GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Jun 2019, 00:05

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

D, E and F are points on the sides of triangle ABC above, such that qu

Author Message
TAGS:

Hide Tags

Board of Directors
Joined: 17 Jul 2014
Posts: 2544
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, 04:40
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 4407 times ]

Originally posted by mvictor on 03 Oct 2014, 15:05.
Last edited by Bunuel on 12 Sep 2016, 04:40, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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, 13:41
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.

_________________
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: 2544
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, 15:09
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

am I right?
Manager
Joined: 21 Sep 2012
Posts: 213
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, 01:02
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

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, 18:44
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

Save \$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews
Manager
Joined: 08 Oct 2013
Posts: 50
Re: D, E and F are points on the sides of triangle ABC above, such that qu  [#permalink]

Show Tags

28 May 2015, 18:51
So the OA is C or D ?. I Got C...

Regards,
Aj
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2888
Re: D, E and F are points on the sides of triangle ABC above, such that qu  [#permalink]

Show Tags

29 May 2015, 01:26
2
AjChakravarthy wrote:
So the OA is C or D ?. I Got C...

Regards,
Aj

Dear AjChakravarthy

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
_________________
Intern
Joined: 01 Apr 2016
Posts: 11
Re: D, E and F are points on the sides of triangle ABC above, such that qu  [#permalink]

Show Tags

13 Jul 2016, 07:19
Attachments

2016-07-13 16.15.26.jpg [ 190.48 KiB | Viewed 1898 times ]

2016-07-13 16.14.31.jpg [ 118.59 KiB | Viewed 1898 times ]

Non-Human User
Joined: 09 Sep 2013
Posts: 11396
Re: D, E and F are points on the sides of triangle ABC above, such that qu  [#permalink]

Show Tags

05 Jan 2018, 12:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: D, E and F are points on the sides of triangle ABC above, such that qu   [#permalink] 05 Jan 2018, 12:04
Display posts from previous: Sort by