mehdiov wrote:
If x and y are positive, is 3x > 7y?
(1) x > y + 4
(2) -5x < -14y
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 > 14yNOTE: we need to compare 3x and 7y. So, let's fiddle with the inequality 5x > 14yDivide both sides by 2 to get
2.5x > 7yIMPORTANT: 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 > 7yFrom this, we can conclude that
it MUST be the case that 3x > 7xSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer:
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