In the right triangle shown above, what is the the value of a?

Question

https://gmatclub.com/forum/download/file.php?id=35644

(1) c = 5

(2) a < b

niks18 · Answer

Statement 1: from Pythagoras theorem we get a^2 + b^2 = c^2. this implies a^2 = c^2-b^2
or a^2 = 25 - b^2. as no value of "a" & "b" are given and we don't know whether they are integers, "a" & "b" could be any value less than 5. So Insufficient

Statement 2: no values are provided. So insufficient

Combining both 1 & 2, we don't get any exact value of "a".
For example if b=4, then a=3 but if b=4.5, then a=2.18 (apprx). So Insufficient

Hence Option  E

naorba · Answer

Testing 1st statement:

even if were given that c = 5, it does not necessarily mean that the triangle is of the  3:4:5 , since there could be more options:
Pythagorean theorem --->  a^2+b^2=c^2 
 1:\sqrt{24}:5  ------>  1^2+\sqrt{24}^2 = 25  Hence,  not sufficient

Testing 2nd statement:

this information does not help, since the fact that a < b only tells us that a is not equal to be. there's still several options, see statement 1 -  not sufficient

Hence, Answer is  (E)

sasidharrs · Answer

1. C = 5 => a^2+b^2 = 25 => (a,b) = (3,4) or (4,3).. those are the only 2 combinations. NS
2. a<b : this doesn't give any information. NS

combined: (a,b) = (3,4) => a = 3
Answer : c

goalMBA1990 · Answer

Statement 1: c=5. Never assume any unknown as integer unless it is specified. C=5 and triangle is right angle triangle can give a=3 or sqart 3. So not sufficient.

Statement 2: clearly not sufficient.

1+2 is also not sufficient.

So answer is E.

Sent from my XT1663 using  GMAT Club Forum mobile app

akshayk · Answer

S1 -> Insufficient. It can be a 45:45:90 right triangle, or a 30:60:90 right triangle, or any other variation. S2 -> a Angle opposite A is larger than Angle opposite B ; Any Variation possible and no info about C hence, Insufficient. S1+ S2 a Doesn't provide any new insights. Insufficient. E is the answer IMO.

Inten21 · Answer

In the right triangle shown above, what is the the value of a? (1) c = 5 (2) a < b ANSWER: ------- 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

BrentGMATPrepNow · Answer

Target question :    What is the value of a?  
Let's jump straight too....

Statements 1 and 2 combined    
Statement 1 tells us that c = 5.
Statement 2 tells us that a < b
There are several values of a, b and c that satisfy BOTH statements. Here are two cases: 
 Case a : a = 3, b = 4 and c = 5. Notice that the Pythagorean Theorem holds true: 3² + 4² = 5². In this case, the answer to the target question is  a = 3 
 Case b : a = √11, b = √14 and c = 5. Notice that the Pythagorean Theorem still holds true: (√11)² + (√14)² = 5². In this case, the answer to the target question is  a = √11 
Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

In the right triangle shown above, what is the the value of a?

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GMAT Data Sufficiency (DS) Questions

In the right triangle shown above, what is the the value of a?

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