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# Of 220 stamps in a certain stamp collection, exactly 60 were

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Eternal Intern
Joined: 07 Jun 2003
Posts: 470
Location: Lone Star State
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Kudos [?]: 44 [0], given: 0

Of 220 stamps in a certain stamp collection, exactly 60 were [#permalink]  15 Jul 2003, 19:35

Of 220 stamps in a certain stamp collection, exactly 60 were U.S. Stamps and 110 were canceled. If 60 percent of the U.S. stamps were canceled, how many of the stamps were both not U.S. stamps and not canceled?

Idiots choose 50 and go to hell during GMAT!
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Director
Joined: 03 Jul 2003
Posts: 655
Followers: 2

Kudos [?]: 22 [0], given: 0

My Ans: 86
Is it correct?
Eternal Intern
Joined: 07 Jun 2003
Posts: 470
Location: Lone Star State
Followers: 1

Kudos [?]: 44 [0], given: 0

Well, I need the explanations!! Please posting answers doesn't help anyone we need reasoning and rationale!

Manager
Joined: 18 Jun 2003
Posts: 141
Location: Hockeytown
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Kudos [?]: 16 [0], given: 0

Draw a matrix with US/Non-US on one axis, Cancel/Non-Cancel on the other.

You have a 2x2 (4 sections):
1. US, Cancel
2. US, non-Cancel
3. non-US, Cancel
4. non-US, non-Cancel [what the question asks for]

[1+3] = 110. [1+2] = 60. 60% of [1+2] are cancelled, so 60% of 60 are cancelled. So 36 US are cancelled. So [1] = 36.

Since [1] = 36 and [1+3] = 110, [3] = 110-36 = 74.
Since [1] = 36 and [1+2] = 60, [2] = 24.

Now you have [1], [2], and [3], but the question asks for [4].

220 - [1] - [2] - [3] = [4]
220 - 36 - 24 - 74 = 86
SVP
Joined: 03 Feb 2003
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draw a chart -- all will be clear
Eternal Intern
Joined: 07 Jun 2003
Posts: 470
Location: Lone Star State
Followers: 1

Kudos [?]: 44 [0], given: 0

That is definitely the clearest way [#permalink]  16 Jul 2003, 04:34
Easiest way is J.P.'s , that's the best way, you deserve a pat on the back for that.

Another way:

2) Subtract total U.S. 60

3) 36 cancel, U.S. 24 U.S.
4) 74 cancel, non U.S. 36 U.S. canceled

The devil's trap is 50 if your not looking. This happens because you subtract out 36 twice. You cannot do this in Venn diagrams.
That is definitely the clearest way   [#permalink] 16 Jul 2003, 04:34
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