It should be clear that neither statement is sufficient on its own, but you can pick numbers to verify this:shivanigs wrote:Hi,
Request help with understanding of the following question.Thanks..
x + y = ?
1.x^2 + y^2 = 5
2.xy = 2
Statement 1: let x=0, so y= +-√5. So, x+y could be √5 or -√5. INSUFFICIENT.
Statement 2: Let x=1, so y=2, and x+y=3. Or, let x=4, so y=0.5, so x+y=4.5. INSUFFICIENT.
Statements 1&2 combined: You can use both equations to solve for possible values of x and y, but you might take a few seconds to see if you can figure out any possible values just by guessing and checking. x=1 and y=2 is a natural place to start for the second statement, because 2 and 1 are the only integer factors of 2. Plugging these values into statement 1 verifies that it is also a solution of x^2+y^2=5. So, in this case, x+y=3. Notice that x=-1 and y=-2 also solves both equations, but in this case x+y=-3. Thus, the answer is E.
If you don't see any possible solutions right away, you'll probably have to just solve it mathematically:
1. x^2+y^2=5, and y=2/x (Solve statement 2 for y)
2. x^2+(2/x)^2=5 (Substitution)
3. x^2+4/x^2=5
4. x^4+4=5x^2 (Multiplying both sides of the equation by x^2)
5. x^4-5x^2+4=0 (Rearranging equation into standard form)
6. (x^2-4)(x^2-1)=0 (Factoring)
7. x^2=4 or x^2=1, so x=+-2, or x=+-1
Plug these values back into either equation to get the four solutions:
x=1, y=2; x=2, y=1; x=-2, y=-1; x=-1, y=-2
Clearly 3 and -3 are both possible values for x+y, so again the answer is
E
