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In a XY Plan, Y is above the line -x/2. I prefer to solve this DS with the XY plan.

Stat1 y > -1. This brings us to y above the line y=-1. The area covered could be either above -x/2 (when x>0) or below -x/2 (wehn x<10). (Fig1)

INSUFF.

Stat2 (2^x) - 4 >0
<=> 2^x > 4 = 2^2
<=> x > 2

In the XY plan, it does mean that the concerned area is at right of the line x=2. One more time, their is 2 case, y could be either above the line -x/2 (when y > 0) or below the line -x/2 (the point (3,-100)). (Fig2)

INSUFF.

Both (1) and (2): x > 2 and y > -1 represents an area with a not attainable vertice at (-1;2). By drawing the line -x/2 and this point, we observe that this point is on the line. Thus, the whole area of points such that x>2 and y>-1 is above the line -x/2. (Fig3)

(1) y>-1, clearly insufficient as no info about \(x\).

(2) (2^x)-4>0 --> \(2^x>2^2\) --> \(x>2\) --> also insufficient as no info about \(y\).

(1)+(2) \(y>-1\), or \(2y>-2\) and \(x>2\) --> add this inequalities (remember, you can only add inequalities when their signs are in the same direction and you can only apply subtraction when their signs are in the opposite directions) --> \(2y+x>-2+2\) --> \(x+2y>0\). Sufficient.

(1) y>-1, clearly insufficient as no info about \(x\).

(2) (2^x)-4>0 --> \(2^x>2^2\) --> \(x>2\) --> also insufficient as no info about \(y\).

(1)+(2) \(y>-1\), or \(2y>-2\) and \(x>2\) --> add this inequalities (remember, you can only add inequalities when their signs are in the same direction and you can only apply subtraction when their signs are in the opposite directions) --> \(2y+x>-2+2\) --> \(x+2y>0\). Sufficient.

Answer: C.

I chose C.. thats correct.. bt with different approach

bt Bunuel I didnt get this highlighted thing?? How did u do that?
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Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

(1) y>-1, clearly insufficient as no info about \(x\).

(2) (2^x)-4>0 --> \(2^x>2^2\) --> \(x>2\) --> also insufficient as no info about \(y\).

(1)+(2) \(y>-1\), or \(2y>-2\) and \(x>2\) --> add this inequalities (remember, you can only add inequalities when their signs are in the same direction and you can only apply subtraction when their signs are in the opposite directions) --> \(2y+x>-2+2\) --> \(x+2y>0\). Sufficient.

Answer: C.

I chose C.. thats correct.. bt with different approach

bt Bunuel I didnt get this highlighted thing?? How did u do that?

\(2y+x>-2+2\) --> re-arrange the left hand side as x+2y. As for the right hand side: -2 + 2 = 0. So, we get \(x+2y>0\).

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is -x < 2y ?

(1) y > -1 (2) (2^x) - 4 > 0

In the original condition, there are 2 variables(x,y), which should match with the number of equations. So you need 2 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), they become y>-1, 2y>-2 and 2^x>4=2^2 --> x>2, -x<-2, which is -x<-2<2y --> -x<2y. So it is yes and sufficient. Therefore, the answer is C.

-> For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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