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

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:

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

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

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

Answer: Option D

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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

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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