GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Feb 2019, 09:08

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

The water tank shown above is a prism, consisting of 3 rectangular fac

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 772
The water tank shown above is a prism, consisting of 3 rectangular fac  [#permalink]

Show Tags

New post 05 Feb 2019, 11:03
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

40% (02:58) correct 60% (03:31) wrong based on 30 sessions

HideShow timer Statistics

Image

The water tank shown is a prism with 3 rectangular faces and 2 equilateral triangular faces. Each triangular face has height 6, and the water surface is parallel to the face ABCD. If the volume occupied by the water is half the volume of the water tank, which of the following is closest to the length of x ?

(A) 1.73
(B) 2.83
(C) 3.46
(D) 4.24
(E) 5.20


GMATH practice exercise (Quant Class 17)

Attachment:
05-Feb19-5z.gif
05-Feb19-5z.gif [ 25.11 KiB | Viewed 369 times ]

_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Manager
Manager
User avatar
G
Status: Manager
Joined: 27 Oct 2018
Posts: 165
Location: Malaysia
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)
GMAT ToolKit User
Re: The water tank shown above is a prism, consisting of 3 rectangular fac  [#permalink]

Show Tags

New post 05 Feb 2019, 14:14
2
volume of the prism tank = area of side triangle * length of tank

volume of water = \(\frac{1}{2}\) volume of whole tank

(area of triangle with height x)*(length of tank) = \(\frac{1}{2}\) (area of triangle with height 6)*(length of tank)

(area of triangle with height x) = \(\frac{1}{2}\) (area of triangle with height 6)

because the water surface is parallel to the ABCD face of the tank, the two triangles are similar (AAA)

similar triangles have side ratio = \(\frac{x}{y}\) and area ratio of \(\frac{x^2}{y^2}\)

in our case, the ratio of areas = \(\frac{(area-of-triangle-with-height-x)}{(area-of-triangle-with-height-6)}\) = \(\frac{1}{2}\) = \(\frac{x^2}{y^2}\)

so the ratio of sides = \(\frac{x}{y}\) = \(\frac{1}{\sqrt{2}}\)

knowing that the bigger triangle has height 6, then \(x\) = \(\frac{6}{\sqrt{2}}\) = \(\frac{6\sqrt[]{2}}{2}\) = \(3\sqrt[]{2}\) = \(3*1.4\) \(\approx\) \(4.2\)

So D
_________________

...Thanks for KUDOS
Image

GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 772
The water tank shown above is a prism, consisting of 3 rectangular fac  [#permalink]

Show Tags

New post 06 Feb 2019, 05:07
fskilnik wrote:
Image

The water tank shown is a prism with 3 rectangular faces and 2 equilateral triangular faces. Each triangular face has height 6, and the water surface is parallel to the face ABCD. If the volume occupied by the water is half the volume of the water tank, which of the following is closest to the length of x ?

(A) 1.73
(B) 2.83
(C) 3.46
(D) 4.24
(E) 5.20

GMATH practice exercise (Quant Class 17)


Very good, Mahmoudfawzy83 ! Congrats (kudos!) and thank you for your contribution!

Let me offer our "official solution": (It is only different of yours in the "wording".)

Image


\(?\,\, \cong \,\,x\)


\(\frac{1}{2}\,\, = \,\,\frac{{{V_{{\text{water}}}}}}{{{V_{{\text{tank}}}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{{S_{\Delta EFG}} \cdot FH}}{{{S_{\Delta EAD}} \cdot DC}}\,\,\,\mathop = \limits^{FH = DC} \,\,\,\frac{{{S_{\Delta EFG}}}}{{{S_{\Delta EAD}}}}\,\,\,\mathop = \limits^{\left( {**} \right)} \,\,\,{\left( {\frac{x}{6}} \right)^2}\,\,\,\,\, \Rightarrow \,\,\,\,\,\frac{x}{6} = \frac{{\sqrt 2 }}{2}\)

\(\left( * \right)\,\,{\text{formula}}\,\,{\text{given}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {**} \right)\,\,{\text{similarity}}\,\,{\text{property}}\)


\(? = x\,\, = \,\,3\sqrt 2 \,\, \cong \,\,3 \cdot 1.41 = 4.23\)


The correct answer is therefore (D).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Intern
Intern
avatar
B
Joined: 22 Oct 2017
Posts: 13
Re: The water tank shown above is a prism, consisting of 3 rectangular fac  [#permalink]

Show Tags

New post 08 Feb 2019, 02:32
fskilnik wrote:

Very good, Mahmoudfawzy83 ! Congrats (kudos!) and thank you for your contribution!

Let me offer our "official solution": (It is only different of yours in the "wording".)

Image


\(?\,\, \cong \,\,x\)


\(\frac{1}{2}\,\, = \,\,\frac{{{V_{{\text{water}}}}}}{{{V_{{\text{tank}}}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{{S_{\Delta EFG}} \cdot FH}}{{{S_{\Delta EAD}} \cdot DC}}\,\,\,\mathop = \limits^{FH = DC} \,\,\,\frac{{{S_{\Delta EFG}}}}{{{S_{\Delta EAD}}}}\,\,\,\mathop = \limits^{\left( {**} \right)} \,\,\,{\left( {\frac{x}{6}} \right)^2}\,\,\,\,\, \Rightarrow \,\,\,\,\,\frac{x}{6} = \frac{{\sqrt 2 }}{2}\)

\(\left( * \right)\,\,{\text{formula}}\,\,{\text{given}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {**} \right)\,\,{\text{similarity}}\,\,{\text{property}}\)


\(? = x\,\, = \,\,3\sqrt 2 \,\, \cong \,\,3 \cdot 1.41 = 4.23\)



Could you gently explain me the ** passage called "similar property"?
Manager
Manager
User avatar
G
Status: Manager
Joined: 27 Oct 2018
Posts: 165
Location: Malaysia
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)
GMAT ToolKit User
Re: The water tank shown above is a prism, consisting of 3 rectangular fac  [#permalink]

Show Tags

New post 08 Feb 2019, 05:08
Hi paolodeppa

The triangles we are comparing between are similar to each other.
the meaning of 'similar triangles' is that they their corresponding angles are equal.
in our case both triangles has angles of 60 degree each.
If two triangles are proved to be similar, the the ratio between any side and its corresponding side in the other triangle = \(\frac{x}{y}\)
and it can be deduced the ratio between the ares of the two triangles = \(\frac{x^2}{y^2}\)

try revising this link, it is very helpful to grasp the fundamentals:
https://gmatclub.com/forum/math-triangles-87197.html

similar triangles is an important and helpful trick to master for the GMAT. the following links can help you benefit from its applications:
https://gmatclub.com/forum/what-austin-powers-can-teach-you-about-similar-triangles-193035.html
https://gmatclub.com/forum/determining-the-area-of-similar-triangles-on-the-gmat-193413.html
https://gmatclub.com/forum/looking-for-similar-triangles-on-the-gmat-193036.html
_________________

...Thanks for KUDOS
Image

GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 772
Re: The water tank shown above is a prism, consisting of 3 rectangular fac  [#permalink]

Show Tags

New post 08 Feb 2019, 05:21
paolodeppa wrote:
Could you gently explain me the ** passage called "similar property"?

Hi, paolodeppa !

The property: the ratio of areas of two similar polygons is equal to the square of the ratio of similarity of these figures!

In our case, we have used that for the two similar triangles related to (any) one of the triangular faces, as correctly explained by Mahmoudfawzy83 !

Another interesting question/detail: where we use the EQUILATERAL condition presented in the stem?

Answer: to give (unique) meaning to the statement "Each triangular face has height 6". In equilateral triangles, ALL heights are equal!

I hope my explanations were useful.

Regards and success in your studies (to both of you)!
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

GMAT Club Bot
Re: The water tank shown above is a prism, consisting of 3 rectangular fac   [#permalink] 08 Feb 2019, 05:21
Display posts from previous: Sort by

The water tank shown above is a prism, consisting of 3 rectangular fac

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.