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

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Intern
Joined: 20 May 2012
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The length, breadth and height of a room are in the ratio 3 : 2 : 1  [#permalink]

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Updated on: 21 Jul 2015, 23:42
3
5
00:00

Difficulty:

75% (hard)

Question Stats:

61% (01:57) correct 39% (02:06) wrong based on 191 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%

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Source: Gmat Cat By Nill (Peterson)

Originally posted by GMATnavigator on 21 Jul 2015, 09:52.
Last edited by GMATnavigator on 21 Jul 2015, 23:42, edited 1 time in total.
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Re: The length, breadth and height of a room are in the ratio 3 : 2 : 1  [#permalink]

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21 Jul 2015, 21:33
1
1
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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Re: The length, breadth and height of a room are in the ratio 3 : 2 : 1  [#permalink]

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21 Jul 2015, 22:34
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)?
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Concentration: General Management, Finance
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Re: The length, breadth and height of a room are in the ratio 3 : 2 : 1  [#permalink]

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21 Jul 2015, 22:42
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  [#permalink]

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22 Jul 2015, 00:48
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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Re: The length, breadth and height of a room are in the ratio 3 : 2 : 1  [#permalink]

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12 Oct 2015, 10:41
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  [#permalink]

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02 Nov 2015, 08:08
well...damn...what a tricky one...I calculated to have 13.++ % decrease, but this is including top and bottom. balls...
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Posts: 34
Re: The length, breadth and height of a room are in the ratio 3 : 2 : 1  [#permalink]

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02 Nov 2015, 20:35
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  [#permalink]

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20 Mar 2016, 17:36
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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Re: The length, breadth and height of a room are in the ratio 3 : 2 : 1  [#permalink]

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23 Oct 2018, 09:59
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Re: The length, breadth and height of a room are in the ratio 3 : 2 : 1 &nbs [#permalink] 23 Oct 2018, 09:59
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