Author 
Message 
TAGS:

Hide Tags

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4680

In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]
Show Tags
31 May 2016, 09:27
2
This post received KUDOS
Expert's post
4
This post was BOOKMARKED
Question Stats:
57% (01:06) correct 43% (01:02) wrong based on 149 sessions
HideShow timer Statistics
Attachment:
trapezoid.png [ 3.76 KiB  Viewed 2955 times ]
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 degreesGeometry 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 QuestionsMike
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)





Manager
Joined: 04 Apr 2015
Posts: 101

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



Manager
Joined: 03 Jan 2016
Posts: 92
WE: Operations (Manufacturing)

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



Intern
Joined: 21 May 2016
Posts: 17
Location: United Kingdom
GPA: 3.5

Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]
Show Tags
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 306090 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



Manager
Joined: 18 Sep 2014
Posts: 231

Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]
Show Tags
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 306090 angles we get the height to be 5root3. From both statement it's sufficient. Hence C. Posted from my mobile device
_________________
Kindly press the Kudos to appreciate my post !!



Intern
Joined: 21 May 2016
Posts: 17
Location: United Kingdom
GPA: 3.5

Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]
Show Tags
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 306090 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 \(\frac{5}{2}\sqrt{3}\)



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4888
GPA: 3.82

Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]
Show Tags
01 Jun 2016, 06:00
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.
Attachments
variable approach's answer probability.jpg [ 219.74 KiB  Viewed 2768 times ]
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Find a 10% off coupon code for GMAT Club members. “Receive 5 Math Questions & Solutions Daily” Unlimited Access to over 120 free video lessons  try it yourself See our Youtube demo



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4680

Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]
Show Tags
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 306090 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 306090 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 306090 triangles and this length could be anythingequal 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
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Intern
Joined: 21 May 2016
Posts: 17
Location: United Kingdom
GPA: 3.5

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



Current Student
Joined: 18 Oct 2014
Posts: 902
Location: United States
GPA: 3.98

Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]
Show Tags
02 Jun 2016, 10:33
1
This post received KUDOS
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 degreesGeometry 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 QuestionsMike 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. Answer is A
_________________
I welcome critical analysis of my post!! That will help me reach 700+



Intern
Joined: 23 Mar 2015
Posts: 10

Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]
Show Tags
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
Joined: 28 Dec 2011
Posts: 4680

Re: In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this [#permalink]
Show Tags
08 Aug 2017, 09:42
gauravprashar17 wrote: hey mike,
i just wanted to know if from option B, do we get Angle M = 60? Dear gauravprashar17I"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
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Director
Joined: 12 Nov 2016
Posts: 790

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






