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

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Joined: 09 Feb 2011
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A set consists of 12 numbers, all are even or multiple of 5.  [#permalink]

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09 Feb 2011, 14:19
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Question Stats:

66% (01:30) correct 34% (01:35) wrong based on 215 sessions

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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
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Joined: 02 Sep 2009
Posts: 52292
A set consists of 12 numbers, all are even or multiple of 5.  [#permalink]

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10 Feb 2011, 12:55
1
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}.

Since {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).

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Re: A set consists of 12 numbers  [#permalink]

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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]

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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]

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25 Feb 2011, 14:19
1
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]

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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]

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25 Feb 2011, 21:39
Good question, thanks!
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Re: A set consists of 12 numbers  [#permalink]

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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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A set consists of 12 numbers, all are even or multiples of 5. If 5 num  [#permalink]

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21 Sep 2018, 09:04
1
A set consists of 12 numbers, all are even or multiples of 5. If 5 numbers are even and 8 numbers are multiples of 5, how many numbers are multiples of 10?

a) 0
b) 1
c) 2
d) 3
e) 5

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Posts: 7202
Re: A set consists of 12 numbers, all are even or multiples of 5. If 5 num  [#permalink]

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21 Sep 2018, 09:39
2
bettatantalo wrote:
A set consists of 12 numbers, all are even or multiples of 5. If 5 numbers are even and 8 numbers are multiples of 5, how many numbers are multiples of 10?

a) 0
b) 1
c) 2
d) 3
e) 5

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so multiples of 5 = 8 and even = 5
total 5+8=13 but the set has only 12 numbers ..
as all are part of one of the group, the overlap is 13-12=1

B
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Re: A set consists of 12 numbers, all are even or multiples of 5. If 5 num  [#permalink]

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21 Sep 2018, 11:11
bettatantalo wrote:
A set consists of 12 numbers, all are even or multiples of 5. If 5 numbers are even and 8 numbers are multiples of 5, how many numbers are multiples of 10?

a) 0
b) 1
c) 2
d) 3
e) 5

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Yep... Venn diagrams ("overlapping sets"). See image attached.

$$? = x$$

Using the simplifier, we have:

$$\left[ {{\text{even}}} \right] \cup \left[ {{\text{mult}}\,\,{\text{5}}} \right] = \left[ {{\text{even}}} \right] + \left[ {{\text{mult}}\,\,{\text{5}}} \right] - \left[ {{\text{x}}\,\,{\text{ = }}\,\,{\text{mult}}\,{\text{10}}} \right]$$

$$12 = 5 + 8 - x\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 1$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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21Set18_6r.gif [ 12.49 KiB | Viewed 515 times ]

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Re: A set consists of 12 numbers, all are even or multiple of 5.  [#permalink]

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22 Sep 2018, 01:36
bettatantalo wrote:
A set consists of 12 numbers, all are even or multiples of 5. If 5 numbers are even and 8 numbers are multiples of 5, how many numbers are multiples of 10?

a) 0
b) 1
c) 2
d) 3
e) 5

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Merging topics.

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Re: A set consists of 12 numbers, all are even or multiple of 5. &nbs [#permalink] 22 Sep 2018, 01:36
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