=>

Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

Since we have 2 variables and 0 equation, C is most likely to be the answer.

Conditions 1) & 2)

Since x and y are different prime numbers and x – y = 2, both x and y are odd integers. x = 2a + 1 and y = 2b + 1 for some integers a and b. x^2 + y^2 = (2a+1)^2 + (2b+1)^2 = 4a^2 + 4a + 1 + 4b^2 + 4b + 1 = 4(a^2 + a + b^2 + b ) + 2.

Thus, its remainder is 2, when it is divided by 4.

Both condition 1) and 2) are sufficient.

The answer is C.

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.

Answer: C

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare

The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.

"Only $79 for 3 month Online Course"

"Free Resources-30 day online access & Diagnostic Test"

"Unlimited Access to over 120 free video lessons - try it yourself"