Carcass wrote:
Quantity A |
Quantity B |
\(IJ\) |
\(5\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Graphs of any kind (bar, pie, x/y, etc) are drawn to scale on the GRE. Geometric figure are NOT drawn to scale. Therefore, a lot of the time questions like these are really asking "have we given you enough information to clarify the NUMERIC VALUES.
Step by step:
Info 1: H=midpoint, so we now know that IH and HG are equal.
Info 2: J=midpoint, so we now know that IJ=JK. (Note: as of yet, nothing would indicate that these sides are equal).
Info 3: IG=GK=10, so we now know that the left side and the bottom side of the triangle are equal. (Note: this means that we know that the triangle is either an equilateral or isosceles and CANNOT be scalene).
Since there is no info 4, including no further angle measurements, we are left with IK being anywhere from some tiny fraction to a number just below 20 (a number between 0-20, non-inclusive). Since one of the triangle inequalities states that the sum of any 2 sides must be bigger than a third, we know that the max for the side is <(10+10)...or >20. Nothing correlates that side of the triangle to the others. If the prompt told us an angle or gave us general triangular structure information (equilateral vs iso) then we could possible come to a finite value for IK. Without it, we are stuck with a range that is either larger or smaller than 5, and thus, the answer is D.
Personally, I would recommend going through step by step with these type of problems, ESPECIALLY when the answer seems like it should be super easy, as tricking you (like this problem) can work just as well as doing a double fake (making the problem easy...and it looking like there should be a trick but they actually didn't trick you, thus you tricking yourself).