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(1) x^2 + y^2 = 25. Two unknowns, hence can not get the value of x. Not sufficient. (2) xy = 12. Two unknowns, hence can not get the value of x. Not sufficient.
(1)+(2) Now, we can go strictly algebraic way, though I'd suggest the following: x^2 + y^2 = 5^2 always makes me think about Pythagorean triple (3, 4, 5): 3^2+4^2=5^2. Now, 3 and 4 fit perfectly in xy = 12 too, so x can be 3 or 4. Moreover if we take the sign into consideration then there are even more options for (x, y): (3, 4); (4, 3); (-3, -4); (-4, -3). So, we have 4 possible values of x. Not sufficient.
x=? a) x^2 + y^2 = 25 x^2+ y^2 = 5^2 but we cannot deduce value of x ---NS
b) x*y = 12 Clearly not sufficient
a+b) x^2+y^2+2xy= (x+y)^2
25+24= (x+y)^2 7 = x+y need y to calculate X --NS E
From (x+y)^2=49 --> x+y=7 or x+y=-7. Also, the point is not that we need y to calculate x, but that we can get 4 different values of y from this system of equation, which give 4 different values of x.
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Statement 1: \(x^2 + y^2 = 25\) We have one equation and two unknowns. Hence we cannot solve this equaiton.
Statement 2: xy = 12 Again, we have one equation and two unknowns. Hence we cannot solve this equaiton.
Statement 1 and Statement 2 combined: \(x^2 + y^2 = 25\) and xy = 12
Whenever we have something of the form \(x^2 +/- y^2\) , try to make it into perfect squares. We know that \((x+y)^2 = x^2 + y^2 +2xy\) So, we need the value of xy to make statement 1 a perfect square and we have the value of xy from statement 2.
Adding 2xy = 24 on both sides in statement 1, we have \(x^2 + y^2 +2xy = 49\) or \((x+y)^2 = 7^2\) Still we cannot solve for the value of x
INSUFFICIENT Option E is the correct answer
(1) x^2 + y^2 = 25 --> If you remember pythagorean triplets (i.e. one being 3-4-5 triangle). Using this as an example, we have no way of knowing what value x takes on... +/- 3 or +/- 4. Thus, INSUFFICIENT
(2) xy = 12 --> We have no way of knowing what value x takes on. Thus, INSUFFICIENT
...so A, B, and D are out at this point
Trying (1) + (2) together, we still do not have any way of knowing with certainty the value of x. Thus, A,B,C,D are out.
Re: What is the value of x ?
16 Sep 2016, 17:12