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# In an apartment building that has 490 units, 4 out of every

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Joined: 05 Jun 2013
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In an apartment building that has 490 units, 4 out of every [#permalink]

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02 Jul 2013, 23:23
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71% (02:35) correct 29% (03:20) wrong based on 254 sessions

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In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?

(A) 50
(B) 70
(C) 100
(D) 105
(E) 140

Kudos if you find it useful! Thanks!
[Reveal] Spoiler: OA
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Posts: 44293
Re: In an apartment building that has 490 units, 4 out of every [#permalink]

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02 Jul 2013, 23:31
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In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?
(A) 50
(B) 70
(C) 100
(D) 105
(E) 140

Rented = 4/7*490 = 280.
Rented two-bedroom = 6/7*280 = 240;
Rented one-bedroom = 1/7*280 = 40 (or 280-240=40).

Rented one-bedroom units are 1/5 of all one-bedroom: 1/5*{All one bedroom} = 40 --> {All one-bedroom} = 200.

{All two-bedroom} = 490 - 200 = 290.

Two-bedroom not rented = 290 - 240 = 50.

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Re: In an apartment building that has 490 units, 4 out of every [#permalink]

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02 Jul 2013, 23:38
vtran wrote:
In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?

(A) 50
(B) 70
(C) 100
(D) 105
(E) 140

Kudos if you find it useful! Thanks!

Out of every 7 units, 4 are rented. Thus, out of 490 units, $$4*\frac{490}{7}$$ will be rented $$\to 280$$. Total no of not rented bedrooms = (490-280)= 210 units.

Let the total no of 1 bedroom units be 5x.The total rented apartments include x units of 1 bedroom and 6x units of 2 bedrooms $$\to 7x$$ = $$280 \to x$$= 40. Thus, the total no of 1 bedroom units = 5*40 = 200.
Total not rented 1 bedroom units = (200-40)=160
The no of 2 bedroom units not rented = 210-160= 50 units.
A.
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Re: In an apartment building that has 490 units, 4 out of every [#permalink]

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17 Aug 2017, 19:48
Bunuel wrote:
In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?
(A) 50
(B) 70
(C) 100
(D) 105
(E) 140

Rented = 4/7*490 = 280.
Rented two-bedroom = 6/7*280 = 240;
Rented one-bedroom = 1/7*280 = 40 (or 280-240=40).

Rented one-bedroom units are 1/5 of all one-bedroom: 1/5*{All one bedroom} = 40 --> {All one-bedroom} = 200.

{All two-bedroom} = 490 - 200 = 290.

Two-bedroom not rented = 290 - 240 = 50.

Hi Bunuel,

Can we do this question using two dimensional matrix? I tried doing the same but unable to reach to the answer choice.
Math Expert
Joined: 02 Sep 2009
Posts: 44293
Re: In an apartment building that has 490 units, 4 out of every [#permalink]

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17 Aug 2017, 21:41
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Expert's post
ab52 wrote:
Bunuel wrote:
In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?
(A) 50
(B) 70
(C) 100
(D) 105
(E) 140

Rented = 4/7*490 = 280.
Rented two-bedroom = 6/7*280 = 240;
Rented one-bedroom = 1/7*280 = 40 (or 280-240=40).

Rented one-bedroom units are 1/5 of all one-bedroom: 1/5*{All one bedroom} = 40 --> {All one-bedroom} = 200.

{All two-bedroom} = 490 - 200 = 290.

Two-bedroom not rented = 290 - 240 = 50.

Hi Bunuel,

Can we do this question using two dimensional matrix? I tried doing the same but unable to reach to the answer choice.

Check below:
Attachment:

Untitled.png [ 6.14 KiB | Viewed 805 times ]

Hope it helps.
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Re: In an apartment building that has 490 units, 4 out of every [#permalink]

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22 Aug 2017, 16:51
vtran wrote:
In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?

(A) 50
(B) 70
(C) 100
(D) 105
(E) 140

Since 4 out of 7 apartments in the building are rented out, the number of apartments rented out is (4/7)(490) = 280.

We can let the ratio of two-bedroom units to one-bedroom units = 6x : x; thus, the total number of rented apartments is 7x and we can create the following equation:

7x = 280

x = 40

Thus, we have 6(40) = 240 two-bedroom apartments and 40 one-bedroom apartments that are rented out.

Since the 40 one-bedroom apartments that are rented out represent 1/5 of all the one-bedroom apartments in the building, the number of one-bedroom apartments in the building is 40/(1/5) = 200. Thus, there are 490 - 200 = 290 two-bedroom apartments in the building. Finally, since 240 two-bedroom apartments are rented out, 290 - 240 = 50 two-bedroom apartments are not rented out.

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Re: In an apartment building that has 490 units, 4 out of every [#permalink]

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23 Aug 2017, 00:09
vtran wrote:
In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?

(A) 50
(B) 70
(C) 100
(D) 105
(E) 140

Kudos if you find it useful! Thanks!

Total units = 490

Total rented = 4/7(490)=280

given ratio of 2br:1br=6:1

Hence total 2 br rented = 6/7(280)=240

Given 1/5(1BR)=40 (Total rented-2Br rented)
hence Total 1BR=200
Total Units - Total 1BR = Total 2BR
490-200=290= Total 2BR
unrented 2BR = 290-240(Rented 2BR)
Hence answer is 50. Option A
Re: In an apartment building that has 490 units, 4 out of every   [#permalink] 23 Aug 2017, 00:09
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