Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59229

The length, width, and height of a rectangular box, in centimeters, ar
[#permalink]
Show Tags
26 Apr 2019, 03:25
Question Stats:
53% (02:15) correct 47% (01:57) wrong based on 423 sessions
HideShow timer Statistics
The length, width, and height of a rectangular box, in centimeters, are L, W, and H. If the volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters, what is the value of V/A ? (1) At least 2 of L, W, and H are equal to 5. (2) L, W, and H all have the same value. DS50351.01 OG2020 NEW QUESTION
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



examPAL Representative
Joined: 07 Dec 2017
Posts: 1155

Re: The length, width, and height of a rectangular box, in centimeters, ar
[#permalink]
Show Tags
26 Apr 2019, 13:28
Using the Alternative approach, we'll try to find two different possible numeric results in order to eliminate the wrong answers. Statement (1): if the dimensions are 5,5,5 then V=5³ and A=6x5x5. If the dimensions are 5,5,6 then V=5x5x6 and A=4x5x5+2x5x6. The former gives us 5/6 and the latter 150/160, which is not the same. Answer choices (A) and (D) are eliminated. Statement (2): we already saw that if the dimensions are 5,5,5 then V=5³ and A=6x5x5. If the dimensions are 1,1,1 then V=1³ and A=6x1x1. While the former gives 5/6, the latter gives 1/6. Answer (B) is also eliminated. Combining both statements gives only one option (dimensions 5,5,5), so there's only one possible value for V/A. The correct answer is (C). Posted from my mobile device
_________________



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5310
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: The length, width, and height of a rectangular box, in centimeters, ar
[#permalink]
Show Tags
27 Apr 2019, 10:42
Bunuel wrote: The length, width, and height of a rectangular box, in centimeters, are L, W, and H. If the volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters, what is the value of V/A ?
(1) At least 2 of L, W, and H are equal to 5. (2) L, W, and H all have the same value.
DS50351.01 OG2020 NEW QUESTION v= l*w*h TSA= 2*(lw+wh+hl) #1 At least 2 of L, W, and H are equal to 5. v=25h TSA= 2*(50+5h) v/TSA = 25h/2*(50+5h) h not given insufficeint #2 L, W, and H all have the same value v=1 or say 125 if 5 TSA= 6 at 1 and 30 when ratio 1/6 or 125/30 ; 25/6 insufficient combining 1 & 2 we take v=125 and tsa = 30 so ratio 25/6 IMO C



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15498
Location: United States (CA)

Re: The length, width, and height of a rectangular box, in centimeters, ar
[#permalink]
Show Tags
14 May 2019, 19:07
Hi All, We're told that the length, width, and height of a rectangular box, in centimeters, are L, W, and H, respectively, the VOLUME of this box is V cubic centimeters and the TOTAL SURFACE AREA of the 6 sides of this box is A square centimeters. We're asked for the value of V/A. This question is based around some standard Geometry formulas for solids and can be solved by TESTing VALUES. To start, Volume of a rectangular solid is V = (L)(W)(H) and Total Surface area is SA = 2(L)(W) + 2(L)(H) + 2(W)(H). (1) At least 2 of L, W, and H are equal to 5. Fact 1 tells us that 2 (or perhaps all 3) of the dimensions are equal to 5, but that still leads to a number of different answers to the question. IF... L = 5, W = 5, H = 5, then the Volume = (5)(5)(5) = 125 and Total Surface Area = (2)(5)(5) + (2)(5)(5) + (2)(5)(5) = 150... so the answer to the question is 125/150 = 5/6. L = 5, W = 5, H = 1, then the Volume = (5)(5)(1) = 25 and Total Surface Area = (2)(5)(5) + (2)(5)(1) + (2)(5)(1) = 70... so the answer to the question is 25/70 = 5/14. Fact 1 is INSUFFICIENT (2) L, W, and H all have the SAME value. Fact 2 tells us that we're actually dealing with a CUBE, but the answer to the question will still vary depending on the side length. IF.... L = 5, W = 5, H = 5, then the Volume = (5)(5)(5) = 125 and Total Surface Area = (2)(5)(5) + (2)(5)(5) + (2)(5)(5) = 150... so the answer to the question is 125/150 = 5/6. L = 1, W = 1, H = 1, then the Volume = (1)(1)(1) = 1 and Total Surface Area = (2)(1)(1) + (2)(1)(1) + (2)(1)(1) = 6... so the answer to the question is 1/6. Fact 2 is INSUFFICIENT Combined, we know... At least 2 of L, W, and H are equal to 5. L, W, and H all have the SAME value. When combining the two Facts, it's clear that we're dealing with a cube with a side length of 5, so the answer to the question is 5/6. Combined, SUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3142

Re: The length, width, and height of a rectangular box, in centimeters, ar
[#permalink]
Show Tags
15 May 2019, 00:26
Solution Steps 1 & 2: Understand Question and Draw InferencesIn this question, we are given • The length, width, and height of a rectangular box, in centimetres, are L, W, and H. • The volume of this box is V cubic centimetres and the total area of the 6 sides of this box is A square centimetres. We need to determine As the given box is a rectangular one, we can say • Volume V = LWH • Total area of 6 sides = A = 2(LW + LH + WH) With this understanding, let us now analyse the individual statements. Step 3: Analyse Statement 1As per the information given in statement 1, at least 2 of L, W, and H are equal to 5. • However, we do not know the exact values of each of them. Hence, statement 1 is not sufficient to answer the question. Step 4: Analyse Statement 2As per the information given in statement 2, L, W, and H all have the same value. If we assume each of them is equal to ‘a’, then we can write • V/A = a^3/(2(3a^2)) = a^3/(6a^2 ) = a/6 • Therefore, we need to know the value of ‘a’ to get the answer. Hence, statement 2 is not sufficient to answer the question. Step 5: Combine Both Statements Together (If Needed)Combining information from both statements, we can say As we know the value of each of them, we can determine the value of V/A. Hence, the correct answer is option C.
_________________



Manager
Joined: 14 Apr 2017
Posts: 70
Location: Hungary
WE: Education (Education)

Re: The length, width, and height of a rectangular box, in centimeters, ar
[#permalink]
Show Tags
16 May 2019, 13:37
Bunuel wrote: The length, width, and height of a rectangular box, in centimeters, are L, W, and H. If the volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters, what is the value of V/A ?
(1) At least 2 of L, W, and H are equal to 5. (2) L, W, and H all have the same value.
DS50351.01 OG2020 NEW QUESTION The original question: \(V/A=?\) 1) We know that at least two dimensions of the rectangular box have length of 5. Let \(x\) be its unknown dimension. \(\frac{V}{A}=\frac{5\cdot 5\cdot x}{2\cdot 5\cdot 5+2\cdot 5\cdot x+2\cdot 5\cdot x}=\frac{25}{50/x+20}\) Since \(x\) can be any positive real number, we can't get a unique value to answer the original question. \(\implies\) Insufficient2) We know that all of its dimensions have the same value, so it is a cube. Let \(a\) be the unknown side length of this cube. \(\frac{V}{A}=\frac{a^3}{6a^2}=\frac{a}{6}\) Since \(a\) can be any positive real number, we can't get a unique value to answer the original question. \(\implies\) Insufficient1&2) We can infer that \(a=5\), so \(V/A=5/6\). Thus, the answer to the original question is a unique value. \(\implies\) SufficientAnswer: C
_________________
My book with my solutions to all 230 PS questions in OG2018:Zoltan's solutions to OG2018 PS




Re: The length, width, and height of a rectangular box, in centimeters, ar
[#permalink]
16 May 2019, 13:37






