Abhijit K wrote:If x and y are positive, is 3x > 7y?

(1) x > y + 4
(2) -5x < -14y

OA is D. However I am sure the answer should be B. Am I right?

Target question: Is 3x > 7y?

Given: x and y are positive

Statement 1: x > y + 4
This statement doesn't FEEL sufficient, so I'm going to TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 6 and y = 1 (this satisfies the condition that X > y + 4). In this case 3x is GREATER THAN 7y
Case b: x = 10 and y = 5 (this satisfies the condition that X > y + 4). In this case 3x is LESS THAN 7y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: -5x < -14y
Divide both sides by -1 to get 5x > 14y
NOTE: we need to compare 3x and 7y. So, let's fiddle with the inequality 5x > 14y
Divide both sides by 2 to get 2.5x > 7y

IMPORTANT: If x is positive (which we're told it is), then 3x > 2.5x. So, let's add this to our inequality to get...
3x > 2.5x > 7y
From this, we can conclude that it MUST be the case that 3x > 7x
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

Hi Abhijit K,

You can answer this DS question with a combination of TESTing VALUES and Number Properties.

We're told that X and Y are POSITIVE. We're asked if 3X > 7Y. This is a YES/NO question.

Fact 1: X > Y + 4

IF....
Y = 1
X = 6
3(6) > 7(1) so the answer to the question is YES

Notice in this first example that X is SIX TIMES Y. We should look for an example in which the 'multiple' isn't so high....

IF....
Y = 10
X = 15
3(15) is NOT > 7(10) so the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: -5X < -14Y

We can do some algebra to simplify this inequality and make it 'comparable' to the question that is asked....

-5X < -14Y

5X > 14Y

Since the question asks about how 3X relates to 7Y, I'm going to divide both sides of the inequality by 2 (so that we have 7Y in the Fact and in the question).

2.5X > 7Y

From here, we could TEST VALUES, but from a Number Property standpoint, since we know that X and Y are POSITIVE and that 2.5(X) is > 7Y, then 3X would be even greater than 7Y than 2.5X is. The answer to the question is ALWAYS YES
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

mallika hunsur wrote:

Abhijit K wrote:If x and y are positive, is 3x > 7y?

(1) x > y + 4

(2) -5x < -14y

OA is D. However I am sure the answer should be B. Am I right?

How is it D..??

As I see it-

Q stem asks if (x/y)>(7/3)-

Statement 1-> x>(y+4)
Since x and y are +ve, divide the above statement by y
so you get (x/y)>1+(4/y)
But what is y..? you don't know, so Not sufficient
Statement 2-> -5x<-14y
Divide by -1 and flip the sign-
5x>14y or (x/y)>(14/5) or (x/y)>(7/3).
Hence, sufficient.

So B..??

You're right, mallika. The answer is, indeed, B

Cheers,
Brent