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

 It is currently 14 Dec 2018, 09:11

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

December 14, 2018

December 14, 2018

10:00 PM PST

11:00 PM PST

Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.
• ### Free GMAT Strategy Webinar

December 15, 2018

December 15, 2018

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# In the figure above, what is the perimeter of rectangle ABPQ

Author Message
TAGS:

### Hide Tags

Manager
Joined: 27 Jul 2003
Posts: 120
Location: Singapore
In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

06 Oct 2003, 03:36
5
20
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:18) correct 34% (01:36) wrong based on 701 sessions

### HideShow timer Statistics

Attachment:

Untitled.png [ 1.18 KiB | Viewed 7834 times ]
In the figure above, what is the perimeter of rectangle ABPQ?

(1) The area of rectangular region ABCD is 3 times the area of rectangular region ABPQ.
(2) The perimeter of rectangle ABCD is 54.
Manager
Joined: 26 Aug 2003
Posts: 229
Location: United States
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

06 Oct 2003, 09:54
C?

My first would have been E, but then I saw AB was common in both rectangles, so I decided to answer C. But I decided to do a little calculation to verify. That took me like three-four minutes. Now seems like C is a good choice.
CEO
Joined: 15 Aug 2003
Posts: 3378
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

06 Oct 2003, 15:12
araspai wrote:
ABPQ is a smaller rectangle within a bigger rectangle ABCD, what is the peimeter of the rectangle ABPQ?
a. The area of rectangular region ABCD is 3 times the area of the rectangular region ABPQ.
b. The perimeter of bigger rectangle ABCD is 54.

A...clearly insufficient ..we only know A [ ABPQ] = 1/3 * A[ABCD]
3 * L * W1 = L * W
W = 3 W1
B... clearly insufficient
L + W = 27 ....

combine....
A[ ABPQ] = LW/3

L + W =27 W = 27 - L . W1 = 27 - L / 3

Perimeter of ABPQ = 2 L + 2 (27 - L /3)

I dont see how Wonder got C...what did i miss?

Thanks
praetorian
Manager
Joined: 18 Jul 2013
Posts: 73
Location: Italy
GMAT 1: 600 Q42 V31
GMAT 2: 700 Q48 V38
GPA: 3.75
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

06 Aug 2014, 14:38
1
1
Attachment:

Screen shot 2014-08-07 at 12.21.12 AM.png [ 9.48 KiB | Viewed 7812 times ]

Let the sides of ABCD be x and y.
Let the sides of ABPQ be x1 and y.

We want to find $$2x1+2y=?$$

1) tells us : $$2x+2y=54$$ not sufficient
2) tells us $$xy=3*x1*y$$, $$x=3*x1$$ not sufficient

1+2) tells us $$6x1+2y=54$$, so $$3x1+y=27$$

x1 could be equal to 1 and y to 24
or x1 could be equal to 2 and y 21 etc.

Intern
Joined: 16 Jun 2014
Posts: 16
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

20 Mar 2016, 05:25
I read in the Manhattan Geometry Guide (13 ed.)
"If two similar triangles have corresponding side lengths in ratio a: b, then their
areas will be in ratio a^2: b^2.
The lengths being compared do not have to be sides— they can represent heights or perimeters. In fact,
the figures do not have to be triangles."

So I guess, the parameters in this case should be in ratio as well.
Can some one explain this to me.
Math Expert
Joined: 02 Aug 2009
Posts: 7106
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

20 Mar 2016, 05:41
1
1
rickyfication wrote:
I read in the Manhattan Geometry Guide (13 ed.)
"If two similar triangles have corresponding side lengths in ratio a: b, then their
areas will be in ratio a^2: b^2.
The lengths being compared do not have to be sides— they can represent heights or perimeters. In fact,
the figures do not have to be triangles."

So I guess, the parameters in this case should be in ratio as well.
Can some one explain this to me.

Hi,
you are correct --
If two polygons are similar, their corresponding sides, altitudes, medians, diagonals, angle bisectors and perimeters are all in the same ratio.

but here "You are not given anything about similarity", so you cannot apply the same rule here..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 16 Jun 2014
Posts: 16
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

20 Mar 2016, 06:10
chetan2u wrote:
rickyfication wrote:
I read in the Manhattan Geometry Guide (13 ed.)
"If two similar triangles have corresponding side lengths in ratio a: b, then their
areas will be in ratio a^2: b^2.
The lengths being compared do not have to be sides— they can represent heights or perimeters. In fact,
the figures do not have to be triangles."

So I guess, the parameters in this case should be in ratio as well.
Can some one explain this to me.

Hi,
you are correct --
If two polygons are similar, their corresponding sides, altitudes, medians, diagonals, angle bisectors and perimeters are all in the same ratio.

but here "You are not given anything about similarity", so you cannot apply the same rule here..

Thanks, but I am finding it difficult to figure out why ABPQ and ABCD are not similar, since both the figures are rectangle, they have one common side therefore PQ has to be || with CD. is there anything wrong with my concept??
Math Expert
Joined: 02 Aug 2009
Posts: 7106
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

20 Mar 2016, 06:21
1
rickyfication wrote:
chetan2u wrote:
rickyfication wrote:
I read in the Manhattan Geometry Guide (13 ed.)
"If two similar triangles have corresponding side lengths in ratio a: b, then their
areas will be in ratio a^2: b^2.
The lengths being compared do not have to be sides— they can represent heights or perimeters. In fact,
the figures do not have to be triangles."

So I guess, the parameters in this case should be in ratio as well.
Can some one explain this to me.

Hi,
you are correct --
If two polygons are similar, their corresponding sides, altitudes, medians, diagonals, angle bisectors and perimeters are all in the same ratio.

but here "You are not given anything about similarity", so you cannot apply the same rule here..

Thanks, but I am finding it difficult to figure out why ABPQ and ABCD are not similar, since both the figures are rectangle, they have one common side therefore PQ has to be || with CD. is there anything wrong with my concept??

Hi,
since you are also saying one side is equal and the other two side are lesser than their corresponding sides ..
this basically means the sides are not in the same ratio..
whereas ONE set of sides have ratio as 1, the OTHER set is not 1, but something else..
for two triangles - ONE has L= 2 and B= 1, th eOTHER has L=6 and B=3.. these triangles are similar as ratios of sides 2/6 is same as 1/3
BUT if ONE has L= 2 and B= 1, th eOTHER has L=6 and B=1.. these triangles are NOT similar as ratios of sides 2/6 is NOT same as 1/1

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 16 Jun 2014
Posts: 16
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

20 Mar 2016, 06:42
Got you point Chetan. Thanks for the clarification.
Senior Manager
Joined: 19 Oct 2012
Posts: 323
Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35
GMAT 2: 710 Q50 V38
GPA: 3.81
WE: Information Technology (Computer Software)
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

19 Jun 2017, 02:22
Lets dive into statement analysis straight away:

Stmt 1: Since AB is common width between 2 figures, clearly the length of larger rectangle ABCD should be 3 times the length of smaller rectangle ABPQ. But using this alone we dont have concrete values to work with. Hence (1) is insufficient.
Stmt 2: Perimeter of ABCD = 54.
= > 2(l+b) =54
=> l+b = 27. This does not give any clue about the smaller rectangle. Hence (2) is insufficient.

Using (1) & (2)
=> 3l' + b = 27. (where l' is length of ABPQ)
We can't solve this further to get 2(l'+b). Hence E.
_________________

Citius, Altius, Fortius

CEO
Joined: 11 Sep 2015
Posts: 3237
In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

Updated on: 16 Apr 2018, 11:15
1
Top Contributor
1
araspai wrote:
Attachment:
Untitled.png
In the figure above, what is the perimeter of rectangle ABPQ?

(1) The area of rectangular region ABCD is 3 times the area of rectangular region ABPQ.
(2) The perimeter of rectangle ABCD is 54.

Target question: What is the perimeter of rectangle ABPQ?

Statement 1: The area of rectangular region ABCD is 3 times the area of rectangular region ABPQ.
Since we aren't given any information regarding ACTUAL lengths, we cannot determine the perimeter of rectangle ABPQ
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The perimeter of rectangle ABCD is 54
There are many possible cases in which ABCD's perimeter is 54, yet the perimeter of rectangle ABPQ is not fixed (see diagrams below)
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several scenarios that satisfy BOTH statements. Here are two:

Case a: The measurements are as follows:

Notice that the area of ABCD (72 square units) is 3 times the area of rectangular region ABPQ (24 square units)
Also notice that ABCD has perimeter 54
In this case, the perimeter of rectangle ABPQ = 1 + 24 + 1 + 24 = 50

Case b: The measurements are as follows:

Notice that the area of ABCD (126 square units) is 3 times the area of rectangular region ABPQ (42 square units)
Also notice that ABCD has perimeter 54
In this case, the perimeter of rectangle ABPQ = 2 + 21 + 2 + 21 = 46

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com

Originally posted by GMATPrepNow on 26 Feb 2018, 15:15.
Last edited by GMATPrepNow on 16 Apr 2018, 11:15, edited 1 time in total.
Intern
Joined: 20 Dec 2017
Posts: 36
Location: Singapore
Re: In the figure above, what is the perimeter of rectangle ABPQ  [#permalink]

### Show Tags

26 Feb 2018, 17:46
I notice that this is quite a common trick question on areas/perimeters that and can be solved very quickly.

Basically for rectangles, the perimeter and area may not be proportionate to each other (do correct me if I am wrong)

For example a 100 sqft rectangle could be:
1) 100 + 100 + 1 +1 = 202 ft perimeter
2) 20 + 20 + 5 + 5 = 50 ft perimeter

Back to the question,
(1) The area ratio is given, but nothing about the perimeter. Also, the question is asking for a specific value which the statement does not provide any clue - Insufficient
(2) Although the perimeter of ABCD is given, it does not show how ABCD and ABPQ are related to each other - Insufficient
(1) & (2) Since area and perimeter are not proportionate, not possible to derive answer without also knowing any side lengths - Insufficient

If the question was on a square, then it would have been (C) since we could derive the length of its sides from statement (2)
Re: In the figure above, what is the perimeter of rectangle ABPQ &nbs [#permalink] 26 Feb 2018, 17:46
Display posts from previous: Sort by