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

 It is currently 18 Jan 2019, 03:59

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

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.
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp

Author Message
TAGS:

### Hide Tags

Director
Joined: 24 Aug 2007
Posts: 741
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

16 Apr 2010, 05:03
2
2
00:00

Difficulty:

85% (hard)

Question Stats:

59% (02:25) correct 41% (02:50) wrong based on 70 sessions

### HideShow timer Statistics

In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with center B) is drawn. If the circle cuts AB and BC at P and Q respectively, the AP:QC is equal to

A. 1:1
B. 3:2
C. 4:1
D. 3:8

_________________

Tricky Quant problems: http://gmatclub.com/forum/50-tricky-questions-92834.html
Important Grammer Fundamentals: http://gmatclub.com/forum/key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

Current Student
Joined: 12 Jun 2009
Posts: 1765
Location: United States (NC)
Concentration: Strategy, Finance
Schools: UNC (Kenan-Flagler) - Class of 2013
GMAT 1: 720 Q49 V39
WE: Programming (Computer Software)
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

16 Apr 2010, 05:40
1

Well since you know the radis from 36-25 = 11 r= sqrt(11) you can find Ap QC with 6-sqrt(11) and 8 - sqrt(11). Also, another thing to notice is that PB and BQ will be the same value since they are radius for circle B. since AB is shorter than BC you know the ratio will be a smaller value to a larger value so 4 seems to fit the bill..
_________________

Manager
Joined: 09 May 2009
Posts: 181
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

16 Apr 2010, 06:08
1
if we can know the length of BD we can find out AP and QC
now there are two ways to find out the length of BD
one is using pythagoras theorem another is using area(hero's formula)
pythagoras :
using the above eqn we will get BD=24/5
AP=6-24/5=6/5
QC=8-24/5=16/5
ratio=6/16=3/8

hero's formula
s=a+b+c/2=(6+8+10)/2=12
area=Sqrt(s(s-a)(s-b)(s-c)=24
area is also=1/2 * BD*AC=5BD
so BD=24/5
rest is same
_________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Director
Joined: 24 Aug 2007
Posts: 741
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

16 Apr 2010, 10:10
Hi,

I tried to first draw the diagram and when u take a close look u can easily tell what would be the answer .
_________________

Tricky Quant problems: http://gmatclub.com/forum/50-tricky-questions-92834.html
Important Grammer Fundamentals: http://gmatclub.com/forum/key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

Intern
Joined: 07 Apr 2010
Posts: 21
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

16 Apr 2010, 10:33
1
1
apparently, the answer can be found just by observing the choices.

we know that BC > AB => (BC - BD) > (AB - BD) => QC > AP

ie, the only logical choice is 4.
_________________

GMAT, here i come...

impressed?...how bout encouraging me with a kudos

cheers
just another idiot!

Manager
Joined: 05 Mar 2010
Posts: 173
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

17 Apr 2010, 04:26
shaselai wrote:

Well since you know the radis from 36-25 = 11 r= sqrt(11) you can find Ap QC with 6-sqrt(11) and 8 - sqrt(11). Also, another thing to notice is that PB and BQ will be the same value since they are radius for circle B. since AB is shorter than BC you know the ratio will be a smaller value to a larger value so 4 seems to fit the bill..

Where you get 25 from ........... (above in red)
_________________

Success is my Destiny

Manager
Joined: 05 Mar 2010
Posts: 173
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

17 Apr 2010, 04:29
xcusemeplz2009 wrote:
if we can know the length of BD we can find out AP and QC
now there are two ways to find out the length of BD
one is using pythagoras theorem another is using area(hero's formula)
pythagoras :
using the above eqn we will get BD=24/5

AP=6-24/5=6/5
QC=8-24/5=16/5
ratio=6/16=3/8

hero's formula
s=a+b+c/2=(6+8+10)/2=12
area=Sqrt(s(s-a)(s-b)(s-c)=24
area is also=1/2 * BD*AC=5BD
so BD=24/5
rest is same

how do we know the value of AD and DC?
_________________

Success is my Destiny

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2592
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

17 Apr 2010, 12:19
1
ans should be 3/8

as per question abc is right angled at B and using similar triangle in triangle ABC and ABD

we get x = 24/5 , join line DP and DQ , both will be the radius, thus x = DP = DQ

so AP = 6 -24/5 = 6/5

QC = 8-25/5 = 16/5

ratio AP:QC = 6/16 = 3/8
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Manager
Joined: 05 Mar 2010
Posts: 173
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

17 Apr 2010, 12:54
i still dont get it
Can you please explain in more details how you get 24/5

This question is testing my patience!!!!
_________________

Success is my Destiny

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2592
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

17 Apr 2010, 13:03
Draw a triangle ABC with b =90 and draw a perpendicular from b to D as given

now take BD = x

Since ABC and ABD are similar triangles.
We take ratio of the sides of equal angles
angle opp x is 90-c and opp BC is 90-c
similarly angle opp 90 in ABD is AB and in ABC is AC

x/BC = AB/AC => X = 24/5

I hope this helps.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Manager
Joined: 13 Dec 2009
Posts: 113
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

17 Apr 2010, 18:27
ykaiim wrote:
In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with center B) is drawn. If the circle cuts AB and BC at P and Q respectively, the AP:QC is equal to
1. 1:1
2. 3:2
3. 4:1
4. 3:8

Is there any smarter/shorter way?

try this
since it is right angle triangle, altitude BD is given by formula BD = BC*AB/AC => BD = 6*8/10 = 24/5
also from question stem, BP = BQ = BD = 24/5 ( radius of circle )
hence, AP = AB-BP = 6-24/5 = 6/5 and QC = BC-BQ = 8-24/5 = 16/5
so, AP:QC = 6/5:16/5 = 3:8
http://gmatclub.com/forum/what-to-remember-in-gmat-quant-all-time-92840.html
Manager
Joined: 09 May 2009
Posts: 181
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

17 Apr 2010, 22:47
hardnstrong wrote:
xcusemeplz2009 wrote:
if we can know the length of BD we can find out AP and QC
now there are two ways to find out the length of BD
one is using pythagoras theorem another is using area(hero's formula)
pythagoras :
using the above eqn we will get BD=24/5

AP=6-24/5=6/5
QC=8-24/5=16/5
ratio=6/16=3/8
how do we know the value of AD and DC?

no need to find AD and DC
HTH
_________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Math Expert
Joined: 02 Sep 2009
Posts: 52279
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

18 Apr 2010, 03:59
ykaiim wrote:
In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with center B) is drawn. If the circle cuts AB and BC at P and Q respectively, the AP:QC is equal to
1. 1:1
2. 3:2
3. 4:1
4. 3:8

Is there any smarter/shorter way?

First of all we should spot that ABC is a right triangle with right angle at B, as 6-8-10 is a Pythagorean triplet and AC, the longest side, is the hypotenuse.

Next in right triangle: $$\frac{height}{leg_1}=\frac{leg_2}{hypotenuse}$$ --> $$\frac{BD}{AB}=\frac{BC}{AC}$$ --> $$\frac{BD}{6}=\frac{8}{10}$$ --> $$BD=\frac{24}{5}$$.

Now, $$BD=BP=BQ=radius=\frac{24}{5}$$.

$$\frac{AP}{QC}=\frac{BA-BP}{BC-BQ}=\frac{6-\frac{24}{5}}{8-\frac{24}{5}}=\frac{3}{8}$$.

Answer: D ($$\frac{3}{8}$$)
_________________
Director
Joined: 24 Aug 2007
Posts: 741
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

19 Apr 2010, 07:29
One more approach to solve such problems:

Triangle ABC is a right angled triangle. So, we can use the area calculation method:
1/2×BC×AB=1/2×BD×AC >>> 6×8=BD×10

This results BD = 4.8 and BP= BQ= 4.8
So, AP=AB–BP=6–4.8=1.2 and similarly, CQ=BC–BQ=8–4.8=3.2.

Finally, we can derive the result by taking ratio:
AP:CQ=1.2:3.2=3:8
_________________

Tricky Quant problems: http://gmatclub.com/forum/50-tricky-questions-92834.html
Important Grammer Fundamentals: http://gmatclub.com/forum/key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

Manager
Joined: 05 Mar 2010
Posts: 173
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

20 Apr 2010, 03:05
_________________

Success is my Destiny

Manager
Joined: 06 Feb 2011
Posts: 60
WE: Information Technology (Computer Software)
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

13 Oct 2011, 13:15
Ans 4, as QC is greater than AP
Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 206
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

18 Oct 2011, 03:04

AP=6-x; CQ=8-x
CQ is greater than AP so the only possible ans is 3/8
_________________

press +1 Kudos to appreciate posts

Non-Human User
Joined: 09 Sep 2013
Posts: 9424
Re: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp  [#permalink]

### Show Tags

30 Dec 2018, 12:26
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: In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropp &nbs [#permalink] 30 Dec 2018, 12:26
Display posts from previous: Sort by