In triangle JKL shown above, what is the length of segment

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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 amFollowed by: 5 members; Thanked: 1 times

by AbeNeedsAnswers » Sun May 05, 2019 9:22 pm

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

(1) JK = 10
(2) KL = 5

D

Source: Official Guide 2020

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Source: Beat The GMAT — Data Sufficiency | Sun May 05, 2019 9:22 pm

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by [email protected] » Sun May 12, 2019 12:29 pm

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 : Xâˆš3 : 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

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Rich

Contact Rich at [email protected]

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by Ian Stewart » Mon May 13, 2019 4:24 am

In general, if you know all three angles in a triangle (which we do here, since from two angles we can find the third using the fact that a triangle's angles sum to 180), and you know one of the triangle's sides, the other two sides are completely determined, so it must somehow be possible to work out how long they are. So the answer here is instantly D. We don't even need to notice here that we have the familiar 30-60-90 triangle.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon May 13, 2019 9:43 am

AbeNeedsAnswers wrote:

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

(1) JK = 10
(2) KL = 5

D

Source: Official Guide 2020

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

Compare Î”JKL with the BASE 30-60-90 triangle.
Their corresponding hypotenuses are 10 and 2, which tells us that Î”JKL 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 âˆš3)
In other words, JL must have length 5âˆš3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: KL = 5

The corresponding sides here have lengths 5 and 1, which tells us that Î”JKL is 5 times the size of BASE 30-60-90 triangle.
So, JL must have length 5âˆš3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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