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

Question

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

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

Bunuel · Accepted Answer

No, D is not correct, answer should be B. If x and y are positive is 3x>7y ? (1) x > y+4. The best way to deal with this statement will be to pick numbers. On DS questions when plugging numbers, goal is to prove that the statement is not sufficient . So we should try to get an YES answer with one chosen number(s) and a NO with another. Well, we can get an YES answer very easily: just pick large enough x and small enough y (for example 10 and 1 respectively) for NO answer: if x=10 and y=5 then 10>5+4 but 3*10=30<7*5=35 . So this statement is not sufficient. (2) -5x < -14y --> multiple both side by -1/2 and flip the sign because we multiply by a negative value --> 2.5x>7y , as both x and y are positive then 3x>2.5x>7y . Sufficient. Answer: B.

fluke · Answer

Is 3x>7y? (1) x > y+4 x-y> 4 x=6, y=1 18>7. Yes x=10 y=5 30<35. No Not sufficient. (2) -5x < -14y 5x>14y x>(14/5)y x>2.8y 3x>8.4y So; 3x must be greater than 7y. Sufficient. Ans: "B"

Bunuel · Answer

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.

BrentGMATPrepNow · Answer

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 RELATED VIDEOS https://www.youtube.com/watch?v=Od98BOicIq4 https://www.youtube.com/watch?v=S_fjYmCtvy0

Basshead · Answer

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

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