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the high rise

While in Canada, I visited a beautiful high-rise building in the Metropolitan City of Toronto. The manager of the building told me that the building consisted of different kinds of apartments large and small. Two room apartments were 5% in number, 21/2's-7% in number, 3's-15% in number, 31/2's-20% in number, 41/2's-49% in number, 5's-33% in number, 51/2's-12% in number, 6's-3% in number and in addition several 4 room apartments. Altogether the building contained 437 apartments.
Can you figure out how many apartments are there in each type, using round figures?


--- the percentages add up to `144% do we have to convert it base first .. i've no clue how to go abt it
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shilpi84
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shilpi84
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1 Solution
 
brianpsmith81Commented:
Yeah that gives you about 633 apartments rather than 437....perhaps the percentages are sq. footage...??  I don't know.  I'm subscribing to this one!
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AndyAinscowCommented:
I think the building is quantum - only when you look in an apartment does it become a fixed size of rooms.
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gordonkennedyCommented:
I think the trick here is to assume that , for example, the set of 3room appartments overlaps with the set of 31/2 room appartments.  In other words some rooms can be sold as either 3 or 31/2 room appartments.

If on this basis we temporarily exclude appartments with 1/2 rooms, we see that 4 room appartments will account for the remaining 44% (= 100 - 5 - 15 - 33 - 3).
The (whole) number of appartments for each category is then :
2       22
21/2  31
3       66
31/2  87
4       192
41/2  214
5       144
51/2   52
6        13

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AndyAinscowCommented:
Here is a hint - what is 100 in base 8?
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AndyAinscowCommented:
Wrong.
Again -  Here is a hint - what is 100 in base 8?
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ozoCommented:
> we temporarily exclude appartments with 1/2 rooms
That doesn't make sense, since the number of 2 1/2 exceeds the number of 2, and the number of 3 1/2 exceeds the number of 3
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AndyAinscowCommented:
shilpi84 doesn't seem to understand numbers can be to other bases eg. 8, not just base 10.
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ozoCommented:
Although "49% in number" does not usually indicate a base 8 number.
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gordonkennedyCommented:
ozo : my point is that there is no such thing as 1/2 a room ... 21/2 room appts must either be big 2's or small 3's

Andy : so if the percentages are in base 8 and the figures given already total 144%, how can there be any extra 4room appts ? also I would say that "perCENTage" implies base 10
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AndyAinscowCommented:
Hmm - not spotted that, just spotted 144 is 100 in base 8 and as it talked of round numbers I thought the extra few 4 room apartments were due to rounding errors.  
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AndyAinscowCommented:
< ozo : my point is that there is no such thing as 1/2 a room ... 21/2 room appts must either be big 2's or small 3's>

I live in Switzerland, my first flat here was a 2 1/2 room flat later followed by a 3 1/2 room.  The 1/2 is used to indicate separate or combined kitchen/dining areas.
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gordonkennedyCommented:
<The 1/2 is used to indicate separate or combined kitchen/dining areas.>

Point taken, but I think "is" should be replaced with "can be".
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AndyAinscowCommented:
I don't think it is the answer (and my very first comment was meant as a joke)
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