If x and y are letters which correspond to points on the number line s

I do not see how to intuitively do this problem by using algebra and inequalities (not number picking), can someone assist?

coled90 I got you covered!

From the graph we know \(0 < x < \frac{1}{3}\) and \(\frac{1}{3} < y < 1\).

So first we can conclude y > x, so A is incorrect. Observe option B, since both x and y are positive we can get \(\frac{1}{x} > \frac{1}{y}\) so B is incorrect.

Options C and D focus on \(x*y\), since both x and y are positive we can take the maximum value of each piece and multiply to find the maximum of x * y. Therefore \(x*y < \frac{1}{3} * 1\) and we can choose D. (To make option C correct we should have >3 instead of >9).

Note we must confirm either x or y must be positive in order to find such a maximum for xy (since negative*negative might create a new maximum).

Ans: D

according to the graph:
[1][/3]>x>0
and
1>y>.33

1/3>xy>0

therefore 1/3>xy is the correct answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.