GMAT Changed on April 16th - Read about the latest changes here

 It is currently 22 Apr 2018, 13:07

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 the figure above, P is the midpoint of side AB. If the area of the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Math Expert
Joined: 02 Sep 2009
Posts: 44599
In the figure above, P is the midpoint of side AB. If the area of the [#permalink]

Show Tags

11 Oct 2017, 00:52
00:00

Difficulty:

(N/A)

Question Stats:

56% (00:27) correct 44% (00:40) wrong based on 48 sessions

HideShow timer Statistics

In the figure above, P is the midpoint of side AB. If the area of the rectangle ABCD is 24, then the area of the square PCQD is

(A) 12
(B) 18
(C) 24
(D) 25
(E) 30

[Reveal] Spoiler:
Attachment:

2017-10-11_1128.png [ 5.7 KiB | Viewed 1117 times ]

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
[Reveal] Spoiler: OA

_________________
Intern
Joined: 29 Aug 2017
Posts: 35
Re: In the figure above, P is the midpoint of side AB. If the area of the [#permalink]

Show Tags

11 Oct 2017, 03:32
Bunuel wrote:

In the figure above, P is the midpoint of side AB. If the area of the rectangle ABCD is 24, then the area of the square PCQD is

(A) 12
(B) 18
(C) 24
(D) 25
(E) 30

[Reveal] Spoiler:
Attachment:
2017-10-11_1128.png

Given area of rectangle = 24 = DC*AD
Given DC = 6, so AD = 4
DC = AB = 6, P is the midpoint of AB, so AP = 3
AP = 3, AD = 4, so DP = 5
Area of square = Square of side = 5*5 = 25

Director
Joined: 21 May 2013
Posts: 621
Re: In the figure above, P is the midpoint of side AB. If the area of the [#permalink]

Show Tags

11 Oct 2017, 04:14
Bunuel wrote:

In the figure above, P is the midpoint of side AB. If the area of the rectangle ABCD is 24, then the area of the square PCQD is

(A) 12
(B) 18
(C) 24
(D) 25
(E) 30

[Reveal] Spoiler:
Attachment:
2017-10-11_1128.png

Good Qs-Bunuel-Can you tell me what is wrong if we take the diagonal of square as 6 and calculate the side as 3 \sqrt{2}.Area will be 18.
SC Moderator
Joined: 22 May 2016
Posts: 1548
In the figure above, P is the midpoint of side AB. If the area of the [#permalink]

Show Tags

11 Oct 2017, 09:55
Bunuel wrote:

In the figure above, P is the midpoint of side AB. If the area of the rectangle ABCD is 24, then the area of the square PCQD is

(A) 12
(B) 18
(C) 24
(D) 25
(E) 30

[Reveal] Spoiler:
Attachment:
2017-10-11_1128.png

Area of rectangle = LW
L = 6
24 = 6 * W
W = 4

Find the side of the square to find its area. The square's side is the hypotenuse of right triangle BCP

One leg, BC, is rectangle's W = 4

P, midpoint, divides rectangle's length into the other leg of the triangle

Other leg, BP, = 3

It's a 3-4-5 right triangle whose hypotenuse with length = 5 is the side of the square

Square's area = $$5^2 = 25$$

_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Manager
Joined: 22 May 2017
Posts: 93
GMAT 1: 580 Q41 V29
GMAT 2: 580 Q43 V27
Re: In the figure above, P is the midpoint of side AB. If the area of the [#permalink]

Show Tags

12 Oct 2017, 07:08
1
KUDOS

Sent from my Redmi Note 3 using GMAT Club Forum mobile app
Intern
Joined: 27 Aug 2017
Posts: 5
Concentration: International Business, Human Resources
Re: In the figure above, P is the midpoint of side AB. If the area of the [#permalink]

Show Tags

12 Oct 2017, 10:33
4
KUDOS
Easy piece. D is the correct answer.
Intern
Joined: 04 Sep 2017
Posts: 23
Location: United States
Concentration: Finance
GMAT 1: 610 Q36 V36
GMAT 2: 680 Q40 V36
GPA: 3.3
WE: Consulting (Mutual Funds and Brokerage)
Re: In the figure above, P is the midpoint of side AB. If the area of the [#permalink]

Show Tags

12 Oct 2017, 13:34
I'm wondering the same thing as KS15. I saw this as an easy question inside a bunch of fluff.

Since 6 is the diagonal of the square, you should be able to just solve for one of the sides of the square which comes out to S=6/sqrt{2} which when you square it comes out to 36/2 = 18. (choice B)

Then I looked at how others did it and wonder why my way doesn't work. If we find out that AD = 4 and that we have a 3,4,5 triangle. That means that angle APD is around 53.13. Since BC is also 4, that means that BPC also around 53.13. If that is the case, angle DPC would have to be around 74 degrees which would mean shape PCQD is a rhombus and not a square.

Can someone else take a look and tell me if I'm running my calculations wrong or missing something here?
Intern
Joined: 04 Sep 2017
Posts: 23
Location: United States
Concentration: Finance
GMAT 1: 610 Q36 V36
GMAT 2: 680 Q40 V36
GPA: 3.3
WE: Consulting (Mutual Funds and Brokerage)
Re: In the figure above, P is the midpoint of side AB. If the area of the [#permalink]

Show Tags

13 Oct 2017, 09:23
Hey Everyone, this one is driving me nuts. I am trying to see if my logic is incorrect somewhere. Can we have a couple other eyes look this over and give their thoughts on my comments above?

In looking at it more, it seems to me that if P is the midpoint of AB which is shared as a corner of the square PCQD, and both the rectangle ABCD and square PCQD share points D and C which also has to be the diagonal of PCQD. Given just this information and nothing on the area of the rectangle, we can still assume that angles APD and BPC are both 45 degrees since angle DPC has to be 90 (because PCQD is a square). With just this information, we can assume AD and BC are 3 because triangles APD and BPC are 45,45,90. That would mean the area of the rectangle is 18 (3*6) which is the same as the square.

If we do not assume that PCQD is a square (even though we are told so) and we know that the area of the rectangle is 24, then we can look at the third solution Aditya provided and find that the two triangles add up to 24 also, so the area of PCQD is 24 which is actually just a rhombus and not a square.

Does this logic make sense and can somebody else through in their two cents to make sure I'm not missing some bigger point here?

Thanks!
Intern
Joined: 05 Oct 2017
Posts: 13
GMAT 1: 650 Q48 V32
WE: Consulting (Consulting)
Re: In the figure above, P is the midpoint of side AB. If the area of the [#permalink]

Show Tags

17 Oct 2017, 14:35

Sent from my Redmi Note 3 using GMAT Club Forum mobile app

I did it in the same way as adityagmatclub one the right side of his picture.

Imo PBC and APD must both be (3 * 4)/2 -> 6

Therefore PCD must be 24 - 6 - 6 = 12

And as its a square I doubled it and went for C (24).

Whats wrong about it?!
Intern
Joined: 04 Sep 2017
Posts: 23
Location: United States
Concentration: Finance
GMAT 1: 610 Q36 V36
GMAT 2: 680 Q40 V36
GPA: 3.3
WE: Consulting (Mutual Funds and Brokerage)
Re: In the figure above, P is the midpoint of side AB. If the area of the [#permalink]

Show Tags

17 Oct 2017, 15:17

I believe that there is a problem with the question. I made a couple comments about it already and it's driving me nuts. The only way that PCQD can be a square considering that it shares points C and D with rectangle ABCD and also has a corner P touching the midpoint of AB is for triangles APD and BPC to be 90,45,45 triangles. This would mean that sides AD and BC would have to be 3 (not 4). But since the question tells us the area of ABCD is 24 and we are given that one side is 6, AD and BC have to be 4. If this is the case, PCQD is a rhombus (not a square) and the only way to find the area of PCQD with the information we have is to subtract the area of triangles APD and BPC from the area of the rectangle. This is the right hand method in adityagmatclub's image and the way jajanb solved the problem.

I personally don't believe there is a correct solution with the given information, but I can certainly be wrong and completely missing something. I would love to hear other people's thoughts!

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: In the figure above, P is the midpoint of side AB. If the area of the   [#permalink] 17 Oct 2017, 15:17
Display posts from previous: Sort by

In the figure above, P is the midpoint of side AB. If the area of the

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.