Last visit was: 18 Nov 2025, 17:21 It is currently 18 Nov 2025, 17:21
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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 Level|   Geometry|      
User avatar
ChandlerBong
User avatar
Joined: 16 Jan 2022
Last visit: 19 Jan 2025
Posts: 234
Own Kudos:
1,237
 [2]
Given Kudos: 1,013
Location: India
GRE 1: Q165 V165
GPA: 4
WE:Analyst (Computer Software)
GRE 1: Q165 V165
Posts: 234
Kudos: 1,237
 [2]
PQR is an isosceles triangle and PR is greater than PQ. 29 Apr 2023, 07:17
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

33% (03:07) correct 67% (02:32) wrong based on 27 sessions

History

Date
Time
Result
Not Attempted Yet
PQR is an isosceles triangle and PR is greater than PQ. If the area of the triangle is 18 units, what is the positive difference between the unequal sides of the triangle?

(A) PR = \(\sqrt{2}\) PQ

(B) Angle P = Angle R
ShowHide Answer
Official Answer
C
User avatar
ChandlerBong
User avatar
Joined: 16 Jan 2022
Last visit: 19 Jan 2025
Posts: 234
Own Kudos:
1,237
Given Kudos: 1,013
Location: India
GRE 1: Q165 V165
GPA: 4
WE:Analyst (Computer Software)
GRE 1: Q165 V165
Posts: 234
Kudos: 1,237
PQR is an isosceles triangle and PR is greater than PQ. 29 Apr 2023, 08:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ChandlerBong
PQR is an isosceles triangle and PR is greater than PQ. If the area of the triangle is 18 units, what is the positive difference between the unequal sides of the triangle?

(A) PR = \(\sqrt{2}\) PQ

(B) Angle P = Angle R
Show more


Bunuel KarishmaB ThatDudeKnows chetan2u


Hi Experts,

Can you please share your approach to this question?

Thanks in advance.

Regards.
User avatar
ThatDudeKnows
User avatar
Joined: 11 May 2022
Last visit: 27 Jun 2024
Posts: 1,070
Own Kudos:
977
 [2]
Given Kudos: 79
Expert
Expert reply
Posts: 1,070
Kudos: 977
 [2]
PQR is an isosceles triangle and PR is greater than PQ. 29 Apr 2023, 09:21
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ChandlerBong
PQR is an isosceles triangle and PR is greater than PQ. If the area of the triangle is 18 units, what is the positive difference between the unequal sides of the triangle?

(A) PR = \(\sqrt{2}\) PQ

(B) Angle P = Angle R
Show more


Statement I alone:
QR could be equal to either PQ or PR, but we don't know which, so there are two possible triangles, each of which would have its own solution to the question. Does Statement I alone give us enough information to answer the question? No. BCE.

Statement II alone:
We know that QR = PQ, but we don't know whether the triangle is very fat and very short or if the base is just a little wider than the other two sides. Does Statement II alone give us enough information to answer the question? No. CE.

Both together:
We can draw a triangle with two sides of length x and one side of length \(\sqrt{2}\)x. We can imagine inflating or deflating this figure until it has an area of 18. We COULD figure out the dimensions and angles...but we DO NOT HAVE TO. Do we have enough information to answer the question? Yes. C.
User avatar
tsraeroshad
User avatar
Joined: 14 Mar 2023
Last visit: 02 Aug 2023
Posts: 11
Given Kudos: 28
Posts: 11
Kudos: 0
PQR is an isosceles triangle and PR is greater than PQ. 29 Apr 2023, 23:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I didn't get it.
AN isosceles triangle has two sides equal and one side that is either bigger or smaller.
(I) Gives the two different sides. It should be sufficient to answer the difference between two unequal sides.
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,265
Own Kudos:
76,982
 [1]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,265
Kudos: 76,982
 [1]
PQR is an isosceles triangle and PR is greater than PQ. 02 May 2023, 04:38
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
tsraeroshad
I didn't get it.
AN isosceles triangle has two sides equal and one side that is either bigger or smaller.
(I) Gives the two different sides. It should be sufficient to answer the difference between two unequal sides.
Show more

How do you know which side it is equal to?

PR, QR and PQ are the three sides.
PR > PQ so these are not the equal sides. So QR is one of the equal sides. But which side is it equal to? Is QR = PR or is QR = PQ? We don't know.

Using statement 1, we know that we can get two isosceles triangles:

If QR = PQ, then the triangle has sides in the ratio 1: 1: sqrt(2) (a right isosceles triangle)

If QR = PR, then the triangle has sides in the ratio 1: sqrt(2) : sqrt(2) (NOT a right triangle, but nevertheless isosceles)

They are playing on your familiarity with a 45-45-90 triangle and hoping that you will jump to that and forget that another case is possible.

Statement 2 tells us that angle P = angle R so QR = PQ and hence the triangle has sides 1: 1: sqrt(2) and area of (1/2)*leg*leg = 18 so each leg length is 6.
Length of hypotenuse then is 6*sqrt(2) and the difference between them is 6*sqrt(2) - 6

We don't need to do all this calculation at the end.

Answer (C)
Moderators:
Bunuel
Math Expert
105355 posts
kingbucky
496 posts