Problem Solving

canbtg wrote:In the xy coordinate plane, which of the following points must lie on the line kx+3y=6 for every possible value of K ?

A)(1,1)

B)(0,2)

C)(2,0)

D)(3,6)

E) (6,3)

We're looking for a set of coordinates that are not affected by the value of k.
Notice that, in answer choice B (0,2), the x-coordinate is 0 and y = 2
So, if we plug x = 0 and y = 2 into the equation kx + 3y = 6, we get k(0) + 3(2) = 6
Notice that, since x = 0, the value of k is irrelevant.
So, (0, 2) will ALWAYS be a point on the line kx + 3y = 6

Answer: B

Cheers,
Brent

canbtg wrote:In the xy coordinate plane, which of the following points must lie on the line kx+3y=6 for every possible value of K ?

I'd do exactly what Brent did, but maybe it's useful to see a bit more of the theory here. If we write the equation of any line in the form y = mx + b, then m is the slope of the line, and b is the y-intercept (where the line meets the y-axis). So if we rewrite the equation above in that form, we find:

y = (-k/3)x + 2

So we know exactly one point on the line - the y-intercept is 2, so (0, 2) is on the line for sure. But we know nothing about the slope without some info about k, and if we know nothing about the slope, the line could go anywhere as you move away from the y-axis. So we don't know any other points on the line besides the y-intercept.

Hi All,

With this prompt, we’re asked which of the following points will ALWAYS lie on the line (K)(X) + 3(Y) = 6 for EVERY possible value of K. This is a great ‘concept question’, meaning that you don’t have to do a lot of math to answer it if you recognize the concept involved (and that concept is a Number Property Rule that you probably already know…).

To start, if the value of K can vary – and the sum will always be 6 - then the relative values of X and/or Y will almost always change based on the value of K. From the way the question is worded though, we know that one of the co-ordinates will ALWAYS appear on the line. Thus, we have to look for an answer that ‘counters’ the fact that K could vary. If you don’t immediately see it, then you can TEST THE ANSWERS to prove it…

Answer A: (1,1)… With that co-ordinate, the equation would become…
K(1) + (3)(1) = 6…. So K can ONLY equal 3. This does NOT match what we were told.
Eliminate Answer A

Answer B: (0,2)… With that co-ordinate, the equation would become…
K(0) + (3)(2) = 6…. Since (3)(2) = 6, then and K(0) will ALWAYS equal 0, we have a correct equation and the value of K is IRRELEVANT (meaning that if K changes, the point will still appear on the line.

Final Answer: B

GMAT Assassins aren’t born, they’re made,
Rich