Last visit was: 15 Sep 2026, 12:35 It is currently 15 Sep 2026, 12:35
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
655-705 (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 15 Sep 2026
Posts: 113,551
Own Kudos:
841,486
 [7]
Given Kudos: 111,544
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,551
Kudos: 841,486
 [7]
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC 12 Jun 2020, 06:54
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

59% (02:15) correct 41% (02:11) wrong based on 122 sessions

History

Date
Time
Result
Not Attempted Yet
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC such that AP = 6 cm. What is the length of BP?

A. 4
B. 6
C. 8
D. 10
E. 12

Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
A
User avatar
RaghavKhanna
User avatar
Joined: 03 May 2020
Last visit: 23 Aug 2025
Posts: 263
Own Kudos:
317
 [2]
Given Kudos: 675
Location: India
Concentration: Marketing, Strategy
GMAT 1: 700 Q47 V39
GMAT 1: 700 Q47 V39
Posts: 263
Kudos: 317
 [2]
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC Updated on: 12 Jun 2020, 07:17
Originally posted by RaghavKhanna on 12 Jun 2020, 07:02.
Last edited by RaghavKhanna on 12 Jun 2020, 07:17, edited 1 time in total.
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
In triangle ABP:

BP < AP + AB
=> BP < 14

In triangle BPC

BP < PC + BC
=> BP < 6

only option A satisfies this.

=> Answer : A

Posted from my mobile device
User avatar
yashikaaggarwal
User avatar
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Last visit: 10 Aug 2026
Posts: 3,095
Own Kudos:
3,220
 [1]
Given Kudos: 1,510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Schools: Cranfield (A) Warwick MiM "23 (M)
Posts: 3,095
Kudos: 3,220
 [1]
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC 12 Jun 2020, 07:08
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
In Triangle ABC,
AB = AC = 8
BC = 4
AP = 6, PC = 6
∆ABP = AB+AP>BP
(Sum of two sides of triangle is greater than third side)
8+6>BP
BP < 14 -------(1)

∆CBP = CB+CP>BP
(Sum of two sides of triangle is greater than third side)
4+2>BP
BP < 6 -------(2)

Since BP is < 6&14 both. Only option that satisfy BP value = 4

IMO A

Posted from my mobile device
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 14 Sep 2026
Posts: 7,342
Own Kudos:
17,507
 [1]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 7,342
Kudos: 17,507
 [1]
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC 12 Jun 2020, 07:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC such that AP = 6 cm. What is the length of BP?

A. 4
B. 6
C. 8
D. 10
E. 12
Show more

PROPERTY: Sum fo any two sides in a Triangle > Third side

Please check the solution as attached here

Answer: Option A


Attachments

Screenshot 2020-06-12 at 7.40.17 PM.png
Screenshot 2020-06-12 at 7.40.17 PM.png [ 576.41 KiB | Viewed 8477 times ]

User avatar
Lipun
User avatar
Joined: 05 Jan 2020
Last visit: 08 Jan 2025
Posts: 140
Own Kudos:
167
 [1]
Given Kudos: 291
Posts: 140
Kudos: 167
 [1]
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC 12 Jun 2020, 07:31
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AC = AP + PC => PC = 8 - 6 = 2

In triangle BPC, BP < BC + PC => BP < 4 + 2 => BP < 6

Only option is A.
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 13 Sep 2026
Posts: 4,146
Own Kudos:
11,543
 [3]
Given Kudos: 98
Location: United States
GMAT 1: 780 Q51 V47
Expert
Expert reply
GMAT 1: 780 Q51 V47
Posts: 4,146
Kudos: 11,543
 [3]
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC 12 Jun 2020, 08:24
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
The solutions above rely purely on estimates, using triangle inequalities, which is fine when the answer choices are this spread out, but would not work with different choices. The reason the answer is exactly 4 here is that the small triangle BPC, with sides 2, 4, x, is similar to the large triangle ABC with sides 4, 8, and 8. One way to see that: in general, if you have two lengths with a fixed angle between them, there's only one triangle you can possibly make. In this problem, we know, looking at triangle ABC, that if we put the angle C between a side of length 4 and a side of length 8, the opposite side is of length 8. But in triangle BPC, we have the same angle C between sides of length 2 and 4. Those are exactly half the lengths angle C sits between in triangle ABC, so triangle BPC is just half as big (in length) as ABC, and its third side is of length 4.

I'm using side-angle-side similarity (SAS) here, which is often used in trigonometry, but which I don't think I've ever needed for a real GMAT question.
User avatar
AnirudhaS
User avatar
LBS Moderator
Joined: 30 Oct 2019
Last visit: 25 Jun 2024
Posts: 771
Own Kudos:
906
Given Kudos: 1,575
Posts: 771
Kudos: 906
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC 12 Jun 2020, 08:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IanStewart
The solutions above rely purely on estimates, using triangle inequalities, which is fine when the answer choices are this spread out, but would not work with different choices. The reason the answer is exactly 4 here is that the small triangle BPC, with sides 2, 4, x, is similar to the large triangle ABC with sides 4, 8, and 8. One way to see that: in general, if you have two lengths with a fixed angle between them, there's only one triangle you can possibly make. In this problem, we know, looking at triangle ABC, that if we put the angle C between a side of length 4 and a side of length 8, the opposite side is of length 8. But in triangle BPC, we have the same angle C between sides of length 2 and 4. Those are exactly half the lengths angle C sits between in triangle ABC, so triangle BPC is just half as big (in length) as ABC, and its third side is of length 4.

I'm using side-angle-side similarity (SAS) here, which is often used in trigonometry, but which I don't think I've ever needed for a real GMAT question.
Show more
I never knew you can use congruency to find out the ratio of sides!

So you are saying:
Traingle congruency: S A S
Big triangle: 4 angleC 8 --> third side 8
Small traingle: 2 angleC 4 --> therefore third side = 8/2=4
avatar
vipulshahi
avatar
Joined: 24 Sep 2013
Last visit: 30 Aug 2021
Posts: 162
Own Kudos:
114
 [1]
Given Kudos: 40
Location: Saudi Arabia
GPA: 3.8
WE:Project Management (Energy)
Posts: 162
Kudos: 114
 [1]
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC 12 Jun 2020, 22:50
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AB = AC = 8
BC = 4
AP = 6 ; PC = 2
BP=?

In Tri. ABP,
1) BP < AB+ PA [ Property : Sum of two sides of the triangle is always greater than third side]
BP< 8+6
BP< 14
2) BP > 8-6 [ Property : Difference of two sides of the triangle is always less than the third side]
BP > 2

Thus, 2<BP<14 - equation 1

In Tri. BPC,
1) BP < BC+PC
BP< 4+2
BP < 6

2) BP> BC-PC
BP > 4-2
BP> 2

Thus , 2< BP< 6 - equation 2

From Eq1 & Eq2,
BP will be 3,4,5

Only option A suits the condition.

Answer : A
User avatar
sambitspm
User avatar
Joined: 05 Aug 2019
Last visit: 13 Jan 2022
Posts: 317
Own Kudos:
316
Given Kudos: 130
Location: India
Concentration: Leadership, Technology
GMAT 1: 600 Q50 V22
GMAT 2: 670 Q50 V28 (Online)
GPA: 4
GMAT 2: 670 Q50 V28 (Online)
Posts: 317
Kudos: 316
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC 13 Jun 2020, 22:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Solved this by option matching. Clearly BP < BC+ PC. The Sum of 2 sides is greater than 3rd.
BP< 6
Only Option matching is A.
Attachments

1.PNG
1.PNG [ 19.01 KiB | Viewed 7830 times ]

User avatar
HoneyLemon
User avatar
Stern School Moderator
Joined: 26 May 2020
Last visit: 02 Oct 2023
Posts: 627
Own Kudos:
572
Given Kudos: 219
Status:Spirited
Concentration: General Management, Technology
Schools: Stern '23 LBS '23 Said '23 IIMB EPGP'22 INSEAD Jan'23 intake
WE:Analyst (Computer Software)
Schools: Stern '23 LBS '23 Said '23 IIMB EPGP'22 INSEAD Jan'23 intake
Posts: 627
Kudos: 572
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC 14 Jun 2020, 20:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC such that AP = 6 cm. What is the length of BP?

A. 4
B. 6
C. 8
D. 10
E. 12
Show more

In triangle ABP:

AP-AB < BP < AP + AB
=> 2 <BP < 14

In triangle BPC

BC- PC < BP < BC + PC
=> 2<BP < 6

only option A satisfies this.
A
is my Answer
User avatar
dimri10
User avatar
Joined: 16 May 2011
Last visit: 25 Sep 2023
Posts: 237
Own Kudos:
368
Given Kudos: 64
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE:Law (Law)
Posts: 237
Kudos: 368
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC 15 Jun 2020, 07:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
well,
i did the hard way. it is so funny to see the simple solutions.
i found the upper side of an isoceles trapezoide to b e 3.
bc is than being cut to 1/2:3:1/2
H of trapezoide is root 15/4 (WAS EASIER TO WORK WITH FRACTIONS)
so H^2+3.5^2=BP^2
SO BP^2 =64/4=16
BP=4. took me about 4-5 minutes.
But then i saw the other answers. i didnt even think of triangles sides.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,225
Own Kudos:
1,159
Posts: 39,225
Kudos: 1,159
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point оn side AC 04 Nov 2023, 06:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderator:
Bunuel
Math Expert
113550 posts