On a street with 24 houses, 9 houses have fewer than 6 rooms, 8 houses have more than 7 rooms, and 4 house have more than 8 room. What is the total number of houses on the street that are either 6-, 7- or 8-room houses?

8
9
11
13
14

Question

On a street with 24 houses, 9 houses have fewer than 6 rooms, 8 houses have more than 7 rooms, and 4 house have more than 8 room. What is the total number of houses on the street that are either 6-, 7- or 8-room houses?

 8 
 9 
 11 
 13 
 14

e.mccormick · Answer

So, how far did you get with this?

anonymous · Answer

i had got 11 and it wqas wrong

debbieg · Answer

I was in the process of replying on your OTHER post of this same question when you closed it. I'll try again.

e.mccormick · Answer

They key here is you are lookng for things that are from 6 to 8, right?  So what in the information excludes parts of that?

debbieg · Answer

Starting with 24 houses, 9 have FEWER than 6 rooms. So those are NOT in the category of 6, 7 or 8 room houses, so eliminate those.

That leaves 24 - 9 =15 houses to consider.

debbieg · Answer

Since 8 houses have MORE THAN 7 (includes the 8-room houses that we want to count), and 4 houses have MORE THAN 8 (which we DONT want to include in our count), that tells us to eliminate how many more, from the 15 we are now down to?

anonymous · Answer

14

debbieg · Answer

How did you get 14?

debbieg · Answer

If 8 have more than 7, and 4 have more than 8, then how many of the 8 that have more than 7, do we need to eliminate from our count?

debbieg · Answer

We WANT the 8-room houses, but not the more-than-8-room houses.

If 8 houses have more than 7, and 4 have more than 8, then how many MORE houses should we EXCLUDE from our count?

debbieg · Answer

hmmmm.... you say that you answered 11 and it was wrong?

anonymous · Answer

yea

debbieg · Answer

Well, lets see what @e.mccormick says, because I think that's the correct answer too. lol

e.mccormick · Answer

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e.mccormick · Answer

Becaue you are looking for 6, 7, and 8, you need to see what eliminates more than 8 and less than 6.  Any data that talks about more than 7 is extraneous.

e.mccormick · Answer

Oh, and there are exactly 4 houses with 8 rooms, but that doe not matter.

anonymous · Answer

it's 11

debbieg · Answer

You start with 24. 

You eliminate: 
9 that have fewer than 6 rooms 
4 that have more than 8 rooms 

So that's 9+4=13 

24 - 13 = the ones that have 6 - 8 rooms.

e.mccormick · Answer

Yes.  There are 11.  So if you answered that, it is correct.

e.mccormick · Answer

So yah, you are not crazy and 24-9-4=11 is still true.