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

If x and y are letters which correspond to points on the number line shown above, which of the following statements must be true?


A. \(x > y\)

B. \(\frac{1}{x} < \frac{1}{y}\)

C. \(\frac{1}{x}*\frac{1}{y} > 9\)

D. \(xy < \frac{1}{3}\)

E. \(x+y > 1\)

Attachment:
di new.jpg

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

1/3>xy>0

therefore 1/3>xy is the correct answer
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