Problem Solving

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

I cant seem to get the correct answer. I have attached the table.

Can someone tell me where is my mistake?

Total = 490
Rented = 280
Not rented = 490-280 = 210

Let x be the total number of 1 BR apartments.

The question says - including 1/5 of the one-bedroom units.

1/5 = 0.2

so 0.2 x should be included in the 280.
I solve for x = 70 which gives me the final answer as 224.

Your table is right but this should be your equation.

(280 - 0.2x)/0.2x = 6/1. If you solve this you get x=200

Faraz, I don't know how long this approach took you. I think it might be quicker to try the approach below.

Rented = 280
Given the ratio 6:1, 40 1BR and 240 2BR are rented.
Now you calculated yourself that the total 2BRs are 290. In the above equation, we calculated 240 2BRs are rented so there must be 290-240=50 not rented.

faraz_jeddah 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

This is an EITHER/OR group problem.
Every unit is EITHER rented OR not rented.
Every unit has EITHER 2 bedrooms OR 1 bedroom.
Use a GROUP GRID (also known as a DOUBLE-MATRIX) to organize the data.

Try to insert into the grid actual numbers rather than variables.

An apartment building that has 490 units



4 out of every 7 units are currently rented.
Since (4/7)490 = 280, we get:



Of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units.
Since 6+1 = 7, and the actual number of rented units is 280 -- 40 times 7 -- the multiplier for the ratio is 40:
(40*6) : (40*1) = 240:40.

Since rented 2-bedroom units = 240 and rented 1-bedroom units = 40, we get:



4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units.
Thus, the 40 rented 1-bedroom units are 1/5 of the TOTAL number of 1-bedroom units.
Since 40 is equal to 1/5 of 200, there are a total of 200 1-bedroom units, yielding the following grid:



According to the grid above, the number of 2-bedroom units NOT RENTED = 50.

The correct answer is A.

jitsy wrote:Faraz, I don't know how long this approach took you. I think it might be quicker to try the approach below.

Rented = 280
Given the ratio 6:1, 40 1BR and 240 2BR are rented.
Now you calculated yourself that the total 2BRs are 290. In the above equation, we calculated 240 2BRs are rented so there must be 290-240=50 not rented.

Jitsy: How did you calculate 290 2BRs. Could you please explain it.

Regards
Uva.

Jitsy: How did you calculate 290 2BRs. Could you please explain it.

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We calculated 40 rented 1BRs and 240 rented 2BRs. Now given one rented 1BR for every 5 (1/5 in the question) there must be 5*40=200 total 1BRs. Out of the total 490 units there must then be 490-200=290 2BRs (since there are only 1 and 2 BRs). We calculated 240 rented 2 BRs so there must be 290-240=50 non rented 2BRs.