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

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Math Expert
Joined: 02 Sep 2009
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In the right triangle shown above, what is the the value of a?  [#permalink]

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06 Jun 2017, 09:16
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67% (00:48) correct 33% (00:50) wrong based on 215 sessions

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

(1) c = 5

(2) a < b

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Re: In the right triangle shown above, what is the the value of a?  [#permalink]

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06 Jun 2017, 09:34
Bunuel wrote:

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

(1) c = 5

(2) a < b

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
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Re: In the right triangle shown above, what is the the value of a?  [#permalink]

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06 Jun 2017, 09:38
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Bunuel wrote:

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

(1) c = 5

(2) a < b

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

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Re: In the right triangle shown above, what is the the value of a?  [#permalink]

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07 Jun 2017, 17:29
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
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Re: In the right triangle shown above, what is the the value of a?  [#permalink]

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07 Jun 2017, 17:53
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.

Sent from my XT1663 using GMAT Club Forum mobile app
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Re: In the right triangle shown above, what is the the value of a?  [#permalink]

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12 Jun 2017, 11:43
Bunuel wrote:

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

(1) c = 5

(2) a < b

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.

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Re: In the right triangle shown above, what is the the value of a?  [#permalink]

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17 Jul 2017, 08:45
1
In the right triangle shown above, what is the the value of a?

(1) c = 5

(2) a < b[/quote]

-------

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.
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Re: In the right triangle shown above, what is the the value of a?  [#permalink]

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06 Aug 2018, 10:35
Top Contributor
Bunuel wrote:

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

(1) c = 5
(2) a < b

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

Cheers,
Brent
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Re: In the right triangle shown above, what is the the value of a?   [#permalink] 06 Aug 2018, 10:35
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