Last visit was: 25 Apr 2026, 06:26 It is currently 25 Apr 2026, 06:26
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
805+ (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,827
Own Kudos:
811,175
 [5]
Given Kudos: 105,878
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: 109,827
Kudos: 811,175
 [5]
A rectangle with positive integer side lengths in cm has area A cm^2 a 25 Apr 2019, 02:27
Kudos
Add Kudos
5
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:

95% (hard)

Question Stats:

26% (02:18) correct 74% (02:44) wrong based on 76 sessions

History

Date
Time
Result
Not Attempted Yet
A rectangle with positive integer side lengths in cm has area A cm^2 and perimeter P cm. Which of the following numbers cannot equal A + P ?

(A) 100
(B) 102
(C) 104
(D) 106
(E) 108
ShowHide Answer
Official Answer
B
avatar
Shobhit7
avatar
Joined: 01 Feb 2017
Last visit: 29 Apr 2021
Posts: 239
Own Kudos:
432
 [3]
Given Kudos: 148
Posts: 239
Kudos: 432
 [3]
A rectangle with positive integer side lengths in cm has area A cm^2 a 29 Apr 2019, 04:35
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
To test numbers, we need to determine approx values.

Max A+P is for a square as square has max A for a given P.

Testing on squares:
For side 8, A+P= 64+32= 96
For side 9, A+P= 81+36= 117

All choices are within this range.

Let's test rectangles with sides:
9,8= 72+34= 106
10,7= 70+34= 104
11,6= 66+34= 100
Note that 102 has missed out from this sequence.
12,6= 72+36= 108

Ans B
User avatar
TheNightKing
User avatar
Joined: 18 Dec 2017
Last visit: 20 Mar 2024
Posts: 1,124
Own Kudos:
1,381
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
GMAT 1: 600 Q46 V27
Posts: 1,124
Kudos: 1,381
A rectangle with positive integer side lengths in cm has area A cm^2 a 06 Oct 2019, 21:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel Hello Sir,
Can you please provide OE or your explanation for this one? :)
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 24 Apr 2026
Posts: 22,286
Own Kudos:
26,536
 [3]
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: 22,286
Kudos: 26,536
 [3]
A rectangle with positive integer side lengths in cm has area A cm^2 a 09 Oct 2019, 20:15
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A rectangle with positive integer side lengths in cm has area A cm^2 and perimeter P cm. Which of the following numbers cannot equal A + P ?

(A) 100
(B) 102
(C) 104
(D) 106
(E) 108
Show more

Let L and W be the length and width of the rectangle, respectively. Since A = LW and P = 2L + 2W, we have:

A + P = LW + 2L + 2W = L(W + 2) + 2W

Let’s add and subtract 4 to the last expression:

A + P = L(W + 2) + 2W + 4 - 4 = L(W + 2) + 2(W + 2) - 4 = (W + 2)(L + 2) - 4

Using the last equality, we can test each answer choice:

A) A + P = 100

100 = (W + 2)(L + 2) - 4

(W + 2)(L + 2) = 104

We can let, for instance, L + 2 = 26 and W + 2 = 4. Then, L = 24 and W = 2. We see that 100 is a possible value for A + P.

B) A + P = 102

102 = (W + 2)(L + 2) - 4

(W + 2)(L + 2) = 106

The only way to factor 106 is 106 x 1 or 53 x 2. If W + 2 = 1, then W is negative and if W + 2 = 2, then W is zero. Neither are possible values for the width of a rectangle; therefore A + P = 102 is not possible.

Answer: B
User avatar
satya2029
User avatar
Joined: 10 Dec 2017
Last visit: 29 Sep 2025
Posts: 229
Own Kudos:
254
Given Kudos: 138
Location: India
Posts: 229
Kudos: 254
A rectangle with positive integer side lengths in cm has area A cm^2 a 09 Oct 2019, 21:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A rectangle with positive integer side lengths in cm has area A cm^2 and perimeter P cm. Which of the following numbers cannot equal A + P ?

(A) 100
(B) 102
(C) 104
(D) 106
(E) 108
Show more
Let one side of the rectangle is X
other side is X+k(where K >0 and Kmin=1 for X+k= integer)
A+P=X(X+k)+2[X+X+k]
A+P=X^2+X(k+4)+2k
According to the options
Plug
X=9
Just by looking at the equation we will get to know that this value will exceed the given values in the options.
so start with X=8
A+P= 96+10k For k=1- 106
X=6
A+P=60+8k For k=5-100, For K=6-108

X=4
A+P=32+6k-For K=12-104
B:)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,981
Own Kudos:
1,117
Posts: 38,981
Kudos: 1,117
A rectangle with positive integer side lengths in cm has area A cm^2 a 11 Jul 2022, 07:44
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.
Moderators:
Bunuel
Math Expert
109827 posts
Krunaal
Tuck School Moderator
852 posts