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# Is 2x > 2y ? (1) x > y (2) 3x > 3y

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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink]
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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]
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]
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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]
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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]
4
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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.

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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink]
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]
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]
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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]
Top Contributor
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.

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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink]
We need to understand what the question stem REALLY wants us to answer. In this case, it is whether x>y? A definite yes or no will help us reach the answer.

Let us take a look at the statements:

S1: literally answers the question stem for us, but we should still make sure our reasoning is correct. Ask the question- what are the restraints on x and y? do they need to be positive? or integers? The answer in both cases is no- there are no constraints. We can now try to resolve 2x>2y with every possibility. I tried with x=3, y=2; x=1/2, y=1/5, x=-3, y=5.
In all the cases, the answer is a firm Yes. Sufficient.

S2: Very similarly, cancel out the 3s from both sides and we are left with the same inequality as S1 and can solve in the exact same way. Sufficient.

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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink]
1
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Bunuel wrote:
Is 2x > 2y ?

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

Solution:

We need to determine whether 2x > 2y. Dividing both sides by 2, we have x > y. Therefore, if we can determine x > y, then we have 2x > 2y.

Statement One Alone:

Since we are given that x > y, we do know that 2x > 2y. Statement one alone is sufficient.

Statement Two Alone:

Dividing the inequality by 3, we see that x > y, which is exactly the same as the inequality in statement one. Therefore, statement two alone is also sufficient.

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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink]
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Re: Is 2x > 2y ? (1) x > y (2) 3x > 3y [#permalink]
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