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

 It is currently 23 Sep 2018, 13:09

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

ABCD is a quadrilateral, as shown in the diagram below. What is the

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49320
ABCD is a quadrilateral, as shown in the diagram below. What is the  [#permalink]

Show Tags

23 Jul 2017, 23:35
1
5
00:00

Difficulty:

85% (hard)

Question Stats:

25% (01:03) correct 75% (01:33) wrong based on 68 sessions

HideShow timer Statistics

ABCD is a quadrilateral, as shown in the diagram below. What is the minimum possible sum of areas of triangles AOD and BOC?

(1) Area of triangles AOB and COD are 16 and 36, respectively.
(2) Area of triangle AOD is equal to the area of triangle BOC.

Attachment:

2017-07-24_1034.png [ 9.32 KiB | Viewed 931 times ]

_________________
Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1386
Location: Viet Nam
ABCD is a quadrilateral, as shown in the diagram below. What is the  [#permalink]

Show Tags

24 Jul 2017, 02:35
1
Bunuel wrote:
ABCD is a quadrilateral, as shown in the diagram below. What is the minimum possible sum of areas of triangles AOD and BOC?

(1) Area of triangles AOB and COD are 16 and 36, respectively.
(2) Area of triangle AOD is equal to the area of triangle BOC.

Attachment:
2017-07-24_1034.png

(1) We have $$S_{AOB} = 16$$ and $$S_{COD} = 36$$

Also $$\frac{S_{AOB}}{S_{BOC}}=\frac{AO}{OC}$$
$$\frac{S_{AOD}}{S_{DOC}}=\frac{AO}{OC}$$

Hence $$\frac{S_{AOB}}{S_{BOC}} = \frac{S_{AOD}}{S_{DOC}} \\ \implies S_{AOD} * S_{BOC} = S_{AOB} *S_{DOC} = 16 * 36$$

ALso $$16 * 36 = S_{AOD} * S_{BOC} \leq \frac{1}{4}( S_{AOD} + S_{BOC})^2 \implies S_{AOD} + S_{BOC} \geq 48$$

Sufficient.

(2) We have no more information about the area of AOD and BOC, hence we can't know the minimum possible sum of areas of triangles AOD and BOC. Insufficient.

_________________
Manager
Joined: 18 Nov 2009
Posts: 73
Location: Switzerland
Concentration: Entrepreneurship, Technology
GMAT 1: 740 Q47 V45
Re: ABCD is a quadrilateral, as shown in the diagram below. What is the  [#permalink]

Show Tags

07 Nov 2017, 03:59
1
Hi Broall

Thanks for your answer. Your mathematical notation was somehow not well interpreted by the system. Could you please edit if you a have a minute?

Many Thanks
Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1386
Location: Viet Nam
Re: ABCD is a quadrilateral, as shown in the diagram below. What is the  [#permalink]

Show Tags

07 Nov 2017, 05:24
1
Octobre wrote:
Hi Broall

Thanks for your answer. Your mathematical notation was somehow not well interpreted by the system. Could you please edit if you a have a minute?

Many Thanks

Done. Thank you

Posted from my mobile device

Posted from my mobile device
_________________
Intern
Joined: 28 Dec 2010
Posts: 49
Re: ABCD is a quadrilateral, as shown in the diagram below. What is the  [#permalink]

Show Tags

07 Nov 2017, 05:42
broall wrote:
Bunuel wrote:
ABCD is a quadrilateral, as shown in the diagram below. What is the minimum possible sum of areas of triangles AOD and BOC?

(1) Area of triangles AOB and COD are 16 and 36, respectively.
(2) Area of triangle AOD is equal to the area of triangle BOC.

Attachment:
2017-07-24_1034.png

(1) We have $$S_{AOB} = 16$$ and $$S_{COD} = 36$$

Also $$\frac{S_{AOB}}{S_{BOC}}=\frac{AO}{OC}$$
$$\frac{S_{AOD}}{S_{DOC}}=\frac{AO}{OC}$$

Hence $$\frac{S_{AOB}}{S_{BOC}} = \frac{S_{AOD}}{S_{DOC}} \\ \implies S_{AOD} * S_{BOC} = S_{AOB} *S_{DOC} = 16 * 36$$

ALso $$16 * 36 = S_{AOD} * S_{BOC} \leq \frac{1}{4}( S_{AOD} + S_{BOC})^2 \implies S_{AOD} + S_{BOC} \geq 48$$

Sufficient.

(2) We have no more information about the area of AOD and BOC, hence we can't know the minimum possible sum of areas of triangles AOD and BOC. Insufficient.

Hey,

What does S mean? (Area)
and how is
$$\frac{S_{AOB}}{S_{BOC}}=\frac{AO}{OC}$$
_________________

_________________________________________

Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1386
Location: Viet Nam
Re: ABCD is a quadrilateral, as shown in the diagram below. What is the  [#permalink]

Show Tags

07 Nov 2017, 07:29
1
Abhishiek wrote:
Hey,

What does S mean? (Area)
and how is
$$\frac{S_{AOB}}{S_{BOC}}=\frac{AO}{OC}$$

Yep, S mean the area.

Attachment:

2017-07-24_1034.png [ 9.59 KiB | Viewed 516 times ]

BH is perpendicular to AC.

We have
$$S_{AOB} = \frac{1}{2} * AO * BH$$
$$S_{BOC} = \frac{1}{2} * OC * BH$$

Hence
$$\frac{S_{AOB}}{S_{BOC}}=\frac{\frac{1}{2} * AO * BH}{\frac{1}{2} * OC * BH}=\frac{AO}{OC}$$

Hope this helps.
_________________
Re: ABCD is a quadrilateral, as shown in the diagram below. What is the &nbs [#permalink] 07 Nov 2017, 07:29
Display posts from previous: Sort by

ABCD is a quadrilateral, as shown in the diagram below. What is the

Events & Promotions

 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®.