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26 May 2016, 05:41
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Is x > 0 ?
(1) xy + y = y
(2) xy + x = x
Answer was given as E, but why couldn't A 1 be sufficient?
Is my algebra incorrect if I factor out Y?
xy + y = y
y(x+1)=y
(x+1)=1
x=0
sufficient
this was a kaplan question categorized as difficult
Given explanation:
The question stem does not give any information about x, so let's look at the statements.
Statement (1): insufficient. Let's subtract y from both sides of the equation xy + y = y. Then xy = 0. When the product of a group of numbers is 0, at least one of the numbers must be 0. So either x = 0 or y = 0. If y = 0 and x is any positive number, (for example, x = 7), then xy = 0, and x > 0; so statement (1) is true, and the answer to the question is "yes." If x = 0, it does not matter what y equals because xy = 0, but x is not greater than 0; so statement (1) is true, but the answer to the question is "no." Since there can be more than one answer to the question, Statement (1) is insufficient. We can eliminate choices (A) and (D).
Note that when dealing with the equation xy = 0, you cannot simply divide both sides by y to find that x = 0, because it might have been the case that y = 0, and you cannot divide by 0.
(1) xy + y = y
(2) xy + x = x
Answer was given as E, but why couldn't A 1 be sufficient?
Is my algebra incorrect if I factor out Y?
xy + y = y
y(x+1)=y
(x+1)=1
x=0
sufficient
this was a kaplan question categorized as difficult
Given explanation:
The question stem does not give any information about x, so let's look at the statements.
Statement (1): insufficient. Let's subtract y from both sides of the equation xy + y = y. Then xy = 0. When the product of a group of numbers is 0, at least one of the numbers must be 0. So either x = 0 or y = 0. If y = 0 and x is any positive number, (for example, x = 7), then xy = 0, and x > 0; so statement (1) is true, and the answer to the question is "yes." If x = 0, it does not matter what y equals because xy = 0, but x is not greater than 0; so statement (1) is true, but the answer to the question is "no." Since there can be more than one answer to the question, Statement (1) is insufficient. We can eliminate choices (A) and (D).
Note that when dealing with the equation xy = 0, you cannot simply divide both sides by y to find that x = 0, because it might have been the case that y = 0, and you cannot divide by 0.
26 May 2016, 11:37
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Hi jcava972,
To start, you should really post this in the DS sub-Forum here:
gmat-data-sufficiency-ds-141/
As far as your work on this question is concerned, you have to be really careful about 'dividing out' variables in calculations because you might end up removing a potential solution. Here's a simple example:
X^2 = X
IF you divide both sides by X, then you end up with X = 1. However, by dividing you removed another possible solution (X=0). The proper way to manipulate that equation is...
X^2 = X
X^2 - X = 0
X(X-1) = 0
X = 0 or 1
In THIS question, we're asked if X is greater than 0. This is a YES/NO question.
1) XY + Y = Y
Subtract Y from both sides....
XY = 0
This tells us that at least one of the two variables = 0, but we don't know which one. If Y = 0, then X could be ANYTHING (so the answer to the question could be YES OR NO). Thus, Fact 1 is INSUFFICIENT.
GMAT assassins aren't born, they're made,
Rich
To start, you should really post this in the DS sub-Forum here:
gmat-data-sufficiency-ds-141/
As far as your work on this question is concerned, you have to be really careful about 'dividing out' variables in calculations because you might end up removing a potential solution. Here's a simple example:
X^2 = X
IF you divide both sides by X, then you end up with X = 1. However, by dividing you removed another possible solution (X=0). The proper way to manipulate that equation is...
X^2 = X
X^2 - X = 0
X(X-1) = 0
X = 0 or 1
In THIS question, we're asked if X is greater than 0. This is a YES/NO question.
1) XY + Y = Y
Subtract Y from both sides....
XY = 0
This tells us that at least one of the two variables = 0, but we don't know which one. If Y = 0, then X could be ANYTHING (so the answer to the question could be YES OR NO). Thus, Fact 1 is INSUFFICIENT.
GMAT assassins aren't born, they're made,
Rich
26 May 2016, 12:48
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Thanks for the explanation. I see your point, especially in a question where there is a squared variable. I guess I'm still just unsure of why my simplification was invalid. Especially since there were no squared variables and often the goal of simplification is to eliminate a variable if you can. Any kind of rule I am missing?
