NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 10:49 It is currently 26 Apr 2024, 10:49
Decision Tracker
My Rewards
New posts
New comers' posts

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

The length, width, and height of a rectangular box, in centimeters, ar

SORT BY:
Date
Kudos
Tags:
Difficulty: 605-655 Levelx   Geometryx               
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619208 [89]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   26 Apr 2019, 03:25
3
Kudos
86
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

66% (02:13) correct 34% (02:02) wrong based on 3196 sessions
Hide Show 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
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
ZoltanBP
Manager
Manager
Joined: 14 Apr 2017
Posts: 79
Own Kudos [?]: 863 [28]
Given Kudos: 565
Location: Hungary
GMAT 1: 760 Q50 V42
WE:Education (Education)
Send PM
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   16 May 2019, 13:37
19
Kudos
9
Bookmarks
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. \(\implies\) Insufficient

2) 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. \(\implies\) Insufficient

1&2) We can infer that \(a=5\), so \(V/A=5/6\). Thus, the answer to the original question is a unique value. \(\implies\) Sufficient

Answer: C
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21846
Own Kudos [?]: 11668 [8]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   14 May 2019, 19:07
4
Kudos
3
Bookmarks
Expert Reply
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:
Show Spoiler
C


GMAT assassins aren't born, they're made,
Rich
General Discussion
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16844 [3]
Given Kudos: 165
Send PM
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   15 May 2019, 00:26
2
Kudos
1
Bookmarks
Expert Reply

Solution


Steps 1 & 2: Understand Question and Draw Inferences
In 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
    • The value of V/A.

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 1
As 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 2
As 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
    • L = W = H = 5.
As we know the value of each of them, we can determine the value of V/A.
Hence, the correct answer is option C.

User avatar
P
DavidTutorexamPAL
examPAL Representative
Joined: 07 Dec 2017
Posts: 1050
Own Kudos [?]: 1777 [1]
Given Kudos: 26
Send PM
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   26 Apr 2019, 13:28
1
Bookmarks
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
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8020
Own Kudos [?]: 4098 [1]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   27 Apr 2019, 10:42
1
Kudos
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
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5962
Own Kudos [?]: 13391 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   24 Jul 2020, 07:00
1
Bookmarks
Expert Reply
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


Answer: Option C

Please check the step-by-step video solution



Subscribe to my YouTube Channel for FREE resource (1000+ Videos)



Subscribe Topic-wise UN-bundled Video course. CHECK FREE Sample Videos
User avatar
L
dabaobao
Director
Director
Joined: 24 Oct 2016
Posts: 583
Own Kudos [?]: 1322 [0]
Given Kudos: 143
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
GMAT 3: 690 Q48 V37
GMAT 4: 710 Q49 V38 (Online)
Send PM
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   14 Mar 2020, 16:12
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



LWH/(2(LW + WH + HL) = ?

1) Suppose L = W = 5

5*5*H/(2(5*5 + 5H + 5H)) = 25H/(2(25+10H) => Not Sufficient

2) L^3/(2(L^2 + L^2 + L^2) = L^3/(6L^2) = L/6 => Not Sufficient

1+2)
L = 6
Therefore, L/6 = 5/6 => Sufficient

ANSWER: C
User avatar
B
Tamalmallick13
Intern
Intern
Joined: 11 Aug 2019
Posts: 20
Own Kudos [?]: 3 [0]
Given Kudos: 15
Send PM
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   14 Mar 2020, 20:39
Why this question is tagged under 700 level. Can anybody explain?
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5962
Own Kudos [?]: 13391 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   24 Jul 2020, 07:02
Expert Reply
Tamalmallick13 wrote:
Why this question is tagged under 700 level. Can anybody explain?


Tamalmallick13

40% takers of this question have got wrong answer which is enough reason to tag it 700 level. :)

I am sure you are good and therefore you are finding it unworthy of 700.
User avatar
B
mrcentauri
Manager
Manager
Joined: 18 Feb 2017
Posts: 53
Own Kudos [?]: 12 [0]
Given Kudos: 28
Send PM
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   28 Aug 2020, 14:38
This question seems ambiguous, 2 of l, w and h ?

I mean they should retire this question for this reason alone. 2 of l can been 2 * l

This can be interpreted as either 2l or 2w = 5 or 2w and 2h =5

or it could be interpreted as 2l 2w and 2h =5 or 3l 3w and 3h =5

one of the worst questions i've ever seen, and this is coming from GMAC.
User avatar
P
MHIKER
Director
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 972
Own Kudos [?]: 4928 [0]
Given Kudos: 690
Concentration: Accounting
Send PM
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   30 Sep 2020, 11:01
Top Contributor
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 volume of Rectangular Solid = LHW
Area of 6 sides is = 2LH +2WH+2WL

1) We need to know all sides of the rectangle [ Insufficient]

2) L= W=H
So, this is a cube but we don't know any value for the variables. Insufficient.

V/A = 8/64 = 1/8


Considering both the options that this is cube and each side has unique value . Sufficient.

Ans. C.
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18764
Own Kudos [?]: 22060 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   14 May 2021, 06:57
Expert Reply
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

Solution:

Question Stem Analysis:

We need to determine the value of V/A. Notice that V = LWH and A = 2(LW + LH + WH).

Statement One Alone:

Without loss of generality, we can let L and W be 5. So, in terms of H, we have V = LWH = 5 x 5 x H = 25H, and A = 2(LW + LH + WH) = 2(5 x 5 + 5H + 5H) = 10(5 + 2H). Therefore, V/A = 25H/[10(5 + 2H)] = 5H/[2(5 + 2H)]. Notice that the value of the ratio changes as the value of H changes. For example, if H = 1, V/A = 5/14. However, if H = 2, V/A = 10/18 = 5/9. Statement one alone is not sufficient.

Statement Two Alone:

We can let L = W = H = s. So, in terms of s, we have V = LWH = s x s x s = s^3, and A = 2(LW + LH + WH) = 2(s x s + s x s + s x s) = 6s^2. Therefore, V/A = s^3 / 6s^2 = s/6. Notice again that the value of the ratio changes as the value of s changes. For example, if s = 1, V/A = 1/6. However, if s = 2, V/A = s/6 = 1/3. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we see that L = W = H = 5. From statement two, we have V/A = s/6. Therefore, s = 5 yields V/A = 5/6. Both statements together are sufficient.

Answer: C
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5962
Own Kudos [?]: 13391 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   23 May 2021, 07:47
Expert Reply
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


Solve the Official Questions more productively


Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course


Answer: Option C

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub :)
User avatar
D
avigutman
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 2287 [0]
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Send PM
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   11 Oct 2021, 05:10
Expert Reply
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
User avatar
DDPathak
Intern
Intern
Joined: 23 Jan 2022
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 5
Send PM
Re: The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   12 Oct 2022, 03:42
Do not kill your time
we know
V= LWH
A= 2(LW+LH+WH)
1) given 2 sides = 5 but no information about third so insufficient (AD out)
2) all sides are equal but value is not given so insufficient (B also out)
Combine
L= W= H=5 NOW all information are given we can determine value
And (c)

Posted from my mobile device
User avatar
B
Nrj0601
Intern
Intern
Joined: 15 May 2019
Status:Engineering Manager
Posts: 49
Own Kudos [?]: 11 [0]
Given Kudos: 27
Concentration: Leadership, Strategy
Schools: IIMA PGPX"20
WE:Engineering (Consulting)
Send PM
GMAT ToolKit User
The length, width, and height of a rectangular box, in centimeters, ar [#permalink] New post   22 Jul 2023, 01:36
V=LWH, A = 2(LH+WH+LW) | V/A = LWH/2(LH+WH+LW) = ?

1. 2 of L, W, H is 5.
either of the two is 5. Can't be solved. (Insufficient)

2. all are same, say x
putting values in V/A = x/6. (Insufficient)

Combining 1 and 2, we get 5/6. And C.
GMAT Club Bot
gmatclubot
The length, width, and height of a rectangular box, in centimeters, ar [#permalink]
22 Jul 2023, 01:36
Moderator:
Bunuel
Math Expert
92947 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions