Oct 14 08:00 PM PDT  11:00 PM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R2.**Limited for the first 99 registrants. Register today! Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

The water tank shown above is a prism, consisting of 3 rectangular fac
[#permalink]
Show Tags
05 Feb 2019, 12:03
Question Stats:
39% (02:48) correct 61% (03:27) wrong based on 38 sessions
HideShow timer Statistics
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:
05Feb195z.gif [ 25.11 KiB  Viewed 530 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Director
Status: Manager
Joined: 27 Oct 2018
Posts: 669
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)

Re: The water tank shown above is a prism, consisting of 3 rectangular fac
[#permalink]
Show Tags
05 Feb 2019, 15:14
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 = \(\frac{(areaoftrianglewithheightx)}{(areaoftrianglewithheight6)}\) = \(\frac{1}{2}\) = \(\frac{x^2}{y^2}\) 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
_________________



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

The water tank shown above is a prism, consisting of 3 rectangular fac
[#permalink]
Show Tags
06 Feb 2019, 06:07
fskilnik wrote: 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".) \(?\,\, \cong \,\,x\) \(\frac{1}{2}\,\, = \,\,\frac{{{V_{{\text{water}}}}}}{{{V_{{\text{tank}}}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{{S_{\Delta EFG}} \cdot FH}}{{{S_{\Delta EAD}} \cdot DC}}\,\,\,\mathop = \limits^{FH = DC} \,\,\,\frac{{{S_{\Delta EFG}}}}{{{S_{\Delta EAD}}}}\,\,\,\mathop = \limits^{\left( {**} \right)} \,\,\,{\left( {\frac{x}{6}} \right)^2}\,\,\,\,\, \Rightarrow \,\,\,\,\,\frac{x}{6} = \frac{{\sqrt 2 }}{2}\) \(\left( * \right)\,\,{\text{formula}}\,\,{\text{given}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {**} \right)\,\,{\text{similarity}}\,\,{\text{property}}\) \(? = x\,\, = \,\,3\sqrt 2 \,\, \cong \,\,3 \cdot 1.41 = 4.23\) 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 highlevel "quant" preparation starts here: https://gmath.net



Intern
Joined: 22 Oct 2017
Posts: 19

Re: The water tank shown above is a prism, consisting of 3 rectangular fac
[#permalink]
Show Tags
08 Feb 2019, 03:32
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".) \(?\,\, \cong \,\,x\) \(\frac{1}{2}\,\, = \,\,\frac{{{V_{{\text{water}}}}}}{{{V_{{\text{tank}}}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{{S_{\Delta EFG}} \cdot FH}}{{{S_{\Delta EAD}} \cdot DC}}\,\,\,\mathop = \limits^{FH = DC} \,\,\,\frac{{{S_{\Delta EFG}}}}{{{S_{\Delta EAD}}}}\,\,\,\mathop = \limits^{\left( {**} \right)} \,\,\,{\left( {\frac{x}{6}} \right)^2}\,\,\,\,\, \Rightarrow \,\,\,\,\,\frac{x}{6} = \frac{{\sqrt 2 }}{2}\) \(\left( * \right)\,\,{\text{formula}}\,\,{\text{given}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {**} \right)\,\,{\text{similarity}}\,\,{\text{property}}\) \(? = x\,\, = \,\,3\sqrt 2 \,\, \cong \,\,3 \cdot 1.41 = 4.23\) Could you gently explain me the ** passage called "similar property"?



Director
Status: Manager
Joined: 27 Oct 2018
Posts: 669
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)

Re: The water tank shown above is a prism, consisting of 3 rectangular fac
[#permalink]
Show Tags
08 Feb 2019, 06:08
Hi paolodeppaThe 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/mathtriangles87197.htmlsimilar 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/whataustinpowerscanteachyouaboutsimilartriangles193035.htmlhttps://gmatclub.com/forum/determiningtheareaofsimilartrianglesonthegmat193413.htmlhttps://gmatclub.com/forum/lookingforsimilartrianglesonthegmat193036.html
_________________



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: The water tank shown above is a prism, consisting of 3 rectangular fac
[#permalink]
Show Tags
08 Feb 2019, 06:21
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 highlevel "quant" preparation starts here: https://gmath.net




Re: The water tank shown above is a prism, consisting of 3 rectangular fac
[#permalink]
08 Feb 2019, 06:21






