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Difficulty:
35%
(medium)
Question Stats:
68% (01:20) correct
32%
(01:28)
wrong
based on 227
sessions
History
Date
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Is x > y ?
(1) x + y > 0
(2) x^2 - y^2 > 0
(1) x + y > 0
(2) x^2 - y^2 > 0
For 1) x+y>0
x> -y Insufficient
For 2) x^2-y^2>0
x^2>y^2
--> x<-y OR x>y
1) and 2)
x> -y
and x<-y OR x>y
So the answer should be E.
However, the answer key says C. What concept am I missing?
Thanks.
Source of the question is a file that I downloaded from the "Downloads" section here. Advanced GMAT question with readyforGMAT.com on the bottom of the page.
x> -y Insufficient
For 2) x^2-y^2>0
x^2>y^2
--> x<-y OR x>y
1) and 2)
x> -y
and x<-y OR x>y
So the answer should be E.
However, the answer key says C. What concept am I missing?
Thanks.
Source of the question is a file that I downloaded from the "Downloads" section here. Advanced GMAT question with readyforGMAT.com on the bottom of the page.
21 Aug 2013, 01:27
Kudos
Bookmarks
Is x>y?
Is x>y? --> is x-y>0?
(1) x+y>0. The sum of two numbers is greater than 0, from this we cannot say which one is greater. Consider (x, y)=(1, 2) and (x, y)=(2, 1). Not sufficient.
(2) x^2-y^2>0 --> x^2>y^2 --> |x|>|y|. This implies that x is further from 0, then y is. Not sufficient. Consider: (x, y)=(-2, 1) and (x, y)=(2, 1).
(1)+(2) From (2) we have that (x-y)(x+y)>0 and from (1) we have that x+y>0, thus x-y>0. Sufficient.
Answer: C.
Hope it's clear.
Is x>y? --> is x-y>0?
(1) x+y>0. The sum of two numbers is greater than 0, from this we cannot say which one is greater. Consider (x, y)=(1, 2) and (x, y)=(2, 1). Not sufficient.
(2) x^2-y^2>0 --> x^2>y^2 --> |x|>|y|. This implies that x is further from 0, then y is. Not sufficient. Consider: (x, y)=(-2, 1) and (x, y)=(2, 1).
(1)+(2) From (2) we have that (x-y)(x+y)>0 and from (1) we have that x+y>0, thus x-y>0. Sufficient.
Answer: C.
Hope it's clear.
General Discussion
15 Nov 2015, 01:47
Kudos
Bookmarks
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>y?
(1) x+y>0
(2) x^2-y^2>0
There are 2 variables (x,y) and 2 equations are given from the 2 conditions, making it likely that (C) will be our answer.
Looking at them together,
x+y>0 and (x-y)(x+y)>0, x+y>0, so x-y>0. This answers the question 'yes' and it is therefore sufficient; the answer is (C).
For cases where we need 2 more equation, 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.
Is x>y?
(1) x+y>0
(2) x^2-y^2>0
There are 2 variables (x,y) and 2 equations are given from the 2 conditions, making it likely that (C) will be our answer.
Looking at them together,
x+y>0 and (x-y)(x+y)>0, x+y>0, so x-y>0. This answers the question 'yes' and it is therefore sufficient; the answer is (C).
For cases where we need 2 more equation, 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.
