Three models (A, B, and C) of cars are distributed among three showroo

Question

Three models (A, B, and C) of cars are distributed among three showrooms. The number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom. There are 19 cars of Model A, 17 cars of Model B, and 15 cars of Model C. What is the maximum number of cars of model A in any showroom ?

A. 17
B. 16
C. 15
D. 14
E. 13

A. 17
B. 16
C. 15
D. 14
E. 13

CounterSniper · Answer

we have,
N1=N2=N3(1 ,2 , 3 representing each of the showrooms)
cars available
model A=19
model B=17
model C=15
The max number of cars of model A can only be minimum number of cars among model A,B,C as the number of cars should be same in each of the showrooms.
therefore N1=N2=N3=15

EMPOWERgmatRichC · Answer

Hi amithyarli,

I'm going to give you a couple of hints so that you can reattempt this question on your own. Among all of the various pieces of information that you're given to work with, there are 2 that are really important:

1) The TOTAL number of cars in each showroom is SAME.
2) At least one of each type of car is in each showroom.

Can you figure out how many total cars are in each showroom? After you figure that out, if you put one of each type of car into each of the 3 showrooms, how many possible Model A cars can you put in any one showroom?

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

MathRevolution · Answer

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

Three models (A, B, and C)of cars are distributed among three showrooms. The number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom. There are 19 cars of Model A, 17 cars of Model B, and 15 cars of Model C. What is the maximum number of cars of model A in any showroom ?

A. 17
B. 16
C. 15
D. 14
E. 13

The total number of cars is 51. So each showroom has 17 cars(since the number of cars in each showrooms should be equal 51/3=17). 
Moreover that the number of model A is maximum means that the numbers of model B and C should be minimum. Since each model must be represented by at least one car in every showroom that minimum number should be 1.

So Maximum number of model A is 17-2= 15.

The answer is (C)

chetan2u · Answer

Hi,
although you have got the answer correct, the logic is not fully correct..
 say model C had 12 cars , would you then say answer is 12 since "The max number of cars of model A can only be minimum number of cars among model A,B,C as the number of cars should be same in each of the showrooms."... ans is NO..

the method is to find average, which will give you the number of cars in each showroom....
then two steps..

i) if the number of that model car is >average... subtract 2 from average(1 each for the remaining models of car as atleast 1 of each model is must)

ii) if the number of that model car is <average... subtract 2 from the number of car of that model...

CounterSniper · Answer

Got It !!

btw
if model C has 12 cars.

each of the showroom will have 16 cars.

no of cars of model A = (total cars which can be accomodated in a showroom -(min model B + min model C))
=16-(1+1)
=14

chetan2u · Answer

yes you are correct ...
similar will be the case for model B..
but for model C it will be 12-2=10...

ehsan090 · Answer

Easy if you understand what is asked
Step#01
total all vehicles:51/3=17(every showroom must have 17 vehicles)
Condition: Every showroom must have atleast single vehicle of each model then max number of vehicle of model A any showroom can have is 15
since 17-2(model b and c)=15
option:C

shashankism · Answer

Total number of cars = 19 +17 +15 = 51..
Number of cars in each showroom must be equal. So, the total number of cars in each showroom must be 51/3 = 17

Also, Each model must be represented by at least one car in every showroom.
So, any one showroom can have maximum of 17-2 =15 cars of Model A. In this way 4 cars of model A will be left and hence condition of representation of model A in other showrooms will also be fulfilled.
 
Answer C

jainil7 · Answer

We have 34 spots left across Showroom 2 and Showroom 3 (17 each).
 
  Remaining Model A:  4 cars 
  Remaining Model B:  16 cars 
  Remaining Model C:  14 cars  
In Showroom 2 and 3, we must also have at least one of each model.
 
  Showroom 2:  Could take 2 cars of A, 1 car of B, and 14 cars of C. 
  Showroom 3:  Could take 2 cars of A, 15 cars of B, and 0 cars of C?  No.  Showroom 3  must  have at least one C.  
Let's refine the distribution to ensure everyone has at least one of everything:
 
  Showroom 1:  15 (A), 1 (B), 1 (C) — Total 17. 
  Showroom 2:  2 (A), 1 (B), 7 (C) — Total 10... wait, we need to reach 17. 
  Showroom 2:  2 (A), 8 (B), 7 (C) — Total 17. 
  Showroom 3:  2 (A), 8 (B), 7 (C) — Total 17.  
 Final Totals check: 
 
  Model A:  $15 + 2 + 2 = 19$ (Correct) 
  Model B:  $1 + 8 + 8 = 17$ (Correct) 
  Model C:  $1 + 7 + 7 = 15$ (Correct)

Three models (A, B, and C) of cars are distributed among three showroo

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Three models (A, B, and C) of cars are distributed among three showroo

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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Perfect 805 Score Debrief by Julia

My Rewards