Is x 2y? (1) 2x + y 6

Question

Is x > 2y?

(1) 2x + y < 6

(2) 3x - y > 6

chetan2u · Answer

Clearly individual statements can give many solutions that can give us answer either way - Yes or No 1) 2x+y<6 x=1, y can be 3.....NO x=1, y can be -1.....YES 2) 3x-y>6 x=1, y can be -2....YES x=3, y can be 2.....NO Combined Add both inequalities 2x+y+6<6+3x-y........2x+y<3x-y......x>2y C

Russ19 · Answer

BrentGMATPrepNow , Can I have your solution to the problem above? Thanks in advance.

BrentGMATPrepNow · Answer

Target question : Is x > 2y? Statement 1 : 2x + y < 6 Since there's no extra information about x and y, it's unlikely that statement 1 is sufficient, so let's test some values There are several values of x and y that satisfy statement 1. Here are two: Case a : x = 0 and y = -1. In this case, the answer to the target question is YES, x is greater than 2y Case b : x = -1 and y = 0. In this case, the answer to the target question is NO, x is not greater than 2y Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2 : 3x - y > 6 Once again, since there's no additional information how about the values of x and y, there's a good chance that statement 2 is not sufficient. So let's test more values. There are several values of x and y that satisfy statement 2. Here are two: Case a : x = 0 and y = -10. In this case, the answer to the target question is YES, x is greater than 2y Case b : x = 5 and y = 5. In this case, the answer to the target question is NO, x is not greater than 2y Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that 2x + y < 6 Statement 2 tells us that 3x - y > 6 Useful property: If the inequality symbols of two inequalities are facing the same direction, you can ADD those inequalities. To get the inequality symbols facing the same way, we can rewrite the bottom inequality to get: 2x + y < 6 6 < 3x - y ADD the inequalities to get: 2x + y + 6 < 3x - y + 6 Subtract 6 from both sides to get: 2x + y < 3x - y Subtract 2x from both sides: y < x - y Add y to both sides: 2y < x So, the answer to the target question is YES, x is greater than 2y Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C Cheers, Brent RELATED VIDEO https://www.youtube.com/watch?v=S_fjYmCtvy0

QuantMadeEasy · Answer

Rephrasing the question Is x - 2y > 0 Step 1: Understanding statement 1 alone (1) 2x + y < 6 When x = 1, y = 1; x - 2y < 0 When x = 0, y = -1; x - 2y > 0 Insufficient Step 2: Understanding statement 2 alone (2) 3x - y > 6 When x = 1, y = -4; x - 2y > 0 When x =3, y = 2; x - 2y < 0 Insufficient Step 3: Combining Multiplying -1 on both the sides of the inequality 2x + y < 6; -2x - y > -6 3x - y > 6 Adding above two inequalities x - 2y > 0 Sufficient C is correct

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Is x > 2y? (1) 2x + y < 6 (2) 3x - y > 6

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