Last visit was: 27 Apr 2026, 06:23 It is currently 27 Apr 2026, 06:23
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
desaichinmay22
User avatar
Joined: 21 Sep 2012
Last visit: 22 May 2016
Posts: 188
Own Kudos:
469
 [7]
Given Kudos: 31
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE:General Management (Consumer Packaged Goods)
Schools: CBS '17
Posts: 188
Kudos: 469
 [7]
What is the area of rectangle ABCD? 04 Dec 2014, 01:47
2
Kudos
Add Kudos
5
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:

38% (01:41) correct 63% (01:35) wrong based on 136 sessions

History

Date
Time
Result
Not Attempted Yet
What is the area of rectangle ABCD?

(1) Two of the vertices of rectangle ABCD lie on the X-axis

(2) The longer side of the rectangle measures 12 cms and one of the diagonals has a slope of 1.5
ShowHide Answer
Official Answer
C
User avatar
manpreetsingh86
User avatar
Joined: 13 Jun 2013
Last visit: 19 Dec 2022
Posts: 218
Own Kudos:
1,194
 [1]
Given Kudos: 14
Posts: 218
Kudos: 1,194
 [1]
What is the area of rectangle ABCD? 04 Dec 2014, 08:26
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
desaichinmay22
What is the area of rectangle ABCD?

(1) Two of the vertices of rectangle ABCD lie on the X-axis

(2) The longer side of the rectangle measures 12 cms and one of the diagonals has a slope of 1.5
Show more

st.1 clearly not sufficient.
st.2 not sufficient, as we need to know about the vertices of rectangle.

st.1 + st.2 we know that vertices of the rectangle lie on x-axis. also, slope of 1.5 indicates that for every unit move on x-axis, y goes by 1.5 unit. also since longer side of the rectangle is 12 unit. thus, 12=1.5(x) (x= units by which x moves.)
thus x=12/1.5 or x=8. hence area of rectangle ABCD = 12*8=96

hence C
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 03 Apr 2026
Posts: 2,286
Own Kudos:
2,681
 [1]
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,286
Kudos: 2,681
 [1]
What is the area of rectangle ABCD? 04 Dec 2014, 08:30
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Image attached

We basically need the sides of the rectangle to calculate the area

STAT1: STAT1 by itself is not sufficient as we do not anything about the length of the rectangle to find the area.
Two possible cases (there can be many more) for the rectangle are shown in the image 1
So, INSUFFICIENT

STAT2: STAT2 by itself is SUFFICIENT as doesn't matter however we draw the rectangle we can always find the vertices
If the longer side is base then while using : tan (theta) = slope = height/base we will have height = base * slope = 12 * 1.5, which is not possible as the longer side is 12, so this side cannot be longer than 12
If the longer side is height then while using : tan (theta) = slope = height/base we will have base = height / slope = 12 / 1.5, so Area = height * base = 12 * 12 / 1.5
So, SUFFICIENT

I think answer should be B?

desaichinmay22
What is the area of rectangle ABCD?

(1) Two of the vertices of rectangle ABCD lie on the X-axis

(2) The longer side of the rectangle measures 12 cms and one of the diagonals has a slope of 1.5
Show more

Attachments

File comment: image 2
image 2.png
image 2.png [ 5.94 KiB | Viewed 4443 times ]

File comment: Image 1
image 1.png
image 1.png [ 11.06 KiB | Viewed 4483 times ]

User avatar
desaichinmay22
User avatar
Joined: 21 Sep 2012
Last visit: 22 May 2016
Posts: 188
Own Kudos:
469
 [1]
Given Kudos: 31
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE:General Management (Consumer Packaged Goods)
Schools: CBS '17
Posts: 188
Kudos: 469
 [1]
What is the area of rectangle ABCD? 04 Dec 2014, 08:54
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
nktdotgupta
Image attached

We basically need the sides of the rectangle to calculate the area

STAT1: STAT1 by itself is not sufficient as we do not anything about the length of the rectangle to find the area.
Two possible cases (there can be many more) for the rectangle are shown in the image 1
So, INSUFFICIENT

STAT2: STAT2 by itself is not sufficient as longer side can be the base of the rectangle or can be the height. (image 2)
If the longer side is base then while using : tan (theta) = slope = height/base we will have height = base * slope = 12 * 1.5, so Area = height * base = 12 * 12 * 1.5
If the longer side is height then while using : tan (theta) = slope = height/base we will have base = height / slope = 12 / 1.5, so Area = height * base = 12 * 12 / 1.5
So, we are getting two different values for Area
So, INSUFFICIENT

Taking both together
We will have the two cases (and similar cases with positive and negative values for x) as shown in Image 1

Now, the case with the rectangle with one edge on x-axis is straight forward
if you take the longer side as base then height/base = slope = 1.5 so, height = 1.5* base = 1.5 * 12 which is not possible as base was longer side, not the height
So, height is 12 and base will be height /slope = 12/1.5 = 8. So, Area will be 12* 8 = 96

Now, the case with the two diagonal vertices on x-axis
Now only possible case when the other diagonal will have a positive slope is in the second case of image 1. But this will not be possible as the smaller side will be 12 * 1.5, which is greater than the other side of the rectangle.

So, we will have only one case. So, SUFFICIENT.

So, Answer will be C
Hope it helps!

desaichinmay22
What is the area of rectangle ABCD?

(1) Two of the vertices of rectangle ABCD lie on the X-axis

(2) The longer side of the rectangle measures 12 cms and one of the diagonals has a slope of 1.5
Show more

Please help me understand below point :

I have highlighted some portion from your solution. If assumption is that longer side is base then how can height be base*slope (we already know slope is > 1). Initially I chose B only since I couldn't think of any other combination of l*b except (12*8)

STAT2: STAT2 by itself is not sufficient as longer side can be the base of the rectangle or can be the height. (image 2)
If the longer side is base then while using : tan (theta) = slope = height/base we will have height = base * slope = 12 * 1.5, so Area = height * base = 12 * 12 * 1.5
If the longer side is height then while using : tan (theta) = slope = height/base we will have base = height / slope = 12 / 1.5, so Area = height * base = 12 * 12 / 1.5
So, we are getting two different values for Area
So, INSUFFICIENT
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 03 Apr 2026
Posts: 2,286
Own Kudos:
2,681
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,286
Kudos: 2,681
What is the area of rectangle ABCD? 04 Dec 2014, 09:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I did a mistake there, i will change it.
The answer should be B right? We know that the longer side is 12 and doesn't matter how we draw the rectangle we know that the slope of one diagonal is 1.5 and the height for that slope (if we talking in terms of tan theta) will be 12 and base will be 12/1.5, which is 8 right? What else can we draw anyways?
desaichinmay22
nktdotgupta
Image attached

We basically need the sides of the rectangle to calculate the area

STAT1: STAT1 by itself is not sufficient as we do not anything about the length of the rectangle to find the area.
Two possible cases (there can be many more) for the rectangle are shown in the image 1
So, INSUFFICIENT

STAT2: STAT2 by itself is not sufficient as longer side can be the base of the rectangle or can be the height. (image 2)
If the longer side is base then while using : tan (theta) = slope = height/base we will have height = base * slope = 12 * 1.5, so Area = height * base = 12 * 12 * 1.5
If the longer side is height then while using : tan (theta) = slope = height/base we will have base = height / slope = 12 / 1.5, so Area = height * base = 12 * 12 / 1.5
So, we are getting two different values for Area
So, INSUFFICIENT

Taking both together
We will have the two cases (and similar cases with positive and negative values for x) as shown in Image 1

Now, the case with the rectangle with one edge on x-axis is straight forward
if you take the longer side as base then height/base = slope = 1.5 so, height = 1.5* base = 1.5 * 12 which is not possible as base was longer side, not the height
So, height is 12 and base will be height /slope = 12/1.5 = 8. So, Area will be 12* 8 = 96

Now, the case with the two diagonal vertices on x-axis
Now only possible case when the other diagonal will have a positive slope is in the second case of image 1. But this will not be possible as the smaller side will be 12 * 1.5, which is greater than the other side of the rectangle.

So, we will have only one case. So, SUFFICIENT.

So, Answer will be C
Hope it helps!

desaichinmay22
What is the area of rectangle ABCD?

(1) Two of the vertices of rectangle ABCD lie on the X-axis

(2) The longer side of the rectangle measures 12 cms and one of the diagonals has a slope of 1.5

Please help me understand below point :

I have highlighted some portion from your solution. If assumption is that longer side is base then how can height be base*slope (we already know slope is > 1). Initially I chose B only since I couldn't think of any other combination of l*b except (12*8)

STAT2: STAT2 by itself is not sufficient as longer side can be the base of the rectangle or can be the height. (image 2)
If the longer side is base then while using : tan (theta) = slope = height/base we will have height = base * slope = 12 * 1.5, so Area = height * base = 12 * 12 * 1.5
If the longer side is height then while using : tan (theta) = slope = height/base we will have base = height / slope = 12 / 1.5, so Area = height * base = 12 * 12 / 1.5
So, we are getting two different values for Area
So, INSUFFICIENT
Show more
User avatar
desaichinmay22
User avatar
Joined: 21 Sep 2012
Last visit: 22 May 2016
Posts: 188
Own Kudos:
469
Given Kudos: 31
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE:General Management (Consumer Packaged Goods)
Schools: CBS '17
Posts: 188
Kudos: 469
What is the area of rectangle ABCD? 04 Dec 2014, 09:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I chose B as answer, but OA was given as C. I don't have OE for this problem. We need expert's opinion.

Bunuel :- Request you to provide solution for given problem.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 Apr 2026
Posts: 109,928
Own Kudos:
811,542
 [3]
Given Kudos: 105,914
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: 109,928
Kudos: 811,542
 [3]
What is the area of rectangle ABCD? 06 Dec 2014, 08:46
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nktdotgupta
Image attached

We basically need the sides of the rectangle to calculate the area

STAT1: STAT1 by itself is not sufficient as we do not anything about the length of the rectangle to find the area.
Two possible cases (there can be many more) for the rectangle are shown in the image 1
So, INSUFFICIENT

STAT2: STAT2 by itself is SUFFICIENT as doesn't matter however we draw the rectangle we can always find the vertices
If the longer side is base then while using : tan (theta) = slope = height/base we will have height = base * slope = 12 * 1.5, which is not possible as the longer side is 12, so this side cannot be longer than 12
If the longer side is height then while using : tan (theta) = slope = height/base we will have base = height / slope = 12 / 1.5, so Area = height * base = 12 * 12 / 1.5
So, SUFFICIENT

I think answer should be B?

desaichinmay22
What is the area of rectangle ABCD?

(1) Two of the vertices of rectangle ABCD lie on the X-axis

(2) The longer side of the rectangle measures 12 cms and one of the diagonals has a slope of 1.5
Show more

For (2) consider the following case:
Attachment:
Untitled.png
Untitled.png [ 12.65 KiB | Viewed 4284 times ]
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 03 Apr 2026
Posts: 2,286
Own Kudos:
2,681
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,286
Kudos: 2,681
What is the area of rectangle ABCD? 06 Dec 2014, 21:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks Bunuel. I drew this case in my image 1 part 2 but took theta wrong :)
Bunuel
nktdotgupta
Image attached

We basically need the sides of the rectangle to calculate the area

STAT1: STAT1 by itself is not sufficient as we do not anything about the length of the rectangle to find the area.
Two possible cases (there can be many more) for the rectangle are shown in the image 1
So, INSUFFICIENT

STAT2: STAT2 by itself is SUFFICIENT as doesn't matter however we draw the rectangle we can always find the vertices
If the longer side is base then while using : tan (theta) = slope = height/base we will have height = base * slope = 12 * 1.5, which is not possible as the longer side is 12, so this side cannot be longer than 12
If the longer side is height then while using : tan (theta) = slope = height/base we will have base = height / slope = 12 / 1.5, so Area = height * base = 12 * 12 / 1.5
So, SUFFICIENT

I think answer should be B?

desaichinmay22
What is the area of rectangle ABCD?

(1) Two of the vertices of rectangle ABCD lie on the X-axis

(2) The longer side of the rectangle measures 12 cms and one of the diagonals has a slope of 1.5

For (2) consider the following case:
Attachment:
Untitled.png
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 Apr 2026
Posts: 109,928
Own Kudos:
811,542
Given Kudos: 105,914
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: 109,928
Kudos: 811,542
What is the area of rectangle ABCD? 07 Dec 2014, 05:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nktdotgupta
Thanks Bunuel. I drew this case in my image 1 part 2 but took theta wrong :)
Show more

Yes, theta is an angle between the diagonal and x-axis, not the diagonal and the side of the rectangle.
avatar
avikroy
avatar
Joined: 04 Jun 2010
Last visit: 26 Mar 2020
Posts: 94
Own Kudos:
34
Given Kudos: 264
Location: India
GMAT 1: 660 Q49 V31
GPA: 3.22
GMAT 1: 660 Q49 V31
Posts: 94
Kudos: 34
What is the area of rectangle ABCD? 17 May 2019, 00:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
nktdotgupta
Image attached

We basically need the sides of the rectangle to calculate the area

STAT1: STAT1 by itself is not sufficient as we do not anything about the length of the rectangle to find the area.
Two possible cases (there can be many more) for the rectangle are shown in the image 1
So, INSUFFICIENT

STAT2: STAT2 by itself is SUFFICIENT as doesn't matter however we draw the rectangle we can always find the vertices
If the longer side is base then while using : tan (theta) = slope = height/base we will have height = base * slope = 12 * 1.5, which is not possible as the longer side is 12, so this side cannot be longer than 12
If the longer side is height then while using : tan (theta) = slope = height/base we will have base = height / slope = 12 / 1.5, so Area = height * base = 12 * 12 / 1.5
So, SUFFICIENT

I think answer should be B?

desaichinmay22
What is the area of rectangle ABCD?

(1) Two of the vertices of rectangle ABCD lie on the X-axis

(2) The longer side of the rectangle measures 12 cms and one of the diagonals has a slope of 1.5

For (2) consider the following case:
Attachment:
Untitled.png
Show more


Bunuel: Hello sir, i have a query ...How come you are considering thr equation of the line as y=mx........... It can be also of the form Y=mX +c..............
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 Apr 2026
Posts: 109,928
Own Kudos:
811,542
Given Kudos: 105,914
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: 109,928
Kudos: 811,542
What is the area of rectangle ABCD? 17 May 2019, 00:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avikroy

Bunuel: Hello sir, i have a query ...How come you are considering thr equation of the line as y=mx........... It can be also of the form Y=mX +c..............
Show more

In my post I showed why the second statement is not sufficient by drawing two rectangles with different areas. You are right, the diagonal could be on any line with the slope 3/2, so it's on the line y = 3/2*x + c. I just showed two rectangles with two different areas having their diagonals on y = 3/2*x (one of many possibilities), which is enough to prove insufficiency.
Moderators:
Bunuel
Math Expert
109928 posts
kingbucky
498 posts
Gmat860sanskar
212 posts