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Bigger or Smaller?? (Posted on 2007-02-22) Difficulty: 3 of 5
Given that x=111110/111111, y=222221/222223, z=333331/333334, which is the biggest and which is the smallest?

No Solution Yet Submitted by Ansh    
Rating: 1.7500 (4 votes)

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Hints/Tips Good idea | Comment 3 of 6 |
I like hoodat's solution more than my own. I think the point of this problem is to do only mental calculations, and his fits.

My strategy is similar but more complicated. It would be to take them piece wise and cross multiply, but evaluate without finding the answer.

111110/(111110+1)<>222221/(222221+2), and multiplying by (111110+1)(222221+2), each term would have 222221*111110 but x (the left side) would have 2*111110 and y (the right side) would have 222221, thus y is greater.

Similarly multiply y and z by (222221+2)(333331+3) to get 666663>666662, and x and z by (111110+1)(333331+3) to get 333331>333330

So x<z<y

  Posted by Gamer on 2007-02-22 21:02:49
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