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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # D, E and F are points on the sides of triangle ABC above, such that qu  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Board of Directors Joined: 17 Jul 2014 Posts: 2618 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) D, E and F are points on the sides of triangle ABC above, such that qu [#permalink] ### Show Tags Updated on: 12 Sep 2016, 03:40 10 00:00 Difficulty: 95% (hard) Question Stats: 42% (02:49) correct 58% (02:56) wrong based on 167 sessions ### HideShow timer Statistics D, E and F are points on the sides of triangle ABC above, such that quadrilateral AEFD is a rectangle. If DC=1, and CF=4, what is the value of AD? (1) 3EB = AB (2) FB = 2 Attachment: DS.jpg [ 13.2 KiB | Viewed 4185 times ] Originally posted by mvictor on 03 Oct 2014, 14:05. Last edited by Bunuel on 12 Sep 2016, 03:40, edited 2 times in total. Renamed the topic, edited the question and added the OA. ##### Most Helpful Community Reply Tutor Joined: 20 Apr 2012 Posts: 99 Location: Ukraine GMAT 1: 690 Q51 V31 GMAT 2: 730 Q51 V38 WE: Education (Education) Re: D, E and F are points on the sides of triangle ABC above, such that qu [#permalink] ### Show Tags 04 Oct 2014, 12:41 4 3 mvictor wrote: D, E and F are points on the sides of triangle ABC above, such that quadrilateral AEFD is a rectangle. If DC=1, and CF=4, what is the value of AD? (1) 3EB = AB (2) FB = 2 It is very easy to solve if you mention two similar triangles. Triangle CDF is similar to FEB since angle D=angle E=90 degrees angle DFC=angle EBF since DF||AB. Because of similarity the corresponding sides of triangles must be proportional. Our task is to find such ratio. (1) Sufficient. Here we know that proportional coefficient is 2, since DF=AE=AB-EB=3EB-EB=2EB. Each side in triangle CDF must be twice the corresponding side of triangle FEB. Therefore, AD=FE=1/2 (2) Sufficietnt CF=4, FB=2, hence proportional coefficient is 2. Each side in triangle CDF must be twice the corresponding side of triangle FEB. Therefore, AD=FE=1/2. The correct answer is D. _________________ I'm happy, if I make math for you slightly clearer And yes, I like kudos:) ##### General Discussion Board of Directors Joined: 17 Jul 2014 Posts: 2618 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: D, E and F are points on the sides of triangle ABC above, such that qu [#permalink] ### Show Tags 03 Oct 2014, 14:09 since <FDA=90 we can conclude that <CDF=90 knowing CD & CF, we can find DF in order to find AD, we need to know AE & EB (1) we can find AE & AB since DF = AE. but we cannot find FB (2) does not tell us anything about AB 1+2 can solve for DA answer C am I right? Manager Joined: 21 Sep 2012 Posts: 214 Location: United States Concentration: Finance, Economics Schools: CBS '17 GPA: 4 WE: General Management (Consumer Products) Re: D, E and F are points on the sides of triangle ABC above, such that qu [#permalink] ### Show Tags 04 Oct 2014, 00:02 Given :- DC=1 and CF=4 AEFD is a rectangle. DF=(4^2-1^2)^1/2 DF=(16-1)^1/2 DF=15^1/2 Therefore AE=15^1/2... AEFD is a rectangle Statement 1 : 3EB = AB Therefore, AE=AB*2/3 AB=3AE/2 AB=(3*15^1/2)/2 Therefore EB=(15^1/2)/2 Let AD be x. Therefore FE=x using Pythagoras, AC^2+AB^2=BC^2 (1+x)^2+[(3*15^1/2)/2]^2=(4+FB)^2 ..............1 Length of FB can be derived in terms of x using Pythagoras. FB^2=[(15^1/2)/2]^2 +x^2 So equation 1 can be solved to get value of x. statement is sufficient. statement 2 : FB = 2 BC= CF+FB BC=4+2 BC=6 Let AD be x, therefore FE=x (AEFD is a rectangle) using Pythagoras, AC^2+AB^2=BC^2 (1+x)^2+[(15^1/2)/2+EB]^2= 6^2 .............. 1 EB can be derived in terms of x using Pythagoras EB^2= FB^2-FE^2 EB^2= 2^2-x^2 Value of EB^2 can be put in equation 1 and value of x can be obtained. Statement is sufficient. Ans - D Veritas Prep GMAT Instructor Joined: 23 Oct 2013 Posts: 144 Re: D, E and F are points on the sides of triangle ABC above, such that qu [#permalink] ### Show Tags 17 May 2015, 17:44 With data sufficiency questions, particularly geometry ones, you always want to make as many inferences as you can upfront. We can see that triangle CDF is a right triangle, because using the supplementary angle rule we know that angle CDF is 90 degrees. When they give us that leg DC = 1 and hypotenuse CF = 4 then, we can use the formula a^2 + b^2 = c^2 to see that leg DF = sqrt15. Because AEFD is a rectangle, AE must also be sqrt15. Statement 1 tells us that 3EB = AB, and therefore we know that EB = AB/2. Using the supplementary angle rule again we see that angle FEB is a 90 degree angle, and therefore triangle FEB is also a right triangle. Statement 2 gives us the hypotenuse of this triangle, and because we already have the information for leg EB (its sqrt15/2), we know that we can find the other leg EF. Again using the fact that AEFD is a rectangle, we know that EF will equal AD, and therefore with both statements together we can find AD, yielding answer choice C. We of course would not do the actual math, because all we want to prove is sufficiency. I hope this helps! _________________ Brandon Veritas Prep | GMAT Instructor If you found this post helpful, please give me kudos!!! 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Joined: 08 Oct 2013
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Re: D, E and F are points on the sides of triangle ABC above, such that qu  [#permalink]

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28 May 2015, 17:51
So the OA is C or D ?. I Got C...

Regards,
Aj
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Joined: 04 Jan 2015
Posts: 2313
Re: D, E and F are points on the sides of triangle ABC above, such that qu  [#permalink]

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29 May 2015, 00:26
2
AjChakravarthy wrote:
So the OA is C or D ?. I Got C...

Regards,
Aj

Dear AjChakravarthy

The correct answer is D.

Here's an easy solution for this question.

Let the length of AD be x.

First of all, let's represent the given information on the diagram.

By applying Pythagoras Theorem on right Triangle CDF, we can see that DF = $$\sqrt{15}$$.

Since opposite sides of a rectangle are equal, AE = $$\sqrt{15}$$.

Analyzing Statement 1
3EB = AB

This means, EB = $$\frac{AB}{3}$$

Now, AB = AE + EB
So, AB = $$\sqrt{15} +\frac{AB}{3}$$.

Upon solving this equation, we get $$AB = \frac{3√15}{2}$$

Now, in right triangle CAB, $$tanC = \frac{AB}{AC} = \frac{3√15}{2(1+x)}$$ . . . (1)

In right triangle CDF, $$tanC = \frac{DF}{CD} =\frac{√15}{1}$$ . . . (2)

Upon equating (1) and (2) and solving for x, we get x = 1/2

So, St. 1 alone is sufficient to determine a unique value of x.

Analyzing Statement 2
FB = 2

This means, BC = 4 + 2 = 6

in right triangle CAB, $$cosC = \frac{AC}{BC} = \frac{(1+x)}{6}$$ . . . (1)

In right triangle CDF, $$cosC = \frac{CD}{CF} =\frac{1}{4}$$ . . . (2)

Upon equating (1) and (2) and solving for x, we get x = 1/2

So, St. 2 alone is sufficient to determine a unique value of x.

Hope this helped!

Best Regards

Japinder
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Re: D, E and F are points on the sides of triangle ABC above, such that qu  [#permalink]

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13 Jul 2016, 06:19
My answer with THALES
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Re: D, E and F are points on the sides of triangle ABC above, such that qu  [#permalink]

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05 Jan 2018, 11:04
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