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.

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....

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

• 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
  Graphic approach to problems with inequalities
  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.

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.

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

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

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.

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

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.

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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