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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, 15:19

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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?

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

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)

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, all are even or multiple of 5. [#permalink]

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09 Feb 2015, 10:35

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