In a apartment there are 5 floors each with 4 water taps on each

Question

In a apartment there are 5 floors each with 4 water taps on each floor. Any 2 taps in the same floor are connected with 4 pipes and any 2 taps in different floors are connected with 4 pipes. In one of the floors all the pipes connecting the taps with the taps in the other floors burst and in another floor all the pipes connecting the taps in that floor amongst themselves burst, though all other pipes remain intact. What is the percentage reduction in the number of pipes?

(A) 28
(B) 32
(C) 33
(D) 35
(E) 36

[Might not be a GMAT Level Question, but I came across a similar one in one of the resources I was following]
[Ambiguous and Difficult]

(A) 28
(B) 32
(C) 33
(D) 35
(E) 36

Danush649 · Answer

im getting 36
64+6/ 190

Natashaairan · Answer

Can somebody please explain 
I didn’t get the pipes logic.. how many to consider..

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Charleeagni · Answer

To find the percentage reduction in the number of pipes in the apartment building, we first need to calculate the total number of pipes before and after the bursts.

Total number of taps:

There are 5 floors, each with 4 taps. 
 Total taps TT = 5×4=205×4=20 taps.   
  Pipes connecting taps on the same floor:

Each floor has 4 taps. 
 The number of ways to choose 2 taps out of 4 is (42)=6(24​)=6. 
 Each pair of taps is connected by 4 pipes. 
 Pipes per floor = 6×4=246×4=24 pipes. 
 For 5 floors, total pipes on the same floor = 5×24=1205×24=120 pipes.   
  Pipes connecting taps on different floors:

Total taps = 20. 
 The number of ways to choose 2 taps out of 20 is (202)=190(220​)=190. 
 Each pair of taps is connected by 4 pipes. 
 Total pipes between floors = 190×4=760190×4=760 pipes.   
  Total number of pipes initially:

Total pipes = 120120 (same floor) + 760760 (different floors) = 880880 pipes.    
Now, we consider the two types of bursts:

Bursting pipes connecting taps between one floor and other floors:

Choose any one floor: it has 4 taps. 
 Each of these 4 taps must be connected to each of the other 16 taps (in different floors). 
 Each connection is via 4 pipes. 
 Total burst pipes for this floor = 4×16×4=2564×16×4=256 pipes.   
  Bursting pipes connecting taps within one floor:

Choose any one floor: it has 4 taps. 
 As calculated, the number of pipes connecting these taps = 24 pipes.   
  Total burst pipes:

Total burst pipes = 256256 (between floors) + 2424 (within one floor) = 280280 pipes.   
  Number of pipes after the bursts:

Remaining pipes = Initial pipes - Burst pipes = 880−280=600880−280=600 pipes.   
  Percentage reduction in the number of pipes:

Percentage reduction = Burst pipesInitial pipes×100%InitialpipesBurstpipes​×100% 
 Percentage reduction = 280880×100%≈31.82%880280​×100%≈31.82%    
Thus, the percentage reduction in the number of pipes is approximately 31.82%

The closest is 32.

Natashaairan · Answer

Your answer is not matching

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TheVDR · Answer

This has ambiguous and has multiple meanings. There can be combinations of 2 taps, on from different floor, each connected with 4 pipes, making a total of 20 pipes. It is also possible that each tap is connected to some other tap of all other floors, making a total of 9! * 4 pipes. Neither is giving a 35% reduction (as the OA is D)

Regor60 · Answer

Not a good question due to ambiguous description of the layout.

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aryamanchadha · Answer

4 pipes connecting any 2 pipes on one floor - As there are 6 lines (sides and diagonals) that connect all 4 taps on one floor.
As each line has 4 pipes, pipes connecting taps on one floor = 6*4 = 24
Total Pipes connecting taps on their own floor = 5*24 = 120.

4 pipes connecting any 2 taps on any two floors - Lets calculate how many connections are there between 2 floors.

As each tap connects to the 4 taps above it, there are 4 lines running from each tap to the floor above. 
Each line is 4 pipes => each tap has 16 pipes running to each floor. 
pipes running out to one floor from another floor = 4 * pipes running from one tap to each floor.
Pipes running from one floor to another floor = 4 * 16 = 64.

Total pipes running between floors (not on the same floor) = 64*4 + 64*3 + 64*2 + 64*1 = 64*(4+3+2+1) = 64*11 = 704
(first floor will connect to the other 4 floors and the second floor will connect to the 3 above it as the connections going down are already counted.)

Total Pipes = 704 + 120 = 824

Pipes burst on one floor = 24 (all the pipes)

Pipes burst goint to another floor = 64*4 = 256 (64 pipes each going to the other 4 floors)

Total Pipes burst = 256+24 = 280.

%pipes burst = (280/824) * 100 = 33.9%

Rounded off to 34 I guess but still not 35 :/

Please tell me where I messed up

Maydey23 · Answer

Also, since we're picking any two taps between all floors, won't there be an overlap of the same floor taps?

Maydey23 · Answer

Here's how I got the solution.

Same floor - total pipes between 4 taps = 24
Total same floor pipes across 5 floors = 24×5 = 120

Now, for seperate floors. 
Each tap is connected to any other tap on any floor via 4 pipes.
So, any tap on floor one is connected to 16 other taps via 4 pipes , hence pipe count for floor
1 =16*4*4
Each tap on Floor 2 is connected to 12 other taps - 12*4*4 ( it's connection with first floor taps have already been counted) 
Total pipes ( seperate floors) = 16*4*4+12*4*4+8*4*4+16*4 = 640

Total pipes combined = 120+640= 760

Pipes burst = 24 + 256 = 280

% reduction in pipes = 280/760*100 ---> 7/19*100 (rounding off the 19 to 20) -----> 700/20 = 35%

In a apartment there are 5 floors each with 4 water taps on each

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In a apartment there are 5 floors each with 4 water taps on each