Donnie84
Interesting question. My attempt:
If x=y (y = x) were true, we are looking at an upward sloping line passing through origin (0,0). The slope is 1 and y-intercept is 0. Keeping this in mind, let's look at the statements:
1. 4x - 2y = 80
Reducing it to 2x - y = 40
Rearranging it to y = 2x - 40
Slope of such a line is 2, y-intercept is -40 (0, -40) and it does not pass through the origin. x will never be equal to y on any point on this line. Sufficient.
2. 2x - y = 40 -> y = 2x - 40
Same equation as above. Same answer. Sufficient.
Answer (D).
You should always check for ALL the conditions or cases possible. For statement 1, you end up getting 2x-y=40 , which you also get from statement 2. So your final answer will either be D or E depending on 1 statement.
Lets analyse statement 1 in detail. You are given, 2x-y=40 and you need to see whether x=y on this line. In order to check this, try substituting x=y in 2x-y=40 to see if you get logical values.
You indeed get (x,y) = (40,40) as 1 solution set while the point (20,0) also lies on 2x-y=40. Thus you get "yes" with (40,40) but "no" with (20,0). NOT sufficient to answer the question asked as you do not get either a definite yes or a definite no.
As statement 1 is NOT sufficient, statement 2 is also automatically not sufficient as both the statements provide the same equation.
E is thus the correct answer.
Hope this helps.