BrainLab wrote:

If x and y are positive numbers such that x + y = 1, which of the following could be the value of 100x + 200y?

I. 80

II. 140

III. 199

(A) II only

(B) III only

(C) I and II

(D) I and III

(E) II and III

Another method is to take extreme values of x and y to figure out the range

x + y = 1

Say x is almost 1 (infinitesimally smaller than 1) and y is almost 0 (infinitesimally greater than 0)

Then 100x + 200y = 100*1 + 100*0 = approx. 100

Say y is almost 1 (infinitesimally smaller than 1) and x is almost 0 (infinitesimally greater than 0)

Then 100x + 200y = 100*0 + 200*1 = approx. 200

Now if x = 1/2 and y is 1/2,

Then 100x + 200y = 100*(1/2) + 200*(1/2) = 150

So we see that value of the expression will vary from 100 to 200.

Hence answer will be (E)

why are you multiplying by 0. Zero is neither negative nor positive. No ?