GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 08 Dec 2019, 14:02 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In a certain apartment building, there are one-bedroom and two-bedroom

Author Message
TAGS:

### Hide Tags

Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4471
In a certain apartment building, there are one-bedroom and two-bedroom  [#permalink]

### Show Tags

5
25 00:00

Difficulty:   65% (hard)

Question Stats: 68% (03:07) correct 32% (03:10) wrong based on 225 sessions

### HideShow timer Statistics

In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let R be the average rental price for all apartments in the building. If R is $5,600 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is$10,400 higher that R, then what percentage of apartments in the building are two-bedroom apartments?
(A) 26%
(B) 35%
(C) 39%
(D) 42%
(E) 52%

One tricky category of problems on the GMAT Quant section are Weighted Average problems. For a full discussion of very strategies to use on these problems, as well as the OE for this problem, see
https://magoosh.com/gmat/2015/gmat-math ... -averages/

Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Intern  B
Joined: 22 Oct 2016
Posts: 21
In a certain apartment building, there are one-bedroom and two-bedroom  [#permalink]

### Show Tags

6
1
Hi Amber Bajaj,

Initially it looked strange for me as well to see 5600/10400, but while working out from scratch you will get it.
Average Rent = R
Rent of 1BHK = R1
Rent of 2BHK = R2
Avg. Rent R = [X (R1) + Y (R2)]/X+Y
From the question stem we know,
Avg. Rent R = 5600 + R1
Avg. Rent R + 10400 = R2
Avg. Rent R will look like R = [X (R-5600) + Y (R+10400)]/ X+Y
RX + RY = RX - 5600X + RY + 10400Y
5600X = 10400Y
Since we need ratio of 2BHK
Y/X = 5600/10400 = 7/13
Hence Percentage of 2BHK becomes (7/20)*100 = 35% - where 20 is total parts

_________________
Regards,
Sarugiri
##### General Discussion
Math Expert V
Joined: 02 Aug 2009
Posts: 8290
In a certain apartment building, there are one-bedroom and two-bedroom  [#permalink]

### Show Tags

mikemcgarry wrote:
In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let R be the average rental price for all apartments in the building. If R is $5,600 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is$10,400 higher that R, then what percentage of apartments in the building are two-bedroom apartments?
(A) 26%
(B) 35%
(C) 39%
(D) 42%
(E) 52%

One tricky category of problems on the GMAT Quant section are Weighted Average problems. For a full discussion of very strategies to use on these problems, as well as the OE for this problem, see
https://magoosh.com/gmat/2015/gmat-math ... -averages/

Mike hi,
straight forward question of weighted mixture...
here we have the price of two BR:one BR away from average by 10400:5600....
therefore the number of two is 5600/16000 *100= 35%
ans B
_________________
Manager  Joined: 27 Oct 2013
Posts: 198
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Re: In a certain apartment building, there are one-bedroom and two-bedroom  [#permalink]

### Show Tags

1

Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 5400 : 104000 -----> 7 : 13

Let total number of Apartments be X

No. of 2 Bedroom Apartment = (7 / 20) * X

percentage of apartments in the building are two-bedroom apartments ---->

(7/20) * 100 ---> 35%

option B is correct
Director  G
Joined: 23 Jan 2013
Posts: 522
Schools: Cambridge'16
Re: In a certain apartment building, there are one-bedroom and two-bedroom  [#permalink]

### Show Tags

1
1
Differential approach

1room<-------R--------------->2rooms

5600x=10400y

x/y=10400/5600=1.8/1

(y/x+y)*100=1/2.8=0.35*100=35%

B
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4125
Re: In a certain apartment building, there are one-bedroom and two-bedroom  [#permalink]

### Show Tags

Top Contributor
1
mikemcgarry wrote:
In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let R be the average rental price for all apartments in the building. If R is $5,600 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is$10,400 higher that R, then what percentage of apartments in the building are two-bedroom apartments?
(A) 26%
(B) 35%
(C) 39%
(D) 42%
(E) 52%

Another approach:

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

R = Weighted average of BOTH types
R - 5600 = average rent for 1-bedroom apartments
R + 10400 = average rent for 2-bedroom apartments

Let P = percentage of apartments that are two-bedroom apartments. This means P/100 represents to PROPORTION of apartments that are 2-bedroom.
So, 100 - P = percentage of apartments that are one-bedroom apartments. This means (100-P)/100 represents to PROPORTION of apartments that are 1-bedroom.

We can now plug all of this information into the formula to get:

R = (P/100)(R + 10400) + [(100-P)/100](R - 5600)
Multiply both sides by 100 to get: 100R = (P)(R + 10400) + (100-P)(R - 5600)
Expand to get: 100R = PR + 10400P + 100R - 560000 - PR + 5600P
Simplify to get: 0 = 16000P - 560000
Rearrange to get: 16000P = 560000
Divide both sides by 1000 to get: 16P = 560
Divide both sides by 16 to get: P = 35

RELATED VIDEO

_________________
Intern  S
Joined: 28 Aug 2016
Posts: 17
GMAT 1: 560 Q44 V23 Re: In a certain apartment building, there are one-bedroom and two-bedroom  [#permalink]

### Show Tags

chetan2u wrote:
mikemcgarry wrote:
In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let R be the average rental price for all apartments in the building. If R is $5,600 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is$10,400 higher that R, then what percentage of apartments in the building are two-bedroom apartments?
(A) 26%
(B) 35%
(C) 39%
(D) 42%
(E) 52%

One tricky category of problems on the GMAT Quant section are Weighted Average problems. For a full discussion of very strategies to use on these problems, as well as the OE for this problem, see
https://magoosh.com/gmat/2015/gmat-math ... -averages/

Mike hi,
straight forward question of weighted mixture...
here we have the price of two BR:one BR away from average by 10400:5600....
therefore the number of two is 5600/16000 *100= 35%
ans B

Hi, Here divident is 5600. Please help me to understand why we did not take 10400 as divident.

5600/16000 *100= 35%

Regards
AMber Bajaj
Senior Manager  G
Joined: 04 Aug 2010
Posts: 496
Schools: Dartmouth College
Re: In a certain apartment building, there are one-bedroom and two-bedroom  [#permalink]

### Show Tags

mikemcgarry wrote:
In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let R be the average rental price for all apartments in the building. If R is $5,600 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is$10,400 higher that R, then what percentage of apartments in the building are two-bedroom apartments?
(A) 26%
(B) 35%
(C) 39%
(D) 42%
(E) 52%

Use ALLIGATION -- a great way to handle weighted average problems.

Let S = single-room apartments, T = two-room apartments.

Step 1: Draw a number line, with the two apartment types (S and T) on the ends and the mixture of apartments (R) in the middle:
S-----------------R-----------------T

Step 2: Calculate the distances between the averages.
Since the average for S is 5600 less than the average for R, and the average for T is 10,400 more than the average for R, we get the following distances between the averages:
S-----5600------R----10400------T

Step 3: Determine the ratio in the mixture.
The ratio of S to T is equal to the RECIPROCAL of the distances in red.
S:T = 10400:5600 = 13:7.

Since S:T = 13:7, there are 13 single-room apartments for every 7 two-room apartments.
Thus, of every 20 apartments, 7 are two-room:
$$\frac{7}{20} = \frac{35}{100}= 35$$%

_________________
GMAT and GRE Tutor
New York, NY

Available for tutoring in NYC and long-distance. Re: In a certain apartment building, there are one-bedroom and two-bedroom   [#permalink] 01 Oct 2018, 04:13
Display posts from previous: Sort by

# In a certain apartment building, there are one-bedroom and two-bedroom  