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

 It is currently 20 Feb 2019, 09:42

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

# In the figure above, is the diameter of a circle. Is the area of ΔABD

Author Message
TAGS:

### Hide Tags

Senior RC Moderator
Status: Preparing GMAT
Joined: 02 Nov 2016
Posts: 2240
Location: Pakistan
GPA: 3.39
In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

### Show Tags

10 Feb 2019, 03:07
1
00:00

Difficulty:

65% (hard)

Question Stats:

35% (01:35) correct 65% (01:41) wrong based on 34 sessions

### HideShow timer Statistics

Attachment:

1111.jpg [ 9.18 KiB | Viewed 395 times ]

In the figure above AC, is the diameter of a circle. Is the area of ΔABD equal to the area of ΔBCD ?

(2) BD= 5

_________________

New Project RC Butler 2019 - Practice 2 RC Passages Everyday
Final days of the GMAT Exam? => All GMAT Flashcards.
This Post Helps = Press +1 Kudos
Best of Luck on the GMAT!!

Senior RC Moderator
Status: Preparing GMAT
Joined: 02 Nov 2016
Posts: 2240
Location: Pakistan
GPA: 3.39
In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

### Show Tags

16 Feb 2019, 09:55
2
Hello KanishkM rinkumaa4

Official Explanation

This is a Yes/No Data Sufficiency question. However, there is information in the question stem that should be considered, so use the Pieces of the Puzzle approach to assess the question. The question asks whether the area of triangle ABD is equal to the area of triangle BCD. Since the two triangles share a common height, BD, their areas will be equal only if their bases, AD and DC, are the same length. Therefore, in order to answer the question, the statements must provide information sufficient to determine whether AD = DC. The task of a Yes/No Data Sufficiency question is to determine whether the information in the statements produces a consistent “Yes” or “No” answer to the question. Evaluate the statements one at a time.

Evaluate Statement (1). The length of AD is 2. However, Statement (1) does not provide the length of DC, so it is insufficient to determine whether AD = DC. Write down BCE.

Now, evaluate Statement (2). The length of BD is 5. However, Statement (2) does not provide the lengths of AD and DC, so it is insufficient to determine whether AD = DC. Eliminate (B).

Now, evaluate both statements together. Recognize that triangles ABD and BCD together form a larger triangle, triangle ABC. The Inscribed Angle Theorem dictates that angle ABC must be 90°, so triangle ABC is a right triangle, and $$(AB)^2 + (BC)^2 = (AC)^2$$. From Statement (1), AD = 2. Therefore, AC = DC + 2. Substitute this value of AC into the equation above, so that $$(AB)^2 + (BC)^2 = (DC + 2)^2$$. If the values of $$(AB)^2$$ and $$(BC)^2$$ can be determined, then the length of DC can be determined. Determine the value of $$(AB)^2$$. If AD = 2 and BD = 5, then $$2^2 + 5^2 = (AB)^2$$. Simplify the equation, so that $$(AB)^2 = 29$$. Substitute this value of $$(AB)^2$$ into the equation above, so that $$29 + (BC)^2 = (DC + 2)^2$$. Now, determine the value of $$(BC)^2$$. If BD = 5, then $$(DC)^2 + 5^2 = (BC)^2$$. Simplify the equation, so that $$(BC)^2 = (DC)^2 + 25$$. Substitute this value of $$(BC)^2$$ into the equation above, so that $$29 + (DC)^2 + 25 = (DC + 2)^2$$. Simplify the equation, so that $$(DC)^2 + 54 = (DC)^2 + 4(DC) + 4$$. Combine like terms, so that 50 = 4(DC). Divide both sides of the equation by 4, so that (DC) = 12.5. Since (DC) ≠ (AD), the areas of triangles ABD and BCD are not the same, and the answer is “No.”

Together, both statements are sufficient to answer the question, so eliminate (E). The correct answer is (C).

_________________

New Project RC Butler 2019 - Practice 2 RC Passages Everyday
Final days of the GMAT Exam? => All GMAT Flashcards.
This Post Helps = Press +1 Kudos
Best of Luck on the GMAT!!

##### General Discussion
VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

### Show Tags

10 Feb 2019, 03:14
1
Attachment:
1111.jpg

In the figure above,is the diameter of a circle. Is the area of ΔABD equal to the area of ΔBCD ?

(2) BD= 5

AC is the diameter, right??
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

### Show Tags

Updated on: 16 Feb 2019, 08:34
Attachment:
1111.jpg

In the figure above AC, is the diameter of a circle. Is the area of ΔABD equal to the area of ΔBCD ?

(2) BD= 5

IMO C

Since AC is the diameter < ABC = 90, angle subtended in a semi circle is 90

DB = AD= DC, they all are radius, <DAB = <ABD = 45, So actually by SAS, both triangles can be equal

Area of triangle ABD = Area of triangle BCD

The ratio will be equal to the square of the corresponding sides to the corresponding angles, said that

Area of triangle ABD / Area of triangle BCD = (AD/DC)^2
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Originally posted by KanishkM on 10 Feb 2019, 03:23.
Last edited by KanishkM on 16 Feb 2019, 08:34, edited 1 time in total.
Intern
Joined: 15 Jul 2016
Posts: 28
Location: India
Schools: IIMC
GMAT 1: 560 Q46 V21
GMAT 2: 620 Q48 V26
GPA: 2.67
WE: Operations (Manufacturing)
Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

### Show Tags

16 Feb 2019, 07:11
KanishkM wrote:
Attachment:
1111.jpg

In the figure above AC, is the diameter of a circle. Is the area of ΔABD equal to the area of ΔBCD ?

(2) BD= 5

IMO D

Since AC is the diameter < ABC = 90, angle subtended in a semi circle is 90

DB = AD(radius), <DAB = <ABD = 45 and same goes for BD = DC(radius), < DBC = <BCD = 45

From 1) AD = 2, BD = 2
area of ΔABD is equal to the area of ΔBCD

From 2) BD = 5
area of ΔABD is equal to the area of ΔBCD

I DONT THINK SO

No where D is the center given and we cant infer it also
VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

### Show Tags

16 Feb 2019, 07:16
rinkumaa4 wrote:

I DONT THINK SO

No where D is the center given and we cant infer it also

rinkumaa4

I agree with your thoughts ,I didn't get this one.

TIA
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Intern
Joined: 15 Jul 2016
Posts: 28
Location: India
Schools: IIMC
GMAT 1: 560 Q46 V21
GMAT 2: 620 Q48 V26
GPA: 2.67
WE: Operations (Manufacturing)
Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

### Show Tags

16 Feb 2019, 07:27
1
KanishkM wrote:
rinkumaa4 wrote:

I DONT THINK SO

No where D is the center given and we cant infer it also

rinkumaa4

I agree with your thoughts ,I didn't get this one.

TIA

Ok,

I think it is DS question and for me, we cant infer anything from the image.

So each 1 and 2 are insuff.

Both 1+2.

Say D is not the center point and neither the angle ADB or CDB is a right angle.
no away the area will be equal.

so IMO C.
VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

### Show Tags

16 Feb 2019, 07:31
rinkumaa4 wrote:
KanishkM wrote:
rinkumaa4 wrote:

I DONT THINK SO

No where D is the center given and we cant infer it also

rinkumaa4

I agree with your thoughts ,I didn't get this one.

TIA

Ok,

I think it is DS question and for me, we cant infer anything from the image.

So each 1 and 2 are insuff.

Both 1+2.

Say D is not the center point and neither the angle ADB or CDB is a right angle.
no away the area will be equal.

so IMO C.

rinkumaa4

I got it, I can agree with your reasoning.

My second guess could have been an E

Thank you
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Intern
Joined: 15 Jul 2016
Posts: 28
Location: India
Schools: IIMC
GMAT 1: 560 Q46 V21
GMAT 2: 620 Q48 V26
GPA: 2.67
WE: Operations (Manufacturing)
Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

### Show Tags

16 Feb 2019, 08:11
KanishkM

Yes may be. But can you explain if D is not the center of the semi-circle, then How can the two tri-angle become equal?

I did not get that point.
Please Explain and clear my doubt.

Regards
Abhisek
VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

### Show Tags

16 Feb 2019, 08:33
rinkumaa4 wrote:
KanishkM

Yes may be. But can you explain if D is not the center of the semi-circle, then How can the two tri-angle become equal?

I did not get that point.
Please Explain and clear my doubt.

Regards
Abhisek

I guess you meant, when D is the center ?

If yes, then actually we can say

Since AC is the diameter < ABC = 90, angle subtended in a semi circle is 90

DB = AD= DC, they all are radius, <DAB = <ABD = 45, So actually by SAS, both triangles can be equal

Area of triangle ABD = Area of triangle BCD

The ratio will be equal to the square of the corresponding sides to the corresponding angles

said that

Area of triangle ABD / Area of triangle BCD = (AD/DC)^2

IMO, It will be equal

I think i got the answer.

C
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Manager
Joined: 13 Oct 2018
Posts: 61
Location: India
GPA: 3.1
WE: Information Technology (Computer Software)
Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

### Show Tags

16 Feb 2019, 08:37
Hi Kanishk,

Here we have to give answer yes or no.

If you use both choice you can certainly say the area is not equal .

Hence otion C .

Posted from my mobile device
_________________

Ankit
GMAT is tough so I am ...
Giving Kudos is the best way to enourage and appreciate people.

Re: In the figure above, is the diameter of a circle. Is the area of ΔABD   [#permalink] 16 Feb 2019, 08:37
Display posts from previous: Sort by