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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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.

What is the value of (x + y)^2

(1) x^2 + xy = 3 (2) y^2 + yx = 5

There are 2 variable (x,y) and 2 equations from the question and the conditions; there is high chance (D) will be our answer. If we look at the 2 conditions together, we get x^2+xy+y^2+yx=x^2+2xy+y^2=8, (x+y)^2=8 when we add them together. The conditions are sufficient, and the answer becomes (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.
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From statement 1, (x+y) = 3 or x=3, and from statement 2, (x+y) = 5 or y=5. From any of them we can figure out the value of (x+y)^2 Instead we're adding the statements to derive at the formula (x+y)^2. Could someone please clarify why we're doing this?

From statement 1, (x+y) = 3 or x=3, and from statement 2, (x+y) = 5 or y=5. From any of them we can figure out the value of (x+y)^2 Instead we're adding the statements to derive at the formula (x+y)^2. Could someone please clarify why we're doing this?

Thank you. Regards.

hi, (1) x^2 + xy = 3....... x(x+y) = 3............ this does not mean (x+y) = 3 or x=3.......... It ONLY means x\neq{0} and x+y will depend on x and there can be lot of combinations.. x= 1/3 and x+y = 9 if x= 3, x+y = 1.. x=1, x+y = 3.. so different values..

(2) y^2 + yx = 5 similarly you can find many combinations for x and y.. we are not told if x and y are + or - or integer or fraction
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