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

 It is currently 17 Oct 2019, 01:13

### 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

# Triangles ABC and DEF are similar. What percent of the area of triangl

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58427
Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

### Show Tags

06 Feb 2015, 07:33
1
5
00:00

Difficulty:

15% (low)

Question Stats:

73% (00:58) correct 27% (01:25) wrong based on 188 sessions

### HideShow timer Statistics

Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

(1) Sides AB and DE connect similar angles, and AB is 3 times DE.
(2) Side AB = 9

Kudos for a correct solution.

_________________
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 402
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

### Show Tags

09 Feb 2015, 02:54
1
Well I would go for A. And let me explain.

From the stem we know that the triangles are similar.
This means that their angles have the same measures and their sides are in proportion.

We are asked to find what percent of the area of triangle DEF triangle ABC is.
To find the area, we need to know the base and the height of a triangle.
What else we know about similar triangles is that the proportion of the area of the triangles is the square of the proportion of their sides. So, if their sides are of a ratio 3:1 their areas would be of a ratio of 9:1.

(1) Sides AB and DE connect similar angles, and AB is 3 times DE.
This statement tells us that 2 angles have the same measure and the leg connecting them is of ratio 3:1. Since we have the ratio, we know that the similar triangles will be of a ratio 3:1. So, their areas will be of a ratio of 9:1.

Now, what I do not understand for sure based on the stem, is what is meant by "triangle ABC". Its area? Its perimenter? I would say that triangle ABC is a triangle of area X and perimenter Y, but I don't know how else I would define a triagle.. I will proceed as if I were looking for the area of ABC and DEF.

Since their areas are of a ratio of 9:1, the ratio of ABC is 9 times that of DEF, and this would give us the percentage. So, [1] is sufficient.

(2) Side AB = 9. This doesn't tell us anything, as we don't know the relationship between the sides of the triangles. So, we are missing at least the proportion. So, we cannot find the areas. I would say that [2] is not sufficient.

So....?
Math Expert
Joined: 02 Sep 2009
Posts: 58427
Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

### Show Tags

09 Feb 2015, 05:57
Bunuel wrote:
Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

(1) Sides AB and DE connect similar angles, and AB is 3 times DE.
(2) Side AB = 9

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Solution: A

Start with the easier statement. Statement (2) tells us nothing about the properties of triangle DEF; INSUFFICIENT. Now consider statement (1). If sides AB and DE are similar and side AB is three times side DE, then all three sides and the height of triangle ABC are 3 times their counterparts in triangle DEF. Say the area of ABC is (bh)/2. Since the base and height of triangle DEF are 1/3 of those in ABC, the area of triangle DEF is (1/3b * 1/3h)/2, or (bh/9)/2. Triangle ABC has an area nine times that of triangle DEF, so it is 900% of DEF; SUFFICIENT, (A).
_________________
VP
Status: Learning
Joined: 20 Dec 2015
Posts: 1007
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE: Engineering (Manufacturing)
Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

### Show Tags

24 Jun 2017, 06:30
Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

1 Sides AB and DE connect similar angles, and AB is 3 times DE.
2 Side AB = 9
A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
C Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
D EACH statement ALONE is sufficient to answer the question asked
E Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
_________________
Please give kudos if you find my answers useful
Math Expert
Joined: 02 Sep 2009
Posts: 58427
Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

### Show Tags

24 Jun 2017, 06:33
arvind910619 wrote:
Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

1 Sides AB and DE connect similar angles, and AB is 3 times DE.
2 Side AB = 9
A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
C Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
D EACH statement ALONE is sufficient to answer the question asked
E Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Merging topics. Please search before posting a question. Thank you.
_________________
Retired Moderator
Joined: 19 Mar 2014
Posts: 922
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

### Show Tags

26 Jun 2017, 14:47
Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

(1) Sides AB and DE connect similar angles, and AB is 3 times DE

AB = 3 * DE

Area of T. ABC/Area of T. DEF = AB/DE

Area of T. ABC/Area of T. DEF = 1/3

Area of T. ABC = 33% of Area of T. DEF

Hence, =====> (1) is SUFFICIENT

(2) Side AB = 9

We only have information for 1 triangle and we do not know anything about the other triangle.

Hence, =====> (2), is IN SUFFICIENT

Hence, Answer is A
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Intern
Joined: 25 Mar 2017
Posts: 2
Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

### Show Tags

26 Jun 2017, 14:51

(1) makes the two triangles similar and we know that for similar triangles, Area(ABC)/Area(PQR)=AB^2/PQ^2
So sufficient.

(2) doesn't give any information about PQR, or any thing to relate abc to pqr in any way. So insufficient.

Sent from my Nexus 5 using GMAT Club Forum mobile app
Manager
Joined: 02 Aug 2013
Posts: 64
Location: India
WE: Programming (Consulting)
Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

### Show Tags

29 Jun 2017, 04:45
Referring to Bunuel resources

If two similar triangles have sides in the ratio$$\frac{x}{y}$$, then their areas are in the ratio$$\frac{x^2}{y^2}$$

Statement 1 : AB is 3 times DE and since the both the triangles are similar area will be in ratio$$\frac{3^2}{1^2}$$

=> $$\frac{area ABC}{area DEF} = \frac{9}{1}$$ = 900% Sufficient

Statement 2: No information related to side ration's of triangle, hence insufficient

Ans: A
Non-Human User
Joined: 09 Sep 2013
Posts: 13204
Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

### Show Tags

29 Sep 2018, 06:16
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: Triangles ABC and DEF are similar. What percent of the area of triangl   [#permalink] 29 Sep 2018, 06:16
Display posts from previous: Sort by

# Triangles ABC and DEF are similar. What percent of the area of triangl

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

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