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

It is currently 05 Dec 2019, 20:26

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2548
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt  [#permalink]

Show Tags

New post Updated on: 14 Aug 2017, 06:02
12
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

34% (02:40) correct 66% (02:05) wrong based on 161 sessions

HideShow timer Statistics

Image

In triangle ABC, the measure of angle ABC is 90 degrees, and the lengths of two sides of triangle ABC are shown. Triangle DEF is similar to ABC and has integer side lengths. Which of the following could be the area of triangle DEF ?

A)15
B)48
C)90
D)150
E)204


Source => Kaplan.
Any laconic way to solve this up ?

Attachment:
Untitled.png
Untitled.png [ 1.77 KiB | Viewed 13903 times ]

_________________

Originally posted by stonecold on 14 Aug 2017, 04:48.
Last edited by Bunuel on 14 Aug 2017, 06:02, edited 2 times in total.
Edited the question.
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8284
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt  [#permalink]

Show Tags

New post 14 Aug 2017, 05:52
1
1
stonecold wrote:
Image

In triangle ABC, the measure of angle ABC is 90 degrees, and the lengths of two sides of triangle ABC are shown. Triangle DEF is similar to ABC and has integer side lengths. Which of the following could be the area of triangle DEF ?

A)15
B)48
C)90
D)150
E)204


Source => Kaplan.
Any laconic way to solve this up ?



Hi..
Sides of ∆DEF will be in similar ratio as sides of ∆ABC..
So EF=8x and DE=6x...
Since the sides 6 and 8 have 2 as Common factor, x will be an integer or a fraction with 2 in denominator.
Area of ∆ABC = 1/2 *6*8=24..
Area of∆DEF = 1/2 *6x*8x=24x^2..
Now this x should come out as a fraction with 2 in denominator or INTEGER..

Check with choices..
A)15
24x^2=15.... x=√(5/8).no

B)48
24x^2=48.....X=√2..no

C)90.
24x^2=90...X=√(15/4)=√15/2...no

D)150
24x^2=150...x^2=150/24=25/4..
X=√(25/4)=5/2...yes

E)204..
24x^2=204...X=√34/2 No

D
_________________
Manager
Manager
avatar
B
Joined: 02 Nov 2015
Posts: 162
GMAT 1: 640 Q49 V29
Re: In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt  [#permalink]

Show Tags

New post 14 Aug 2017, 07:04
1
chetan2u wrote:
stonecold wrote:
Image

In triangle ABC, the measure of angle ABC is 90 degrees, and the lengths of two sides of triangle ABC are shown. Triangle DEF is similar to ABC and has integer side lengths. Which of the following could be the area of triangle DEF ?

A)15
B)48
C)90
D)150
E)204


Source => Kaplan.
Any laconic way to solve this up ?



Hi..
Sides of ∆DEF will be in similar ratio as sides of ∆ABC..
So EF=8x and DE=6x...
Area of ∆ABC = 1/2 *6*8=24..
Area of∆DEF = 1/2 *6x*8x=24x^2..
Now this x should come out as a fraction or INTEGER..
Check with choices..
A)15
24x^2=15...no
B)48..no
C)90..no
D)150
24x^2=150...x^2=150/24=25/4..
X=√(25/4)=5/2...yes
E)204..No

D

Hi Chetan,
The way you explain are real awesome and u really deserve a Kudo from me . And I Have given also...[GRINNING FACE WITH SMILING EYES]

But 1 thing I don't understand why They value of x^2 should be a fraction ??
Tough for me to interpret.
Pls help.

Thanks in advance.

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8284
Re: In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt  [#permalink]

Show Tags

New post 14 Aug 2017, 07:20
kumarparitosh123 wrote:
chetan2u wrote:
stonecold wrote:
Image

In triangle ABC, the measure of angle ABC is 90 degrees, and the lengths of two sides of triangle ABC are shown. Triangle DEF is similar to ABC and has integer side lengths. Which of the following could be the area of triangle DEF ?

A)15
B)48
C)90
D)150
E)204


Source => Kaplan.
Any laconic way to solve this up ?



Hi..
Sides of ∆DEF will be in similar ratio as sides of ∆ABC..
So EF=8x and DE=6x...
Area of ∆ABC = 1/2 *6*8=24..
Area of∆DEF = 1/2 *6x*8x=24x^2..
Now this x should come out as a fraction or INTEGER..
Check with choices..
A)15
24x^2=15...no
B)48..no
C)90..no
D)150
24x^2=150...x^2=150/24=25/4..
X=√(25/4)=5/2...yes
E)204..No

D

Hi Chetan,
The way you explain are real awesome and u really deserve a Kudo from me . And I Have given also...[GRINNING FACE WITH SMILING EYES]

But 1 thing I don't understand why They value of x^2 should be a fraction ??
Tough for me to interpret.
Pls help.

Thanks in advance.

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app



Hi..
The sides of TWO similar triangle will have same ratio with corresponding sides.

Say here sides are 6 and 8...
If corresponding side of 6 of similar triangle is 6*1/2=3, so side corresponding to 8 will be 8*1/2=4..

Had it not been given that sides are integer than ofcourse x could be anything...

Yes if sides were 3 and 4 or co-prime, fraction would not have been possible.
Here 6 and 8 have 2 as Common factor so a fraction with 2 in denominator can also be the ratio ..
_________________
Intern
Intern
avatar
B
Joined: 18 Aug 2017
Posts: 29
GMAT 1: 670 Q49 V33
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt  [#permalink]

Show Tags

New post 27 Aug 2017, 20:25
Triangle DEF is similar to ABC, so \(\frac{DE}{6}\) = \(\frac{EF}{8}\) => DE = \(\frac{4EF}{3}\)

Let area of triangle DEF is S, S = \(\frac{(DE*EF)}{2} =\frac{4EF}{3} * \frac{EF}{2} = \frac{2EF^2}{3}\)

So \(\frac{(S *3)}{2}\) = \(EF^2\) we can conclude:
1- S is an even number, eliminate answer A
2-\(\frac{(S * 3)}{2}\) must be a perfect square of an integer.

B- S = 48, \(\frac{(S * 3)}{2} = 144/2\) = 72. No.
C- S = 90, \(\frac{(S * 3)}{2} = 270/2\) = 135. No.
D- S = 150,\(\frac{(S * 3)}{2} = 450/2 = 225\)= \(15^2\). Yes.
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 417
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt  [#permalink]

Show Tags

New post 11 Sep 2017, 02:53
2
Not worth of 95% difficulty:-

Answer is D 150

AB/BC = 6/8 = 3/4 = DE/EF
Area DEF = 1/2 DE xEF
=> 6
6 is the area when 3/4 is the least ratio of integers => if the ratio is increased then it will grow in squares of numbers from 1 ,2,3 and so on
because
3/4 = 3/4
6/8 = 3x2/4x2
9/12 = 3x3/4x3

so we can see both sides are being multiplied by 1,2,3 two times

so possible values of area can be 6 x( 1,4,9,16,25,36)
6x25 is the value => 150 is the answer D
Director
Director
User avatar
P
Joined: 16 Jan 2019
Posts: 507
Location: India
Concentration: General Management
WE: Sales (Other)
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt  [#permalink]

Show Tags

New post 09 Apr 2019, 01:31
By property, if two similar triangles have side lengths in the ratio a:b, then their areas will be in the ratio a^2 : b^2

Let DE=x

Then (Area of ABC)/(Area of DEF) = 6^2/x^2

=> x^2 = 6^2*(Area of DEF)/(Area of ABC)

=> x^2 = 3/2*(Area of DEF) ------------------ [Area of ABC=24]

We know that x^2 must be a perfect square since x is an integer.

Plugging in the options we get Area of DEF = 150

(D)
GMAT Club Bot
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt   [#permalink] 09 Apr 2019, 01:31
Display posts from previous: Sort by

In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne