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A set consists of 12 numbers, all are even or multiple of 5.

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A set consists of 12 numbers, all are even or multiple of 5. [#permalink] New post 09 Feb 2011, 14:19
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81% (02:10) correct 19% (01:56) wrong based on 31 sessions
A set consists of 12 numbers, all are even or multiple of 5. If 5 numbers are even and 8 numbers are multiple of 5, how many numbers is multiple of 10?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
[Reveal] Spoiler: OA
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Re: A set consists of 12 numbers [#permalink] New post 10 Feb 2011, 12:55
Expert's post
loveparis wrote:
38. A set consists of 12 numbers, all are even or multiple of 5. If 5 numbers are even and 8 numbers are multiple of 5, how many numbers is multiple of 10?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5


{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}, as {Neither}=0 ("all are even or multiple of 5") then: 12 = 5 + 8 - {Both} + 0 --> {Both}=1 (so 1 number is both even AND multiple of 5, so it must be a multiple of 10).

Answer: B.
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Re: A set consists of 12 numbers [#permalink] New post 10 Feb 2011, 13:17
A- Elements those are multiple of 2.
B - Elements those are multiple of 5.

n(A \cup B) - Number of elements either multiple of 2 or 5.
n(A) - Number of elements multiple of 5
n(B) - Number of elements multiple of 2.
n(A \cap B) - Number of elements multiple of both 5 and 2(or 10)

n(A \cup B) = n(A) + n(B) - n(A \cap B)
12 = 5+8- n(A \cap B)
n(A \cap B) = 13-12 = 1

Ans: "B"
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Re: A set consists of 12 numbers [#permalink] New post 25 Feb 2011, 14:06
Guys, i understand the way u solved it, but why cant it be 5 as well?

no one told us they are not all multiples of 5 and 2... can someone point out what i am missing?

thanks,
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Re: A set consists of 12 numbers [#permalink] New post 25 Feb 2011, 14:19
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144144 wrote:
Guys, i understand the way u solved it, but why cant it be 5 as well?

no one told us they are not all multiples of 5 and 2... can someone point out what i am missing?

thanks,


It's not clear what you mean. This is overlapping sets problem:

{Total} = {Even} + {Multiple of 5} - {Both} --> 12 = 5 + 8 - {Both} --> {Both}=1 .

Now, how can the answer be other then 1?
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Re: A set consists of 12 numbers [#permalink] New post 25 Feb 2011, 21:02
ye, i got it now. thanks. i didnt read the question well.

thanks.
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Re: A set consists of 12 numbers [#permalink] New post 25 Feb 2011, 21:39
Good question, thanks!
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Re: A set consists of 12 numbers [#permalink] New post 25 Feb 2011, 22:26
B).

Lets say x1 to x12 are the numbers. Assume that x1-x5 are even. The Q says that all numbers are even or multiple of 5. There are 8 multiples of 5 , so lets mark x12 to x6 as multiples of 5 (7 in total) and thus , we will have x5 as the even number that will be multiple of 5.

Thus,
X5 = 5m
X5 = 2n

Since 5 and 2 are primes, the Number X5 = 2.5. (p) where p = m/2 and n/5.
Also, x6 to x12 will have a format of 5.(Odd) since they are odd numbers. Thus they cant be multiple of 10 which is even.
=> x5 will be the only multiple of 10.
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Re: A set consists of 12 numbers   [#permalink] 25 Feb 2011, 22:26
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