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Is 2x > 2y ? (1) x > y (2) 3x > 3y
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Bunuel
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Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink] New post  06 Oct 2016, 00:21
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Is 2x > 2y ?

(1) x > y
(2) 3x > 3y
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msk0657
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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink] New post  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 ? (1) x > y (2) 3x > 3y [#permalink] New post  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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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink] New post  06 Oct 2016, 05:06
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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 ? (1) x > y (2) 3x > 3y [#permalink] New post  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 ? (1) x > y (2) 3x > 3y [#permalink] New post  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 ? (1) x > y (2) 3x > 3y [#permalink] New post  11 Nov 2017, 06:53
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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 ? (1) x > y (2) 3x > 3y [#permalink] New post  08 Jan 2018, 09:57
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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.

Correct answer choice: D.
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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink] New post  29 Jan 2019, 19:00
Bunuel wrote:
Is 2x > 2y ?

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


Question from 2x > 2y becomes

is 2>0 & x>y

If 2x-2y>0, it could have been 2<0(but this cannot be possible ) & x<y

(1) x > y
Sufficient

(2) 3x > 3y
3 > 0 & x>y
Sufficient

D
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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink] New post  29 Jan 2019, 21:27
Is \(2x > 2y ?\)
We can multiply or divide any positive number to the inequality , the inequality doesn't change
If \(a >0\) and \(x > y\)
Then \(ax > ay\) or vice versa

1) Sufficient

2) Sufficient

IMO D
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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink] New post  11 May 2019, 00:52
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Given:

=> 2x > 2y => 2x-2y>0 => x-y>0.

From Statement 1:

=>x-y > 0. Suff.

From Statement 2:

=> 3x > 3y => 3x-3y>0 => x-y>0.Suff.

Ans Choice D.
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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink] New post  14 Dec 2020, 05:00
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Bunuel wrote:
Is 2x > 2y ?

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



We can manipulate the question:

Is 2x>2y

or, x>y [Dividing both sides by 2; we can do it without changing the sign of the inequality as 2 is positive]

The question is whether x>y?

(1) x > y; This the question wants. Sufficient.

(2) 3x > 3y [Dividing both sides by 2; we can do it without changing the sign of the inequality as 3 is positive]

So, x > y; Sufficient.

The answer is D
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