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# Two buildings of equal height start sinking into the ground at the sam

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Intern
Joined: 08 Aug 2012
Posts: 9
GMAT 1: 620 Q47 V30
Two buildings of equal height start sinking into the ground at the sam [#permalink]

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02 Mar 2018, 07:01
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Question Stats:

57% (06:44) correct 43% (02:07) wrong based on 42 sessions

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Two buildings of equal height start sinking into the ground at the same time at a uniform rate. One of the buildings will take 16 days and the other 24 days to sink completely. After how many days will the height of the portion above the ground of one of the buildings is exactly twice that of the other building?

A) 5
B) 6
C) 8
D) 10
E) 12
[Reveal] Spoiler: OA
Intern
Joined: 04 Jan 2018
Posts: 35
Re: Two buildings of equal height start sinking into the ground at the sam [#permalink]

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02 Mar 2018, 07:58
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KUDOS
Ans is E

After 12 days,

one building is sunk to half---
another to 3/4th

so clearly unsunk part of one building is twice the other.
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Joined: 02 Aug 2009
Posts: 5719
Re: Two buildings of equal height start sinking into the ground at the sam [#permalink]

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02 Mar 2018, 08:12
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sameersaluja wrote:
Two buildings of equal height start sinking into the ground at the same time at a uniform rate. One of the buildings will take 16 days and the other 24 days to sink completely. After how many days will the height of the portion above the ground of one of the buildings is exactly twice that of the other building?

A) 5
B) 6
C) 8
D) 10
E) 12

Hi....
Let the height of building be 48m.. 48 is a smart number as it is related to both 16 and 24 as their LCM

so A building goes down by 48/16 or 3 m in one day and building B by 48/24 = 2m

let the condition of twice height is met after x days..
so $$48-2x=2(48-3x)............48-2x=96-6x.........4x=48...............x=12$$days

E
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Re: Two buildings of equal height start sinking into the ground at the sam [#permalink]

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06 Mar 2018, 07:58
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Expert's post
sameersaluja wrote:
Two buildings of equal height start sinking into the ground at the same time at a uniform rate. One of the buildings will take 16 days and the other 24 days to sink completely. After how many days will the height of the portion above the ground of one of the buildings is exactly twice that of the other building?

A) 5
B) 6
C) 8
D) 10
E) 12

We can let the height of each building be 48 meters. Thus, one building will sink at a rate of 3 meters per day while the other 2 meters per day. We can let n = the number of days it takes for the height of the building (sinking at 2 meters per day) above ground be twice that of the building (sinking at 3 meters per day). We can create the following equation:

2(48 - 3n) = 48 - 2n

48 - 3n = 24 - n

24 = 2n

12 = n

(Note that we chose the height of each building to be 48 feet because 48 is the least common multiple of 16 and 24. This made the arithmetic easy. However, we could have chosen any value for the height of each building, and the answer of 12 days still would have been obtained.)

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Re: Two buildings of equal height start sinking into the ground at the sam   [#permalink] 06 Mar 2018, 07:58
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