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At a certain airport there are 22 aircraft. 5 of the jets

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Manager
Joined: 28 Aug 2004
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At a certain airport there are 22 aircraft. 5 of the jets [#permalink]  15 Sep 2004, 20:59
At a certain airport there are 22 aircraft. 5 of the jets are not American-built and not British-owned, 3 of the American-built planes are not British-owned and not jets, and 7 of the British-owned planes are not jets and not American-built. If equal numbers are American-built jets, British-owned jets and American-built and British-owned, and 1 jet is American-built and Brirish-owned, how many British-owned jets are there, and how many American-built aircraft?
Director
Joined: 16 Jun 2004
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[#permalink]  15 Sep 2004, 22:21
I have the answers as 12 and 8 and hope I haven't made any calculation errors.

See the illustration below..
Also, its given that k+1 = 1+y = 1+z
=>k=y=z

We know that 1+5+y+z+k+0+3+7 = 22
=>y+z+k=6
=>3k=6
=>k=2

Question is what is BO=? which is =1+z+7+k = 1+2+7+2 = 12.
Also, AB=? which is = 1+k+y+3=1+2+2+3 = 8.
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Manager
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[#permalink]  16 Sep 2004, 08:03
your answer is not the OA, but I will think about the solution and come back...
Director
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[#permalink]  16 Sep 2004, 08:30
As expected, I think I made a subtle error. The question is how many BO JETS are there and How many American Built aircraft are there.

For the first question it should be (from my illustration) it should only be 1+y+z = 5. I added 7 earlier and is wrong. The 7 is Non jets.

For the second question on American built aircraft (not jets) it is = k+3 = 5.
Intern
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[#permalink]  16 Sep 2004, 14:44
I solved this problem with 3 venn diagrams or I shd say tried to solve and my answer is:
British Jets = 3
American Aircraft(Jets and Non Jets) = 10 (3 non jets and 7 Jets)

scoobee...
Intern
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[#permalink]  16 Sep 2004, 14:59
There are 3 groups American Built, British Owned and Jets. The numbers given fall cleanly in the various buckets of the venn diagram.

Venk,
I think the value 1 corresponds to American Built British Owned Jet which is the area that intersects all the categories, so the equation becomes:

3+7+5 - 3x - 2 = 22
3x = 9
x = 3 = AB+Jets, BO+jets, AB+BO

I think the first question is asking for BO+Jets, so my answer is 3.

The second asks for all American built aircrafts = 3 AB non jets + 3 AB and BO Jets + 3 AB Jets - 1 Jet that is already accounted for which is AB/BO/J. = 8 as opposed to 10 I posted earlier.
Manager
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[#permalink]  17 Sep 2004, 00:55
That's correct. 3,8.
[#permalink] 17 Sep 2004, 00:55
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At a certain airport there are 22 aircraft. 5 of the jets

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