Is y z? (1) -y 2z (2) z -2y

Question

Is y > z?

(1) -y > 2z
(2) z > -2y

GMATBusters · Answer

Statement 1: (-3,1) or (1,-3) both satisfy statement 1 but in one case y>z, in other z>y. 
NOT SUFFICIENT
Statement 2: (-1,4) or (4,-1) both satisfy statement 2 but in one case y>z, in other z>y.
NOT SUFFICIENT.

Combibg statement 1 & 2, we get..
-y-2z>0 (statement 1)
 z+2y>0 (statement 2)
Adding both inequalities, we get
y-z>0 or y>z. Hence SUFFICIENT.

Answer C

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Mo2men · Answer

(1) -y > 2z Let y = 1 & z = -1..........-1 > -2............Answer is Yes Let y = -1 & z = 0...........1 > 0..............Answer is NO Insufficient (2) z > -2y We can make it: -2y < z Let y = 1 & z = -1.............-2 < -1..............Answer is Yes Let y = -1 & z = 10............2 < 10..............Answer is NO Insufficient Combining 1 & 2 -y > 2z z > -2y ----------------Sum the two inequality as sign in same direction z - y > 2z -2y y > z.........we reached certain answer Answer: C

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Since we have 2 variables (y and z) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) Since z > -2y and -y > 2z, we have z > -2y > 4z and z < 0. And -2y < z < 0 and y > 0. Thus y > z Both conditions together are sufficient. Since this question is an inequality question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B. Condition 1) If y = 1 and z = -2, the answer is "yes". If y = -2 and z = -1, the answer is "no". Since we don't have a unique solution, condition 1) is not sufficient. Condition 2) If y = 2 and z = 1, the answer is "yes". If y = 1 and z = 2, the answer is "no". Since we don't have a unique solution, condition 1) is not sufficient. Therefore, the answer is C. Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

Sarjaria84 · Answer

Hi Bunuel GMATNinja VeritasKarishma I have a question for the above, After arriving to the point where I know that both statements are not separately sufficient, I solved as below 1. -y>2z = z<-y/2 and from st. 2 we get z > -2y combining both we get, -2y< z < -y/2 Now if we take y = 2 we get, -4< z < -1 i.e. z will be a negative number, therefore y > z And when we take y = -2 we get, 4< z < 1 i.e. z will be a positive number and therefore, y < z. Therefore, answer is option E. I have seen the video wherein this question was solved by GMATNinja and the above answers as well wherein the 2 equation are solved and that is perfectly fine. What I want to understand is why am I getting a different answer, as in, what is wrong in my logic? Can you please help me on this? Thanks Saurabh

Bunuel · Answer

The point is -2y< z < -y/2 means -2y < -y/2 and this on the other hand gives y > 0, so y cannot be negative. Here is an algebraic solution: Is y > z? (1) -y > 2z (2) z > -2y Each statement is clearly insufficient alone. When taken together: Multiply (1) by 2 to get -2y > 4z. Sum this with z > -2y (we can safely do that because the signs of the inequalities are in the same direction): -2y + z > 4z - 2y, this gives z < 0. Next, multiply (2) by 2 to get 2z > -4y. Sum this with -y > 2z (again, we can safely do that because the signs of the inequalities are in the same direction): 2z - y > -4y + 2z, this gives y > 0. So, we have that z < 0 and y > 0, thus y > z. Sufficient. Answer: C.

bumpbot · Answer

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Is y > z? (1) -y > 2z (2) z > -2y

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