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In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this

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Magoosh GMAT Instructor
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In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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31 May 2016, 09:27
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In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this trapezoid?

Statement #1: KL = 10 and JM = 15

Statement #2: angle J = 60 degrees

Geometry on the GMAT demands careful visual thinking skills, especially on the DS questions. This question is from a collection of ten challenging GMAT DS practice questions on geometry. To see the others, as well as the OE for this question, see:
GMAT Data Sufficiency Geometry Practice Questions

Mike
[Reveal] Spoiler: OA

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Mike McGarry
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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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31 May 2016, 10:25
IMO A

From A we can calculate the height from K to base JM, and we know the measure of parallel (II) sides.

However from B we cannot calculate the measure of II sides.
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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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31 May 2016, 13:28
From statement A, we can easily find area using .5*(sum of // sides)*distance

From B: // sides length, we can not determine.

So IMO, A
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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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01 Jun 2016, 00:24
The answer is D

The two previous posters have articulated why A is sufficient, however they've missed out on why B is also sufficient.

We know the length of aides JK and LM. When a straight line is drawn from point K to the base to form the height, it forms a right triangle. Statement B tells us that angle J is 60°, therefore this is a 30-60-90 triangle (JK is the hypotenuse). Once we solve for the height, we can solve for the area. Statement 2 is sufficient

Therefore the answer is D
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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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01 Jun 2016, 02:00
I am unable to understand how did you find the height from statement A.

From stmt 1 we get the measure of the parallel sides. Not sufficient.
From stmt 2 we get j=60 so from 30-60-90 angles we get the height to be 5root3.
From both statement it's sufficient. Hence C.

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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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01 Jun 2016, 04:48
FightToSurvive wrote:
I am unable to understand how did you find the height from statement A.

From stmt 1 we get the measure of the parallel sides. Not sufficient.
From stmt 2 we get j=60 so from 30-60-90 angles we get the height to be 5root3.
From both statement it's sufficient. Hence C.

Posted from my mobile device

The measure of the parallel lines allow us to solve for the height - imagine drawing a line straight down from point K to the base, forming a right triangle (let's call this JKN).
We can do the same from point L, forming a separate right triangle (let's call this MLP).
As the lines are parellel and JK = LM, we know that JN and PM = $$\frac{5}{2}$$

The hypotenuse of the triangle is given in the question stem (JK = LM = 5), and we know that line JN is $$\frac{5}{2}$$, so given the rules for right triangles, KN is $$\frac{5}{2}\sqrt{3}$$
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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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01 Jun 2016, 06:00
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If we look at the original condition and the question, we need to know the height of JM and KL. However, if we look at the condition 1), from KL=10 and JM=15, the height becomes 2.5√3. We can get the unique answer for the area. Hence, the condition is sufficient. The correct answer is A.
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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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01 Jun 2016, 10:57
Judy1389 wrote:
The answer is D

The two previous posters have articulated why A is sufficient, however they've missed out on why B is also sufficient.

We know the length of aides JK and LM. When a straight line is drawn from point K to the base to form the height, it forms a right triangle. Statement B tells us that angle J is 60°, therefore this is a 30-60-90 triangle (JK is the hypotenuse). Once we solve for the height, we can solve for the area. Statement 2 is sufficient

Therefore the answer is D

Dear Judy1389,
I'm happy to respond. My friend, I don't know whether you realize the error in your line of reasoning.

While it's absolutely true that we have a 30-60-90 triangle on each side and that we therefore know the height, we have no idea how long KL is. The segment KL is entirely outside both 30-60-90 triangles and this length could be anything--equal to the height, equal to JK, or five miles long. The area depends on both the height (which we know from this statement) and the lengths of the bases, which we don't know at all from this statement. This means that Statement #2 is not sufficient on its own.

Does this make sense?
Mike
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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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02 Jun 2016, 00:36
Whoops! Yes, I carried over the info presented from statement 1 to statement 2....
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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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02 Jun 2016, 10:33
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mikemcgarry wrote:
Attachment:
trapezoid.png

In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this trapezoid?

Statement #1: KL = 10 and JM = 15

Statement #2: angle J = 60 degrees

Geometry on the GMAT demands careful visual thinking skills, especially on the DS questions. This question is from a collection of ten challenging GMAT DS practice questions on geometry. To see the others, as well as the OE for this question, see:
GMAT Data Sufficiency Geometry Practice Questions

Mike

Given information:- KL//JM, JK = LM = 5.

That means perpendicular drawn from K and L on line JM will have equal length.

Question asked= What is the area

Ares of trapezoid is 1/2(b1+b2) *h
We know b1 and b2. Any statement that gives value of 'h' will be sufficient.

KL = 10 and JM = 15
Now because KL//JM, JK = LM = 5 and perpendicular drawn from K and L on line JM will have equal length, 5 extra of JM will be equally divided as 2.5 on each sides.
Since we have perpendicular line, we can calculate height with given Hypotenuse and Base. Sufficient.

angle J = 60 degrees

We can't get the information on base and height. Not sufficient.

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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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08 Aug 2017, 09:22
hey mike,

i just wanted to know if from option B, do we get Angle M = 60?
Magoosh GMAT Instructor
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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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08 Aug 2017, 09:42
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gauravprashar17 wrote:
hey mike,

i just wanted to know if from option B, do we get Angle M = 60?

Dear gauravprashar17

I"m happy to respond.

JKLM is not just an ordinary trapezoid: it is something called an isosceles trapezoid, because we are explicitly told that the two legs, JK and LM have equal length.

If the two legs are equal, then the figure has complete symmetry over an imaginary mirror line down the middle. The corresponding angles on each side are equal (angle J = angle M, and angle K = angle L). In fact, the diagonals, JL & KM, not drawn her, are also equal.

Does all this make sense?
Mike
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Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]

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06 Sep 2017, 10:55
mikemcgarry wrote:
Attachment:
trapezoid.png

In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this trapezoid?

Statement #1: KL = 10 and JM = 15

Statement #2: angle J = 60 degrees

Geometry on the GMAT demands careful visual thinking skills, especially on the DS questions. This question is from a collection of ten challenging GMAT DS practice questions on geometry. To see the others, as well as the OE for this question, see:
GMAT Data Sufficiency Geometry Practice Questions

Mike

Simply A

St 1

If we know the hypotenuse of the triangle and the length of one base then we can know the length of the other base- we don't actually need to do the algebra, however.

Suff

St 2

There are no numbers given so we cannot really calculate anything

Insuff
Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this   [#permalink] 06 Sep 2017, 10:55
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In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this

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