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

Question

Is 2x > 2y ?

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

AkshdeepS · Accepted Answer

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.

msk0657 · Answer

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.

PKay · Answer

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)

msk0657 · Answer

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....

ashikaverma13 · Answer

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

Bunuel · Answer

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 
     Theory   
 Inequalities Made Easy! 
 Inequalities: Tips and hints 
 Arithmetic with Inequalities 
 Wavy Line Method Application - Complex Algebraic Inequalities 
 Solving Quadratic Inequalities: Graphic Approach 
 Inequalities - Quadratic Inequalities 
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 Inequalities trick 
 INEQUATIONS(Inequalities) Part 1 
 INEQUATIONS(Inequalities) Part 2 
     Questions   
 Inequality and absolute value questions from my collection 
 DS Questions 
 PS Questions

For more check  Ultimate GMAT Quantitative Megathread

Hope it helps.

Aiena · Answer

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.

KanishkM · Answer

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

4d · Answer

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

kinvestor · Answer

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.

MHIKER · Answer

We can manipulate the question:

Is 2x>2y

or, x>y

The question is whether x>y?

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

(2) 3x > 3y

So, x > y; Sufficient.

The answer is D

palaknayyar · Answer

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.

The answer is therefore, D.

ScottTargetTestPrep · Answer

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.

Answer: D

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

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