devinawilliam83 wrote:
Is x|y|>y^2?
(1) x>y
(2) y>0
I rephrased the question as x|y|>|y| (since y^= |y|. On solving this I rephrased as x>1?
basis this rephrased version. the answer id D. however OA is C..
Have I solved the equation wrongly?
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.
There 2 variables and 0 equation. Thus we need 2 equations to solve for the variables; the conditions provide 2 equations, so there is high chance that (C) will be the answer.
The question \(x|y| > y^2\) is equivalent to \(x|y| > |y|^2\) or \(|y| ( x - |y| ) > 0\).
The equivalent question is if \(|y| ( x - |y| ) > 0\).
Condition 1)
\(x = 2\), \(y = 1\) : It is true.
\(x = 2\), \(y = 0\) : It is false.
This condtion is not true.
Condition 2)
This is not sufficient, since we don't know anything about \(x\).
Condition 1) & 2)
Since \(y > 0\), we have \(|y| > 0\).
Since \(x > y = |y| > 0\), \(x - |y| > 0\).
Thus \(|y| ( x - |y| ) > 0\).
Both conditions together are sufficient.
Normally 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 C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. 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 according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe one-and-only
World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course""Free Resources-30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons - try it yourself"