Last visit was: 11 May 2026, 12:24 It is currently 11 May 2026, 12:24
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
505-555 (Easy)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 May 2026
Posts: 110,273
Own Kudos:
814,310
Given Kudos: 106,185
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: 110,273
Kudos: 814,310
If square ABCD has area x^2 and line segment AE has length 4, and line 18 Jan 2018, 03:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

90% (01:45) correct 10% (01:49) wrong based on 49 sessions

History

Date
Time
Result
Not Attempted Yet

If square ABCD has area x^2 and line segment AE has length 4, and line segment AF has length 3, then what is the area of IGCH in terms of x ?

(A) 4x + 12
(B) 7x - 12
(C) x^2 - 24
(D) x^2 - 3 x + 12
(E) x^2 - 7 x + 12

Show Spoiler
Attachment:
2018-01-18_1411.png
2018-01-18_1411.png [ 5.31 KiB | Viewed 4179 times ]
ShowHide Answer
Official Answer
E
User avatar
DavidTutorexamPAL
User avatar
examPAL Representative
Joined: 07 Dec 2017
Last visit: 09 Sep 2020
Posts: 1,002
Own Kudos:
2,046
 [1]
Given Kudos: 26
Posts: 1,002
Kudos: 2,046
 [1]
If square ABCD has area x^2 and line segment AE has length 4, and line 18 Jan 2018, 04:53
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

If square ABCD has area x^2 and line segment AE has length 4, and line segment AF has length 3, then what is the area of IGCH in terms of x ?

(A) 4 x + 12
(B) 7 x - 12
(C) x^2 - 24
(D) x^2 - 3 x + 12
(E) x^2 - 7 x + 12

Show Spoiler
Attachment:
2018-01-18_1411.png
Show more

Since the calculation looks straightforward, we'll just do it.
This is a Precise approach.

As the area of square ABCD is x^2 its side has length x.
Then IH = x - AE = x - 4 and IG = x - AF = x - 3
So our area is (x-4)(x-3) which is answer (E).

Bunuel I assume that x2 in the question should be x^2?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 May 2026
Posts: 110,273
Own Kudos:
814,310
Given Kudos: 106,185
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: 110,273
Kudos: 814,310
If square ABCD has area x^2 and line segment AE has length 4, and line 18 Jan 2018, 06:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DavidTutorexamPAL
Bunuel

If square ABCD has area x^2 and line segment AE has length 4, and line segment AF has length 3, then what is the area of IGCH in terms of x ?

(A) 4 x + 12
(B) 7 x - 12
(C) x^2 - 24
(D) x^2 - 3 x + 12
(E) x^2 - 7 x + 12

Show Spoiler
Attachment:
2018-01-18_1411.png

Since the calculation looks straightforward, we'll just do it.
This is a Precise approach.

As the area of square ABCD is x^2 its side has length x.
Then IH = x - AE = x - 4 and IG = x - AF = x - 3
So our area is (x-4)(x-3) which is answer (E).

Bunuel I assume that x2 in the question should be x^2?
Show more

Yes. Edited. Thank you for noticing.
User avatar
aeon86
User avatar
Joined: 11 Nov 2017
Last visit: 06 Sep 2022
Posts: 147
Own Kudos:
80
Given Kudos: 12
Location: Belgium
Concentration: Technology, Operations
Schools: IESE '21 (A$) ESADE '21 (WD) IE Sept19 Intake (WD)
GMAT 1: 670 Q47 V34
GMAT 2: 750 Q50 V41
GMAT 3: 750 Q50 V41
GPA: 2.5
WE:Engineering (Aerospace and Defense)
Schools: IESE '21 (A$) ESADE '21 (WD) IE Sept19 Intake (WD)
GMAT 3: 750 Q50 V41
Posts: 147
Kudos: 80
If square ABCD has area x^2 and line segment AE has length 4, and line 18 Jan 2018, 06:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
maybe a suggestion but: if experts solve this, could they wait till some people have posted their answers, or, at least encase their answer in spoiler tags?
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,902
Own Kudos:
5,465
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,902
Kudos: 5,465
If square ABCD has area x^2 and line segment AE has length 4, and line 18 Jan 2018, 07:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

If square ABCD has area x^2 and line segment AE has length 4, and line segment AF has length 3, then what is the area of IGCH in terms of x ?

(A) 4x + 12
(B) 7x - 12
(C) x^2 - 24
(D) x^2 - 3 x + 12
(E) x^2 - 7 x + 12

Show Spoiler
Attachment:
The attachment 2018-01-18_1411.png is no longer available
Show more
Show Spoiler
Attachment:
2018-01-18_1411.png
2018-01-18_1411.png [ 7.07 KiB | Viewed 3515 times ]

Area of IGCH = Area of ABCD - ( Area of AEFI + Area of FIBG + Area of EIDH )

Or, Area of IGCH = \(x^2 - ( 12 + 4x - 12 + 3x - 12 )\)

Or, Area of IGCH = \(x^2 - 7 x + 12\), answer will be (E)

aeon86
maybe a suggestion but: if experts solve this, could they wait till some people have posted their answers, or, at least encase their answer in spoiler tags?
Show more

Done , please solve this question now...
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 11 May 2026
Posts: 22,332
Own Kudos:
26,582
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,332
Kudos: 26,582
If square ABCD has area x^2 and line segment AE has length 4, and line 20 Jan 2018, 07:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

If square ABCD has area x^2 and line segment AE has length 4, and line segment AF has length 3, then what is the area of IGCH in terms of x ?

(A) 4x + 12
(B) 7x - 12
(C) x^2 - 24
(D) x^2 - 3 x + 12
(E) x^2 - 7 x + 12

Show Spoiler
Attachment:
2018-01-18_1411.png
Show more

Since the area of the square ABCD is x^2, we observe that both AB and AD must have length x.

Since AB = x = EG and AF = 3 = EI, then IG = EG - EI = x - 3.

Since AD = x = FH and AE = 4 = FI, then IH = FH - FI = x - 4.

Thus, the area of IGCH is:

(x - 3)(x - 4) = x^2 - 7x + 12

Answer: E
Moderators:
Bunuel
Math Expert
110274 posts
Krunaal
Tuck School Moderator
852 posts