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# Is 2x > 2y ?

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Math Expert
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Is 2x > 2y ?  [#permalink]

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06 Oct 2016, 00:21
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90% (00:33) correct 10% (00:48) wrong based on 444 sessions

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Is 2x > 2y ?

(1) x > y
(2) 3x > 3y

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Joined: 26 Nov 2012
Posts: 592
Is 2x > 2y ?  [#permalink]

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Updated on: 06 Oct 2016, 05:51
Bunuel wrote:
Is 2x > 2y ?

(1) x > y
(2) 3x > 3y

2x > 2y => 2x-2y>0 => 2(x-y)>0...we need to know x-y value.

Stat 1: x-y > 0...Sufficient.

Stat 2: 3x > 3y ..to get 2x>2y then we'll multiply 2/3 on both sides...we get 2x > 2y...Sufficient...

IMO option D.

Originally posted by msk0657 on 06 Oct 2016, 01:09.
Last edited by msk0657 on 06 Oct 2016, 05:51, edited 1 time in total.
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Re: Is 2x > 2y ?  [#permalink]

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06 Oct 2016, 02:58
msk0657 wrote:
Bunuel wrote:
Is 2x > 2y ?

(1) x > y
(2) 3x > 3y

2x > 2y => 2x-2y>0 => 2(x-y)>0...we need to know x-y value.

Stat 1: x-y > 0...Sufficient.

Stat 2: 3(x-y) > 0 ...we are not sure about x-y value...it can be negative or positive..

IMO option A.

Statement 2 states that 3(x-y)>0 => (x-y) > 0. Why'd you be unsure about x-y value? 3*(any -ve value is always -ve; no matter how small that number is eg.-0.0000001*3 is still negative)
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Is 2x > 2y ?  [#permalink]

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06 Oct 2016, 05:06
1
Bunuel wrote:
Is 2x > 2y ?

(1) x > y
(2) 3x > 3y

Question:

Is $$2x > 2y$$ or $$2x - 2y > 0$$ or $$2 (x - y) > 0$$

As $$2 > 0$$, the question is " Is $$(x - y) > 0$$"?

Statement 1: if $$x > y$$, then $$(x - y) > 0$$, Answer to the question is Yes. $$2x > 2y$$. Sufficient

Statement 2: If $$3x > 3y > 0$$

$$3x - 3y > 0$$ or $$3 (x - y) > 0$$

As $$3 > 0$$, then $$(x - y)$$ has to be greater than 0 for statement 2 to be valid.

Therefore, Sufficient. Answer (D). Hope I am not missing something.
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Re: Is 2x > 2y ?  [#permalink]

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06 Oct 2016, 05:50
peekaysan wrote:
msk0657 wrote:
Bunuel wrote:
Is 2x > 2y ?

(1) x > y
(2) 3x > 3y

2x > 2y => 2x-2y>0 => 2(x-y)>0...we need to know x-y value.

Stat 1: x-y > 0...Sufficient.

Stat 2: 3(x-y) > 0 ...we are not sure about x-y value...it can be negative or positive..

IMO option A.

Statement 2 states that 3(x-y)>0 => (x-y) > 0. Why'd you be unsure about x-y value? 3*(any -ve value is always -ve; no matter how small that number is eg.-0.0000001*3 is still negative)

No need of the above information...

We are given 3x > 3y...then if we multiply with 2/3 on both sides...we get 2x > 2y...Hence stat 2 is also sufficient...updating with my analysis....
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Re: Is 2x > 2y ?  [#permalink]

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11 Nov 2017, 06:48
Bunuel wrote:
Is 2x > 2y ?

(1) x > y
(2) 3x > 3y

HI Bunuel,

I wanted to understand how in these question, without knowing the sign of x and y we can take both the value at one side and come to the following conclusion:

2x>2y = 2x-2y>0 = 2(x-y) > 0 meaning we just need to find if x>y!

because I thought we cannot take variables to one side unless we know the signs I took a long winded process of testing cases and getting the answer. Could you please help clear out this concept?

Thanks
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Re: Is 2x > 2y ?  [#permalink]

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11 Nov 2017, 06:53
ashikaverma13 wrote:
Bunuel wrote:
Is 2x > 2y ?

(1) x > y
(2) 3x > 3y

HI Bunuel,

I wanted to understand how in these question, without knowing the sign of x and y we can take both the value at one side and come to the following conclusion:

2x>2y = 2x-2y>0 = 2(x-y) > 0 meaning we just need to find if x>y!

because I thought we cannot take variables to one side unless we know the signs I took a long winded process of testing cases and getting the answer. Could you please help clear out this concept?

Thanks

We cannot multiply/divide an inequality by the variable if we don't know its sign but we can add/subtract whatever we want to/from both sides of an inequality.

For example, we cannot divide x > y by x unless we know the sign of x. If x is positive, then we'll get 1 > y/x but if x is negative, then we'll get 1 < y/x (flip the sign when multiplying/dividing by negative number). On the other hand we can subtract x from both sides of x - x > y - x to get 0 > y - x.

9. Inequalities

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: Is 2x > 2y ?  [#permalink]

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08 Jan 2018, 09:57
Bunuel wrote:
Is 2x > 2y ?

(1) x > y
(2) 3x > 3y

Hi,

This is how I answered it-

QUESTION STEM: is 2x > 2y? Diving both sides by 2, the question becomes: is x > y?

STATEMENT 1: x > y. This statement gives us a YES to our question; hence, it is sufficient.

STATEMENT 2: 3x > 3y. Dividing both sides by 3 gives us a definite YES. So, this statement is sufficient too.

Re: Is 2x > 2y ? &nbs [#permalink] 08 Jan 2018, 09:57
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