Last visit was: 12 Jul 2025, 07:00 It is currently 12 Jul 2025, 07:00
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,636
Own Kudos:
Given Kudos: 98,172
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,636
Kudos: 740,668
 [74]
4
Kudos
Add Kudos
70
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,636
Own Kudos:
Given Kudos: 98,172
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,636
Kudos: 740,668
 [26]
14
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
User avatar
NickHalden
Joined: 15 Feb 2012
Last visit: 19 Jun 2016
Posts: 71
Own Kudos:
425
 [8]
Given Kudos: 216
Status:Perspiring
Concentration: Marketing, Strategy
GPA: 3.6
WE:Engineering (Computer Software)
6
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
General Discussion
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,636
Own Kudos:
740,668
 [5]
Given Kudos: 98,172
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,636
Kudos: 740,668
 [5]
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
Bunuel
What is x in the diagram below?


A. 12/7
B. 24/7
C. 36/7
D. 48/7
E. 72/7


Kudos for a correct solution.

Attachment:
2015-07-02_1254.png

MANHATTAN GMAT OFFICIAL SOLUTION:

You can calculate the area of the triangle, using the side of length 12 as the base:
(1/2)(12)(3) = 18

Next, use the side of length 7 as the base and write the equation for the area:
(1/2)(7)(x) = 18

Now solve for x, the unknown height:
7x = 36
x = 36/7

Answer: C.
User avatar
ArunpriyanJ
Joined: 03 Aug 2015
Last visit: 06 Jun 2017
Posts: 35
Own Kudos:
Given Kudos: 219
Concentration: Strategy, Technology
GMAT 1: 680 Q48 V35
Products:
GMAT 1: 680 Q48 V35
Posts: 35
Kudos: 17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Bunuel
What is x in the diagram below?


A. 12/7
B. 24/7
C. 36/7
D. 48/7
E. 72/7


Kudos for a correct solution.

Attachment:
2015-07-02_1254.png

MANHATTAN GMAT OFFICIAL SOLUTION:

You can calculate the area of the triangle, using the side of length 12 as the base:
(1/2)(12)(3) = 18

Next, use [color=#ff0000]the side of length 7 as the base and write the equation for the area:
(1/2)(7)(x) = 18
[/color]
Now solve for x, the unknown height:
7x = 36
x = 36/7

Answer: C.

Hi Bunel,
Could you kindly explain the highlighted portion in detail?
I am not able to understand why you have equated that to 18?
Thanks,
Arun
User avatar
ENGRTOMBA2018
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,328
Own Kudos:
3,787
 [1]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
GMAT 1: 750 Q49 V44
Posts: 2,328
Kudos: 3,787
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
ArunpriyanJ
Bunuel
Bunuel
What is x in the diagram below?


A. 12/7
B. 24/7
C. 36/7
D. 48/7
E. 72/7


Kudos for a correct solution.

Attachment:
2015-07-02_1254.png

MANHATTAN GMAT OFFICIAL SOLUTION:

You can calculate the area of the triangle, using the side of length 12 as the base:
(1/2)(12)(3) = 18

Next, use [color=#ff0000]the side of length 7 as the base and write the equation for the area:
(1/2)(7)(x) = 18
[/color]
Now solve for x, the unknown height:
7x = 36
x = 36/7

Answer: C.

Hi Bunel,
Could you kindly explain the highlighted portion in detail?
I am not able to understand why you have equated that to 18?
Thanks,
Arun

In the given triangle with solid lines, the area of the triangle = 0.5*base*height.

Now you need to understand that the height can be from any of the 3 vertices and the base will then be the side to which the height is perpendicular to.

In this case, the line with length 3 is the height for the base with length 12, giving you area of the triangle = 0.5*12*3 = 18

Similarly, for the same triangle, the area will also be = 0.5*7*x ...( as the side with x length is perpendicular to the 'base' with length 7 units).

For a particular triangle, the area MUST be the same irrespective of what base or height combination you choose.

Thus , you equate, 0.5*7*x = 18 ---> x = 36/7.

Hope this helps.
avatar
karanrai1991
Joined: 13 Mar 2016
Last visit: 07 Feb 2019
Posts: 3
Own Kudos:
4
 [1]
Given Kudos: 17
Posts: 3
Kudos: 4
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I was trying to solve it with the solid line's length=7, will it be more clearly marked in the exam? After going through the solution i realized that they meant the Solid+dotted line length is equal to 7
avatar
frrcattack
Joined: 17 Dec 2017
Last visit: 09 Dec 2020
Posts: 11
Own Kudos:
Given Kudos: 29
Location: United States
GMAT 1: 720 Q49 V40
GPA: 3.31
WE:Consulting (Consulting)
GMAT 1: 720 Q49 V40
Posts: 11
Kudos: 16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunuel,

I am confused about what the 7 is referring to. Is 7 the solid line? If so, how are we using that 7 as a base of the imaginary triangle drawn by the dotted lines? Also, why are we able to reference the area of 18 from the triangle with solid lines to help us determine the base of the dotted line triangle? This one is driving me crazy. Thank you in advance for your reply!
avatar
frrcattack
Joined: 17 Dec 2017
Last visit: 09 Dec 2020
Posts: 11
Own Kudos:
Given Kudos: 29
Location: United States
GMAT 1: 720 Q49 V40
GPA: 3.31
WE:Consulting (Consulting)
GMAT 1: 720 Q49 V40
Posts: 11
Kudos: 16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
frrcattack
What is x in the diagram below?


A. 12/7
B. 24/7
C. 36/7
D. 48/7
E. 72/7

Hi Bunuel,

I am confused about what the 7 is referring to. Is 7 the solid line? If so, how are we using that 7 as a base of the imaginary triangle drawn by the dotted lines? Also, why are we able to reference the area of 18 from the triangle with solid lines to help us determine the base of the dotted line triangle? This one is driving me crazy. Thank you in advance for your reply!



CE = 3;
AC = 7;
AB = 12;
BD = x.

Consider AB as a base of triangle ABC. The are = 1/2*base*height = 1/2*AB*CE = 1/2*12*3 = 18.

Now, consider AC as a base of the SAME triangle ABC. In this case the height is BD (perpendicular from B to extended base AC) The are = 1/2*base*height = 1/2*AC*BD = 1/2*7*x = 18 --> 36/7.

Answer: C.

Hope it's clear.


Attachment:
Untitled.png

Wow... thank you Bunuel! Makes much more sense.
User avatar
rahul16singh28
Joined: 31 Jul 2017
Last visit: 09 Jun 2020
Posts: 431
Own Kudos:
493
 [5]
Given Kudos: 752
Location: Malaysia
GPA: 3.95
WE:Consulting (Energy)
Posts: 431
Kudos: 493
 [5]
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is x in the diagram below?


A. 12/7
B. 24/7
C. 36/7
D. 48/7
E. 72/7

Kudos for a correct solution.

Attachment:
The attachment 2015-07-02_1254.png is no longer available

I solved it this way...

Triangle DBA is Similar to triangle CEA
So, \(\frac{3}{x} = \frac{7}{12}\), \(x = \frac{36}{7}.\)
Attachments

Untitled.png
Untitled.png [ 11.59 KiB | Viewed 22284 times ]

User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,755
Own Kudos:
34,060
 [4]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,755
Kudos: 34,060
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
What is x in the diagram below?


A. 12/7
B. 24/7
C. 36/7
D. 48/7
E. 72/7

Kudos for a correct solution.

Attachment:
2015-07-02_1254.png

I added some letters to help guide the solution.



Area of triangle = (1/2)(base)(height)
IMPORTANT CONCEPT: we can use ANY of the three sides as our base.

So, for example, if we want to find the area of triangle ABC, we can use side AB as the base, or we can use side AC as the base, or we can use side BC as the base.

If we use side AB as the base, then the base has length 12 and the height is 3
So, area of triangle ABC = (1/2)(12)(3)

If we use side AC as the base, then the base has length 7 and the height is x
So, area of triangle ABC = (1/2)(7)(x)

IMPORTANT: If we use side AB as the base, the area of the triangle will be the same as the area we get if we use side AC as the base.

So, (1/2)(12)(3) = (1/2)(7)(x) [solve for x]
Divide both sides by 1/2 to get: (12)(3) = (7)(x)
Divide both sides by 7 to get: 36/7 = x

Answer: C

Cheers,
Brent
User avatar
Princ
Joined: 22 Feb 2018
Last visit: 04 May 2025
Posts: 352
Own Kudos:
Given Kudos: 34
Posts: 352
Kudos: 881
Kudos
Add Kudos
Bookmarks
Bookmark this Post
OA: C

Sin A =\(\frac{3}{7}=\frac{x}{12}\)
x=\(\frac{36}{7}\)

Sent from my XT1068 using GMAT Club Forum mobile app
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,755
Own Kudos:
34,060
 [4]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,755
Kudos: 34,060
 [4]
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
What is x in the diagram below?


A. 12/7
B. 24/7
C. 36/7
D. 48/7
E. 72/7

Kudos for a correct solution.

Attachment:
2015-07-02_1254.png

A student asked whether we can use similar triangles to answer this question. So.....

First add some letters to the diagram to get:


At this point, we can see that we have two similar triangles:

That is, ∆ACE is similar to ∆ADB

We can see that side AE corresponds to side AB (since both are hypotenuses)
And we can see that side CE corresponds to side BD (since both sides are opposite the angle denoted by the circle)

Key concept: With any two SIMILAR triangles, the ratios of corresponding sides will be equal.
We can write: AE/AB = CE/BD
Replace with actual lengths: 12/7 = x/3
Cross multiply to get: 7x = 36
Solve: x = 36/7

Answer: C

Cheers,
Brent
User avatar
TestPrepUnlimited
Joined: 17 Sep 2014
Last visit: 30 Jun 2022
Posts: 1,226
Own Kudos:
1,067
 [1]
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Expert
Expert reply
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Posts: 1,226
Kudos: 1,067
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is x in the diagram below?


A. 12/7
B. 24/7
C. 36/7
D. 48/7
E. 72/7

Kudos for a correct solution.

Attachment:
The attachment 2015-07-02_1254.png is no longer available

We can start by focusing on similar triangles when there are no obvious lengths to evaluate. Note using the labeling in the attachment, ACE and ABD are similar triangles. This means we have this nice ratio of AC/CE = AB/BD. Then BD = 12*3/7 = 36/7. The answer is C.
Attachments

triangle.png
triangle.png [ 11.59 KiB | Viewed 15313 times ]

User avatar
Kimberly77
Joined: 16 Nov 2021
Last visit: 07 Sep 2024
Posts: 440
Own Kudos:
Given Kudos: 5,899
Location: United Kingdom
GMAT 1: 450 Q42 V34
Products:
GMAT 1: 450 Q42 V34
Posts: 440
Kudos: 42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
BrentGMATPrepNow
Bunuel
What is x in the diagram below?


A. 12/7
B. 24/7
C. 36/7
D. 48/7
E. 72/7

Kudos for a correct solution.

Attachment:
2015-07-02_1254.png

I added some letters to help guide the solution.



Area of triangle = (1/2)(base)(height)
IMPORTANT CONCEPT: we can use ANY of the three sides as our base.

So, for example, if we want to find the area of triangle ABC, we can use side AB as the base, or we can use side AC as the base, or we can use side BC as the base.

If we use side AB as the base, then the base has length 12 and the height is 3
So, area of triangle ABC = (1/2)(12)(3)

If we use side AC as the base, then the base has length 7 and the height is x
So, area of triangle ABC = (1/2)(7)(x)

IMPORTANT: If we use side AB as the base, the area of the triangle will be the same as the area we get if we use side AC as the base.

So, (1/2)(12)(3) = (1/2)(7)(x) [solve for x]
Divide both sides by 1/2 to get: (12)(3) = (7)(x)
Divide both sides by 7 to get: 36/7 = x

Answer: C

Cheers,
Brent

Hi BrentGMATPrepNow, If we use side AC as the base in triangle ABC, not sure why the height is not 3 here but x outside of triangle ABC? As thought x is the height for triangle e.g AEB? Then dotted line CE part will be missing as base if AC/E is use as the base for triangle AEB? Have I missed something here? Thanks Brent
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,755
Own Kudos:
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,755
Kudos: 34,060
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Kimberly77

Hi BrentGMATPrepNow, If we use side AC as the base in triangle ABC, not sure why the height is not 3 here but x outside of triangle ABC? As thought x is the height for triangle e.g AEB? Then dotted line CE part will be missing as base if AC/E is use as the base for triangle AEB? Have I missed something here? Thanks Brent


The height of a triangle is always perpendicular to the triangle's base.
If we choose side AC as the base, DC (with length 3) is perpendicular to the base AC, whereas BE (with length 5) is NOT perpendicular to the base AC.
User avatar
Kimberly77
Joined: 16 Nov 2021
Last visit: 07 Sep 2024
Posts: 440
Own Kudos:
Given Kudos: 5,899
Location: United Kingdom
GMAT 1: 450 Q42 V34
Products:
GMAT 1: 450 Q42 V34
Posts: 440
Kudos: 42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
BrentGMATPrepNow
Kimberly77

Hi BrentGMATPrepNow, If we use side AC as the base in triangle ABC, not sure why the height is not 3 here but x outside of triangle ABC? As thought x is the height for triangle e.g AEB? Then dotted line CE part will be missing as base if AC/E is use as the base for triangle AEB? Have I missed something here? Thanks Brent


The height of a triangle is always perpendicular to the triangle's base.
If we choose side AC as the base, DC (with length 3) is perpendicular to the base AC, whereas BE (with length 5) is NOT perpendicular to the base AC.

Understand now thanks BrentGMATPrepNow. height CD is perpendicular to base AB and BE(x) is perpendicular to base AC.
User avatar
EthanTheTutor
Joined: 08 Jun 2022
Last visit: 11 Jul 2025
Posts: 38
Own Kudos:
Given Kudos: 12
Location: United States
GMAT 1: 780 Q51 V48
GMAT 1: 780 Q51 V48
Posts: 38
Kudos: 66
Kudos
Add Kudos
Bookmarks
Bookmark this Post
You're all making this too complicated.

Problem solving questions are, by default, drawn to scale.

x is clearly bigger than 3, and smaller than 7. It appears to be something like halfway between them. This fits answer C.
Moderators:
Math Expert
102636 posts
PS Forum Moderator
688 posts