Hi All,

This question is perfect for TESTing VALUES. It also has a few fantastic Number Property shortcuts in the answer choices, which can save you a LOT of "calculation time" if you recognize them.

Given the right triangle with no values (the one restriction is that the length is GREATER than the height, we can use ANY right triangle that we choose. The obvious choice would be to use a 3/4/5 right triangle (length = 4, height = 3).

We're told that A = length/height, so A = 4/3. We're asked for the value of diagonal/length, so we're looking for 5/4 when we plug A = 4/3 into the answer choices.

Now, here's where the Number Property shortcuts come into play. Four of the answer choices use the square root sign - for the square root of a number to = 5/4, the number MUST be GREATER than 1. We can use that to our advantage to quickly eliminate some of the answers.

Answer A: 4/3 This is NOT a match

Answer B: Root[(4/3)^2 - 1] = Root[16/9 - 1] = Root[7/9]. Stop working. This is LESS than 1. This is NOT a match.

Answer C: Root[(4/3)^2 + 1] = Root[16/9 + 1] = Root[25/9] = 5/3. This is NOT a match.

Answer D: Root[1 - a fraction]. Stop working. This is going to be LESS than 1. This is NOT a match.

There's only 1 answer left, and we've eliminated the others...

Final Answer:

Here's the proof though:

Answer E: Root[1 + 1/(4/3)^2] = Root[1+ 9/16] = Root[25/16] = 5/4. This IS a match.

GMAT assassins aren't born, they're made,

Rich

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# Rich Cohen

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