PowerPrep II Test 2 -- Hard Quant Section, Question 4

[mattoliver.mattoliver]

Hello there again

Was wondering if anyone had some insight for me on this geometry QC question from PowerPrepII. I missed it today. I think it is in the "hard" section but I'm not sure. Know it's kind of tough without the diagram. I'd attach a screenshot if I could. If that's verboten or frowned upon, sorry, not really sure what the etiquette is here. Thanks for your help.

You've got the triangle IGK (which has a line segment from points H to J through the triangle.

H is the midpoint of IG. J is the midpoint of IK. IG = GK = 10.

Quantity A
IJ

Quantity B
5

[mattoliver.mattoliver]

Think I might have figured it out but please let me know if not correct.

IG and GK are the two legs of the isosceles, and they're both 10. You can still have H be the midpoint and J be the midpoints of IG (which the common info tells you is 10), but IK can be smaller or larger, and depending on its size the length of IJ is going to change. Let's say IK is 8. IJ is 4, Quantity B is greater. On the other hand, assume IK is 11. IJ is now 5.5 > 5, thus Quantity A is greater.

Answer D.

If I'm missing something easier just let me know. Thanks a lot.

[tommywallach]

Hey Matt,

Your explanation is correct. And yes, you're not supposed to publish GRE pictures on the web (though I believe some people have on here without reprisal, they are technically copyrighted). That said, the trick of the question is in making you think that because the cross-line HJ hits the two midpoints, it thus splits the triangle in half. But those two lines that it hits in the middle of are not defined as being equal in the first place.

-t