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Intern  Joined: 20 May 2012
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Concentration: General Management, Finance
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The length, breadth and height of a room are in the ratio 3:2:1. If th  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 53% (02:28) correct 47% (02:40) wrong based on 237 sessions

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The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

(a) remain the same
(b) decrease by 13.64%
(c) decrease by 15%
(d) decrease by 18.75%
(e) decrease by 30%

Source: Gmat Cat By Nill (Peterson)

Originally posted by GMATnavigator on 21 Jul 2015, 09:52.
Last edited by Bunuel on 26 Nov 2018, 06:20, edited 2 times in total.
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Re: The length, breadth and height of a room are in the ratio 3:2:1. If th  [#permalink]

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GMATnavigator wrote:
The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

(a) remain the same
(b) decrease by 13.64%
(c) decrease by 15%
(d) decrease by 18.75%
(e) decrease by 30%

Source: Gmat Cat By Nill (Peterson)

Let, Initially
Length (L) = 6
Height (H) = 2
Total Area of Walls = 2(BH + LH) = 2*(4*2 + 6*2) = 2*(8+12) = 40

Then, Finally
Length (L) = 2*6 = 12
Breadth (B) = 4/2 = 2
Height (H) = 2/2 = 1
Total Area of Walls = 2(BH + LH) = 2*(2*1 + 12*1) = 2*(2+12) = 28

% change in Area of four walls = (Final Area - Initial Area)*100 / Initial Area

i.e. % change in Area of four walls = (28 - 40)*100 /40 = - 30% (Decrease)

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##### General Discussion
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Re: The length, breadth and height of a room are in the ratio 3:2:1. If th  [#permalink]

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1
GMATinsight wrote:
GMATnavigator wrote:
The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

(a) remain the same
(b) decrease by 13.64%
(c) decrease by 15%
(d) decrease by 18.75%
(e) decrease by 30%

Source: Gmat Cat By Nill (Peterson)

Let, Initially
Length (L) = 6
Height (H) = 2
Total Area of Walls = 2(BH + LH) = 2*(4*2 + 6*2) = 2*(8+12) = 40

Then, Finally
Length (L) = 2*6 = 12
Breadth (B) = 4/2 = 2
Height (H) = 2/2 = 1
Total Area of Walls = 2(BH + LH) = 2*(2*1 + 12*1) = 2*(2+12) = 28

% change in Area of four walls = (Final Area - Initial Area)*100 / Initial Area

i.e. % change in Area of four walls = (28 - 40)*100 /40 = - 30% (Decrease)

Hi GMATInsight,

Are we not taking the surface area of a rectangular box? in which case, the formula to calculate the surface area is 2(LH+BH+LB)?
Intern  Joined: 20 May 2012
Posts: 15
Concentration: General Management, Finance
GRE 1: Q168 V162
GPA: 3.82
WE: Research (Health Care)
Re: The length, breadth and height of a room are in the ratio 3:2:1. If th  [#permalink]

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1
jayanthjanardhan wrote:
GMATinsight wrote:
GMATnavigator wrote:
The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

(a) remain the same
(b) decrease by 13.64%
(c) decrease by 15%
(d) decrease by 18.75%
(e) decrease by 30%

Source: Gmat Cat By Nill (Peterson)

Let, Initially
Length (L) = 6
Height (H) = 2
Total Area of Walls = 2(BH + LH) = 2*(4*2 + 6*2) = 2*(8+12) = 40

Then, Finally
Length (L) = 2*6 = 12
Breadth (B) = 4/2 = 2
Height (H) = 2/2 = 1
Total Area of Walls = 2(BH + LH) = 2*(2*1 + 12*1) = 2*(2+12) = 28

% change in Area of four walls = (Final Area - Initial Area)*100 / Initial Area

i.e. % change in Area of four walls = (28 - 40)*100 /40 = - 30% (Decrease)

Hi GMATInsight,

Are we not taking the surface area of a rectangular box? in which case, the formula to calculate the surface area is 2(LH+BH+LB)?

Hi,
@Jayantijanardan,

I think question only asks for the walls in the question in which case, we should not account for the ceiling and the floor. So, i think GMATinsight approach is right!
Correct me experts if i am wrong!

Give kudos if you like!
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Re: The length, breadth and height of a room are in the ratio 3:2:1. If th  [#permalink]

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1
jayanthjanardhan wrote:
GMATinsight wrote:
GMATnavigator wrote:
The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

(a) remain the same
(b) decrease by 13.64%
(c) decrease by 15%
(d) decrease by 18.75%
(e) decrease by 30%

Source: Gmat Cat By Nill (Peterson)

Let, Initially
Length (L) = 6
Height (H) = 2
Total Area of Walls = 2(BH + LH) = 2*(4*2 + 6*2) = 2*(8+12) = 40

Then, Finally
Length (L) = 2*6 = 12
Breadth (B) = 4/2 = 2
Height (H) = 2/2 = 1
Total Area of Walls = 2(BH + LH) = 2*(2*1 + 12*1) = 2*(2+12) = 28

% change in Area of four walls = (Final Area - Initial Area)*100 / Initial Area

i.e. % change in Area of four walls = (28 - 40)*100 /40 = - 30% (Decrease)

Hi GMATInsight,

Are we not taking the surface area of a rectangular box? in which case, the formula to calculate the surface area is 2(LH+BH+LB)?

Question stem says " the total area of the four walls of the room will be???" Walls don't include the top and bottom surface with each area = L*B

I hope it helps!
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One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

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Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Manager  Joined: 08 Sep 2010
Posts: 54
Re: The length, breadth and height of a room are in the ratio 3:2:1. If th  [#permalink]

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GMATnavigator wrote:
The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

(a) remain the same
(b) decrease by 13.64%
(c) decrease by 15%
(d) decrease by 18.75%
(e) decrease by 30%

Give Kudos if you like this question Source: Gmat Cat By Nill (Peterson)

Definitely not a 700 level question.
Solution:
Initial dimension:
length = 3x, breadth = 2x, height = x
Area of four walls = 2*(l+b)*h = 2(3x+2x)*x = 10x^2

New Dimension:
length = 6x, breadth = x, height = x/2
Area of four walls = 2*(6x+x)*x/2 = 7x^2

% change = (new area - old area) / old area = [(7x^2 - 10x^2) / 10x^2 ] * 100 = -30%. Hence option E i.e. decrease by 30%
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Re: The length, breadth and height of a room are in the ratio 3:2:1. If th  [#permalink]

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well...damn...what a tricky one...I calculated to have 13.++ % decrease, but this is including top and bottom. balls...
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Re: The length, breadth and height of a room are in the ratio 3:2:1. If th  [#permalink]

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You are finding the surface area of the 4 walls. Not all 6 faces (no ceiling and floor) and not the volume area.

Surface area of first is 2+2+3+3 = 10
Surface area of second is 3+3+(1/2)+(1/2) = 7

10 to 7 is a 30% decrease
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Re: The length, breadth and height of a room are in the ratio 3:2:1. If th  [#permalink]

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4 walls = bh - hl - hl - bh so 2(bh+hl)
suppose l=30, b=20, h=10. total area = 2(200+300) = 1000
new lengths:
l=60, b=10, h=5. total area = 2(50+300) = 700.
decrease 300
300/1000 = 0.3 * 100% = 30% decrease
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The length, breadth and height of a room are in the ratio 3:2:1. If th  [#permalink]

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GMATnavigator wrote:
The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

(a) remain the same
(b) decrease by 13.64%
(c) decrease by 15%
(d) decrease by 18.75%
(e) decrease by 30%

Source: Gmat Cat By Nill (Peterson)

Given: The length, breadth and height of a room are in the ratio 3:2:1. The breadth and height are halved while the length is doubled.

Asked: Total area of the four walls of the room will

The length, breadth and height of a room are in the ratio 3:2:1.
Let The length, breadth and height of a room be 3x, 2x & x respectively
Total area of the four walls of the room = 2 (3x*x + 2x*x) = 10x^2

The breadth and height are halved while the length is doubled.
The length, breadth and height of a room change to 6x, x & x/2 respectively
Total area of the four walls of the room =$$2 (6x*x/2 + x*x/2) = 7x^2$$

Change in area of the four walls = (7-10)/10 = -3/10 (30% decrease)

IMO E
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Email: kinshook.chaturvedi@gmail.com The length, breadth and height of a room are in the ratio 3:2:1. If th   [#permalink] 12 Aug 2019, 00:43

# The length, breadth and height of a room are in the ratio 3:2:1. If th  