13
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.

Did you try to use a calculator?

(-1/2)^3 = -1/8 < (-1/3)^3 = -1/27
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Joined: 17 Apr 2015
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23 Aug 2017, 12:17
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.

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
Math Expert
Joined: 02 Sep 2009
Posts: 50626

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23 Aug 2017, 12:35
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.

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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Joined: 08 Jun 2015
Posts: 435
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
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24 Oct 2017, 01:51
+1 for A.
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" The few , the fearless "

Intern
Joined: 15 Aug 2013
Posts: 40

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05 Dec 2017, 20:34
Hi brunel,
Cannt we take x=1 and y=1 in that case statement 1 fails??

Thanks
Abhi
Math Expert
Joined: 02 Sep 2009
Posts: 50626

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05 Dec 2017, 20:43
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?

3. Strategies and Tactics for DS Section

For more check below:
ALL YOU NEED FOR QUANT ! ! !
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Joined: 15 Aug 2013
Posts: 40

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06 Dec 2017, 10:46
Bunuel wrote:
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?

3. Strategies and Tactics for DS Section

For more check below:
ALL YOU NEED FOR QUANT ! ! !

Thank you Bunuel
Manager
Joined: 26 Feb 2018
Posts: 79
Location: United Arab Emirates
GMAT 1: 710 Q47 V41
GMAT 2: 770 Q49 V47

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10 Mar 2018, 15:25
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, 15:25
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# M20-30

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