Last visit was: 29 Apr 2026, 16:48 It is currently 29 Apr 2026, 16:48
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
705-805 (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 29 Apr 2026
Posts: 109,975
Own Kudos:
811,984
 [12]
Given Kudos: 105,949
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,975
Kudos: 811,984
 [12]
The bases of a trapezoid have lengths 10 and 15. A segment parallel to 05 Feb 2020, 03:31
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

50% (02:06) correct 50% (02:18) wrong based on 109 sessions

History

Date
Time
Result
Not Attempted Yet
The bases of a trapezoid have lengths 10 and 15. A segment parallel to the bases passes through the point of intersection of the diagonals and extends from one side to the other. What is the length of the segment?

A. 5
B. 12
C. √150
D. 25/√2
E. 18

Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
B
User avatar
lacktutor
User avatar
Joined: 25 Jul 2018
Last visit: 23 Oct 2023
Posts: 658
Own Kudos:
1,449
 [3]
Given Kudos: 69
Posts: 658
Kudos: 1,449
 [3]
The bases of a trapezoid have lengths 10 and 15. A segment parallel to 05 Feb 2020, 04:55
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
There is a formula for Harmonic \(Mean = \frac{2ab}{(a+b)}\)
a, b — lengths of bases

The length of segment = \(\frac{2*10*15}{(10+15)} = \frac{300}{25}= 12\)

The answer is B.

Posted from my mobile device
User avatar
ShankSouljaBoi
User avatar
Joined: 21 Jun 2017
Last visit: 28 Mar 2026
Posts: 599
Own Kudos:
611
 [2]
Given Kudos: 4,090
Location: India
Concentration: Finance, Economics
Schools: Rotman '23 (D) IIMA PGPX'22 (D) Desautels '23 (D) Schulich Sept '23 (D) WBS (D) IIML IPMX'25 (A)
GMAT 1: 660 Q49 V31
GMAT 2: 620 Q47 V30
GMAT 3: 650 Q48 V31
GPA: 3.1
WE:Corporate Finance (Non-Profit and Government)
Products:
My Reviews
Schools: Rotman '23 (D) IIMA PGPX'22 (D) Desautels '23 (D) Schulich Sept '23 (D) WBS (D) IIML IPMX'25 (A)
GMAT 3: 650 Q48 V31
Posts: 599
Kudos: 611
 [2]
The bases of a trapezoid have lengths 10 and 15. A segment parallel to 05 Feb 2020, 05:00
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
lacktutor
There is a formula for Harmonic \(Mean = \frac{2ab}{(a+b)}\)
a, b — lengths of bases

The length of segment = \(\frac{2*10*15}{(10+15)} = \frac{300}{25}= 12\)

The answer is B.

Posted from my mobile device
Show more

How did you recognize HM has to be used ??

Also, is this applicable to all quadrilaterals in similar questions ???


Regards
User avatar
ShankSouljaBoi
User avatar
Joined: 21 Jun 2017
Last visit: 28 Mar 2026
Posts: 599
Own Kudos:
611
Given Kudos: 4,090
Location: India
Concentration: Finance, Economics
Schools: Rotman '23 (D) IIMA PGPX'22 (D) Desautels '23 (D) Schulich Sept '23 (D) WBS (D) IIML IPMX'25 (A)
GMAT 1: 660 Q49 V31
GMAT 2: 620 Q47 V30
GMAT 3: 650 Q48 V31
GPA: 3.1
WE:Corporate Finance (Non-Profit and Government)
Products:
My Reviews
Schools: Rotman '23 (D) IIMA PGPX'22 (D) Desautels '23 (D) Schulich Sept '23 (D) WBS (D) IIML IPMX'25 (A)
GMAT 3: 650 Q48 V31
Posts: 599
Kudos: 611
The bases of a trapezoid have lengths 10 and 15. A segment parallel to 05 Feb 2020, 09:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi chetan2u ,

kindly help wih this one


Regards
User avatar
rajatchopra1994
User avatar
Joined: 16 Feb 2015
Last visit: 22 Jun 2024
Posts: 1,052
Own Kudos:
1,308
 [2]
Given Kudos: 30
Location: United States
Posts: 1,052
Kudos: 1,308
 [2]
The bases of a trapezoid have lengths 10 and 15. A segment parallel to 05 Feb 2020, 20:38
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Explanation:

There is one formula for finding A segment parallel to the bases passes through the point of intersection of the diagonals.

let longer base = A = 15
Shorter base = B = 10
Segment Passing through intersection of diagonals = C
The length of the parallel line segment through the intersection of the diagonals is the harmonic mean of the bases of the trapezoid.
C-B/B = A-C/C
C-10/10 = 15-C/15
5C=60
C= 12

IMO-B

ShankSouljaBoi

For Formula derivation & better understanding, check this URL https://jwilson.coe.uga.edu/emt725/Isos.Trpzd/Diag/diag.html
avatar
metalhead2593
avatar
Joined: 14 Jul 2019
Last visit: 18 Dec 2020
Posts: 31
Own Kudos:
32
 [2]
Given Kudos: 322
Posts: 31
Kudos: 32
 [2]
The bases of a trapezoid have lengths 10 and 15. A segment parallel to 14 Mar 2020, 04:04
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rajatchopra1994
Explanation:

There is one formula for finding A segment parallel to the bases passes through the point of intersection of the diagonals.

let longer base = A = 15
Shorter base = B = 10
Segment Passing through intersection of diagonals = C
The length of the parallel line segment through the intersection of the diagonals is the harmonic mean of the bases of the trapezoid.
C-B/B = A-C/C
C-10/10 = 15-C/15
5C=60
C= 12

IMO-B

ShankSouljaBoi



For Formula derivation & better understanding, check this URL https://jwilson.coe.uga.edu/emt725/Isos.Trpzd/Diag/diag.html
Show more

I didn't know this formula, but I used estimation.

So, the length that we want to find will definitely be smaller than the average of two bases (unless they're equal to): L < (10+15)/2 = 12.5

Look at the choices, we can cross out C, D, E. Since A (L=5) is smaller than the length of one base (10), we're left with 12.
Moderators:
Bunuel
Math Expert
109975 posts
Krunaal
Tuck School Moderator
852 posts