It is currently 11 Dec 2017, 21:44

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 12 Aug 2015
Posts: 2209

Kudos [?]: 898 [0], given: 607

GRE 1: 323 Q169 V154
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]

### Show Tags

14 Aug 2017, 04:48
6
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

38% (01:21) correct 62% (01:27) wrong based on 161 sessions

### HideShow timer Statistics

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 ?

[Reveal] Spoiler:
Attachment:

Untitled.png [ 1.77 KiB | Viewed 2184 times ]
[Reveal] Spoiler: OA

_________________

Give me a hell yeah ...!!!!!

Last edited by Bunuel on 14 Aug 2017, 06:02, edited 2 times in total.
Edited the question.

Kudos [?]: 898 [0], given: 607

 Kaplan GMAT Prep Discount Codes Manhattan GMAT Discount Codes Optimus Prep Discount Codes
Math Expert
Joined: 02 Aug 2009
Posts: 5337

Kudos [?]: 6097 [1], given: 121

In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]

### Show Tags

14 Aug 2017, 05:52
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
stonecold wrote:

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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6097 [1], given: 121

Manager
Joined: 02 Nov 2015
Posts: 176

Kudos [?]: 27 [1], given: 121

GMAT 1: 640 Q49 V29
Re: In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]

### Show Tags

14 Aug 2017, 07:04
1
KUDOS
chetan2u wrote:
stonecold wrote:

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.

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

Kudos [?]: 27 [1], given: 121

Math Expert
Joined: 02 Aug 2009
Posts: 5337

Kudos [?]: 6097 [0], given: 121

Re: In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]

### Show Tags

14 Aug 2017, 07:20
kumarparitosh123 wrote:
chetan2u wrote:
stonecold wrote:

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.

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 ..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6097 [0], given: 121

Intern
Joined: 18 Aug 2017
Posts: 30

Kudos [?]: 10 [0], given: 17

GMAT 1: 670 Q49 V33
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]

### Show Tags

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.

Kudos [?]: 10 [0], given: 17

Senior Manager
Joined: 29 Jun 2017
Posts: 392

Kudos [?]: 78 [1], given: 71

GPA: 4
WE: Engineering (Transportation)
Re: In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]

### Show Tags

11 Sep 2017, 02:53
1
KUDOS
Not worth of 95% difficulty:-

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
_________________

Give Kudos for correct answer and/or if you like the solution.

Kudos [?]: 78 [1], given: 71

Re: In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt   [#permalink] 11 Sep 2017, 02:53
Display posts from previous: Sort by