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

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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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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

[Ian Stewart]

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.

[Brent@GMATPrepNow]

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 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

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