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Math Revolution and GMAT Club Contest Starts!
QUESTION #9:x + y = ?
(1) \(y = 2x - 1\)
(2) \(y^2 = -|1 - 2x|\)
Check conditions below:
Math Revolution and GMAT Club ContestThe Contest Starts November 28th in Quant Forum
We are happy to announce a Math Revolution and GMAT Club Contest
For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday).
To participate, you will have to reply with your best answer/solution to the new questions that will be posted on
Saturday and Sunday at 9 AM Pacific. Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6-months access to
GMAT Club Tests.
PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize:
PS + DS course with 502 videos that is worth $299!
All announcements and winnings are final and no whining

GMAT Club reserves the rights to modify the terms of this offer at any time.
NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.
Thank you!
MATH REVOLUTION OFFICIAL SOLUTION:Since we have 2 variables in the original condition, we also need 2 equations. Since we need both 1) and 2), the correct answer is likely C. Using con 1) & 2) together, we get x=1/2, y=0. This is unique and sufficient. Therefore, the correct answer is C. However, since this is an “absolute value” problem, which is one of the key questions, we should apply Common Mistake Type 4(A).
In case of con 1), the values of x, y are not unique. Therefore, it is not sufficient.
In case of con 2), the only values that satisfy y^2+|1-2x|=0 are x=1/2, y=0. Therefore, it is unique and sufficient.
The correct answer is B. If C and B are both correct answers, B is would be the final correct answer.
Note 1 : a=b=0 is required to satisfy |a|+|b|=0 or a2+b2=0. Also, solving this type of question usually takes over 5 minutes during the actual exam. However, if you understand the relationship between Variable Approach Method and Common Mistake Types, you will be able to solve this type of question in just about 2 minutes.
Note 2 : 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.