Is x - y

Question

Is x - y < 0?

(1) x^2 - y^2 > 1
(2) x/y + 1 > 0, where y > 0

chetan2u · Answer

Hi,

lets see the statements

1)  x^2-y^2>1  
OR (x-y)(x+y)>1..
both x-y and x+y can be positive or BOTH can be -ive
Insuff

2)  \frac{x}{y}+1>0 , where y>0 
(x+y)/y>0
since y is positive, x+y is also positive..
but we cannot say if x-y<0
insuff

combined.. 
 x+y is positive , so x-y is also +ive..
which means x-y>0..
so our answer is NO 
Suff
C

TheUltimateWinner · Answer

Could you please give a shortcut way of this problem?
Thanks...

BrentGMATPrepNow · Answer

Target question : Is x - y < 0? Statement 1 : x² - y² > 1 This statement doesn't FEEL sufficient, so I'll TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 2 and y = 1, in which case x - y = 2 - 1 = 1 . So, x - y > 0 Case b: x = -2 and y = -1, in which case x - y = (-2) - (-1) = -1 . So, x - y < 0 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values Statement 2 : x/y + 1 > 0, where y > 0 This statement doesn't FEEL sufficient either, so I'll TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 2 and y = 2, in which case x - y > 0 Case b: x = 1 and y = 2, in which case x - y < 0 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 2: x/y + 1 > 0, where y > 0 Since y is POSITIVE, we can safely multiply both sides by y to get: x + y >0 In other words, x + y is some POSITIVE # Statement 1: x² - y² > 1 Rewrite as (x + y)(x - y) > 1 In other words, (x + y)(x - y) is POSITIVE Use info from statement 2 to get: ( some POSITIVE # )(x - y) is POSITIVE For this to hold true, it must be the case that x - y is POSITIVE. In other words, x - y > 0 Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer = C Related Resources The following free videos cover the concepts/strategies that are useful for answering this question: - Difference of square factoring: https://www.gmatprepnow.com/module/gmat ... /video/955 - Inequalities – Part I: https://www.gmatprepnow.com/module/gmat ... /video/979 Cheers, Brent

RDhin · Answer

i under stand the concern of any shortut, but frankly this question can be solved in a span of 30-40 sec

1. x^2 - y^2 > 1 
(x-y)(x+y) > 1 ,
means either both are positive or both are negative, still it doesn't provide complete info about x-y sign

2. x+y >0 we don't know about the sign of x-y

so combing both we can say only value exists for both (x+y) & (x-y) are positive , so C

HKD1710 · Answer

stmt-1:

(x+y) * (x-y) > 1

x or y could be positive or negative. any of the two could have higher modulus. these could be making the product > 1. so we are too unsure here if x-y is +ve or _ve. Insuff

stmt-2:
(x+y)/y > 0, where y>0

so X+y is positive. but again we dont know about x-y.

Combining:
(x+y) * (x-y) > 1 and x+y is positive, so definitly x-y is positive.

Answer is C.

MathRevolution · Answer

Is x - y < 0?

(1) x^2 - y^2 > 1
(2) x/y + 1 > 0, where y > 0

There are 2 variables (x and y) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. The condition 1) and the condition 2) each has 1 equation. Therefore, there is high chance that C is the correcty answer. If we use the condition 1) and the condition 2) at the same time, we get (x-y)(x+y)>1>0 and x/y+1>0. As y>0 in (x+y)/y>0, we get x+y>0. Then we get x-y>0. This is no and the conditions are not sufficient. Therefore, the correct answer is C.

l 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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Is x - y < 0?

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Is x - y < 0?

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