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

Question

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

Bunuel · Answer

{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).

Answer: B.

fluke · Answer

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"

144144 · Answer

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,

Bunuel · Answer

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?

144144 · Answer

ye, i got it now. thanks. i didnt read the question well.

thanks.

mattbrown12 · Answer

Good question, thanks!

IndigoIntentions · Answer

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.

bettatantalo · Answer

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

source gmat tutor

chetan2u · Answer

it is about overlapping set...

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

fskilnik · Answer

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

? = x

Using the  simplifier , we have:

\left  \cup \left  = \left  + \left  - \left

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

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

Regards, 
Fabio.

Bunuel · Answer

Merging topics. Please read carefully and follow our rules when posting a question: https://gmatclub.com/forum/rules-for-po ... 33935.html Thank you.

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.

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