In the right triangle shown above, what is the the value of a?
(1) c = 5
(2) a < b[/quote]
ANSWER:
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First statement:
(1) c = 5
We know nothing except the fact that one angle is 90 and one side C = 5.
This doesn't tell us anything using which we can find a.
Hence,
Insufficient.Second statement: a < b
Considering statement two alone doesn't provide us with any useful information. We just know that one angle is 90 and a<b and we have no value to further calculate anything.
Hence,
Insufficient.CONSIDERING BOTH STATEMENTS TOGETHER.
Many people will make mistake here by considering them together and guessing it to be a 30:60:90 triangle.
BEWARECareful with your assumptions. It can be anything. Maybe it's not even a special triangle at all.
Hence, the answer is E Insufficient
PS -- Be careful whenever you are dealing with anything that looks like a Special Right Triangle. GMAT knows that we have our rules and shortcuts sorted for Right triangles.
This question is the proof of that. It wants you to make a mistake by assuming that the triangle is either 45:45:90 or a 30:60:90 (considering both statements together) because we usually find these triangles in GMAT.
NEVER ASSUME ANYTHING when dealing with Data Sufficiency questions.
Hit me with a KUDO is you find this explanation helpful.