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

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Math Expert
Joined: 02 Sep 2009
Posts: 55170
Is y > z? (1) -y > 2z (2) z > -2y  [#permalink]

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09 Apr 2018, 04:48
00:00

Difficulty:

75% (hard)

Question Stats:

46% (02:01) correct 54% (02:08) wrong based on 35 sessions

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Is y > z?

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

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Re: Is y > z? (1) -y > 2z (2) z > -2y  [#permalink]

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09 Apr 2018, 06:40
1
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)
y-z>0 or y>z. Hence SUFFICIENT.

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Re: Is y > z? (1) -y > 2z (2) z > -2y  [#permalink]

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09 Apr 2018, 12:20
Bunuel wrote:
Is y > z?

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

(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

z - y > 2z -2y

y > z.........we reached certain answer

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Re: Is y > z? (1) -y > 2z (2) z > -2y  [#permalink]

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11 Apr 2018, 23:03
Bunuel wrote:
Is y > z?

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

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.

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.
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Re: Is y > z? (1) -y > 2z (2) z > -2y   [#permalink] 11 Apr 2018, 23:03
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