In ΔJKL shown above, what is the length of segment JL ?

Question

https://gmatclub.com/forum/download/file.php?id=47587 In ΔJKL shown above, what is the length of segment JL ? (1) JK = 10 (2) KL = 5 DS83602.01 OG2020 NEW QUESTION 2019-04-26_1358.png

ScottTargetTestPrep · Accepted Answer

We see that we have a 30-60-90 right triangle, which has sides in the following ratio:

x : x√3 : 2x

Thus, if we know the length of either JK or KL, we can determine the length of JL.

Statement One Alone:

JK = 10

Since JK = 10, 2x = 10, so x = 5, and thus JL = 5√3.

Statement one is sufficient to answer the question.

Statement Two Alone:

KL = 5

Since KL = 5, JL = 5√3.

Statement two alone is sufficient to answer the question.

Answer: D

DavidTutorexamPAL · Answer

The Logical approach to this question will use the fact that in order to find the measurements of all of the sides of a 30-60-90 triangle (or a 45-45-90 triangle) all ee need is one side.
In this question each of the statements gives us the length of one side, and thus they each suffice on their own. The correct answer is (D).

Posted from my mobile device

ZoltanBP · Answer

riangle{JKL}  is a 30-60-90 degree special right triangle with a ratio of  1:\sqrt{3}:2  for its corresponding sides. The original question:  JL=?

1) We know that  JK=10 , the angle opposite  JK  is  90^{\circ} , and the angle opposite  JL  is  60^{\circ} , so  JL:10=\sqrt{3}:2 . Thus, we could get a unique value to answer the original question.  \implies   Sufficient

2) We know that  KL=5 , the angle opposite  KL  is  30^{\circ} , and the angle opposite  JL  is  60^{\circ} , so  JL:5=\sqrt{3}:1 . Thus, we could get a unique value to answer the original question.  \implies   Sufficient

Answer: D

EMPOWERgmatRichC · Answer

Hi All,

Based on the triangle JKL above, we know that we're dealign with a 30/60/90 right triangle. We're asked for the length of segment JL. The 30/60/90 triangle has a specific 'ratio of sides' (re: X : X√3 : 2X), meaning that if we know 1 of the sides, then we can determine the lengths of the other 2. By extension, depending on the information in the two Facts, we could potentially answer this question without doing any math at all.

(1) JK = 10

Fact 1 gives us the hypotenuse of the triangle, so we can figure out the exact values of the other two sides. 
Fact 1 is SUFFICIENT

(2) KL = 5 
Fact 2 gives us the 'short leg' of the triangle, so we can figure out the exact values of the other two sides. 
Fact 2 is SUFFICIENT

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

BrentGMATPrepNow · Answer

KEY CONCEPT: 30-60-90 triangles are known as  special right triangles , and we know quite a bit about this kind of triangle

Target question :    What is the length of segment JL ?

Statement 1 : JK = 10  
 https://i.imgur.com/sKEFT1R.png 
Compare ΔJKL with the   BASE 30-60-90 triangle  .
Their corresponding hypotenuses are  10  and   2  , which tells us that ΔJKL is  5 times the size  of   BASE 30-60-90 triangle  .
So, the length of  segment JL  will be  5 times the size  its corresponding side (with length   √3  )
In other words,  JL must have length 5√3 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : KL = 5 
 https://i.imgur.com/hnqrynQ.png 
The corresponding sides here have lengths  5  and   1  , which tells us that ΔJKL is  5 times the size  of   BASE 30-60-90 triangle  .
So,  JL must have length 5√3 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=hC7GwDrR8h4

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=Eiuo6FAtXJI

Jatin108 · Answer

Hi everyone, i just had one doubt cant 30-60-90 has two different lengths : 
like 6,8,10 ( which is 3,4,5 - 30-60-90 triangle) and also 5,5sqrt(3),10 ( 1:sqrt(3):2) ratio)
so in that case 10 Can lead to two diff triangles

EMPOWERgmatRichC · Answer

Hi Jatin108, A 30/60/90 right triangle has a 'fixed' relationship in terms of the lengths of the three sides (the specific 'ratio of sides' is X : X√3 : 2X). By extension, if we know the length of any one of the sides in a 30/60/90 right triangle, then we can determine the exact lengths of the other 2 sides. This DS question asks us for the length of side JL (the side across from the 60-degree angle), so we know the ratio of how that one side relates to each of the other two sides. Fact 1 and Fact 2 each individually provide an exact length for one of the three sides - so we can determine the exact length of the other two (and definitively answer the question that is asked). GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com

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In ΔJKL shown above, what is the length of segment JL ?

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In ΔJKL shown above, what is the length of segment JL ?

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