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Difficulty:
15%
(low)
Question Stats:
71% (00:50) correct
29%
(00:48)
wrong
based on 353
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In the right triangle shown above, what is the the value of a?
(1) c = 5
(2) a < b
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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Bunuel
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
Bunuel
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)
Posts: 33
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
2. a<b : this doesn't give any information. NS
combined: (a,b) = (3,4) => a = 3
Answer : c
Posts: 48
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
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
Bunuel
S1 -> Insufficient.
It can be a 45:45:90 right triangle, or a 30:60:90 right triangle, or any other variation.
S2 -> a<b => Angle opposite A is larger than Angle opposite B ; Any Variation possible and no info about C hence, Insufficient.
S1+ S2
a<b<c => Doesn't provide any new insights.
Insufficient.
E is the answer IMO.
In the right triangle shown above, what is the the value of a?
(1) c = 5
(2) a < b[/quote]
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<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. BEWARE
Careful 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.
(1) c = 5
(2) a < b[/quote]
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<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. BEWARE
Careful 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.
Posts: 6,727
Bunuel
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
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