If x and y are positive, is 3x > 7y? (1) x > y + 4 (2) -5x < -14y

If x and y are positive, is 3x > 7y?

(1) \(x>y+4\) --> if \(x=6\) and \(y=1\) then \(3x=18>7=7y\), so the answer is YES but if \(x=20\) and \(y=15\) then \(3x=60<105=7y\), so the answer is NO. Two different answers, not sufficient.

(2) \(-5x < -14y\) --> \(2.5x>7x\) and as both unknowns are positive then naturally \(3x\) would be more than \(7y\), as \(3x>2.5x>7y\). Sufficient.

Answer: B.

OA must be wrong here, answer should be B.

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:

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If x and y are positive, is 3x > 7y?

(1) x > y + 4

let x = 20 y = 1

3(20) > 7(1); true.

let x = 10 y = 5

3(10) > 7(5); false

INSUFFICIENT.

(2) -5x < -14y
= 2.5x > 7y
thus 3x > 7y

SUFFICIENT.

Answer is B.

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