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Operation "#" is defined as adding a randomly selected two

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Operation "#" is defined as adding a randomly selected two  [#permalink]

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New post 20 Nov 2013, 01:19
2
10
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A
B
C
D
E

Difficulty:

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Question Stats:

88% (01:37) correct 12% (02:06) wrong based on 207 sessions

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Operation "#" is defined as adding a randomly selected two digit multiple of 6 to a randomly selected two digit prime number and reducing the result by half. If operation "#" is repeated 10 times, what is the probability that it will yield at least two integers?

A) 0%
B) 10%
C) 20%
D) 30%
E) 40%
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Posts: 58434
Re: Operation "#" is defined as adding a randomly selected two  [#permalink]

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New post 20 Nov 2013, 01:25
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registerincog wrote:
Operation "#" is defined as adding a randomly selected two digit multiple of 6 to a randomly selected two digit prime number and reducing the result by half. If operation "#" is repeated 10 times, what is the probability that it will yield at least two integers?

A) 0%
B) 10%
C) 20%
D) 30%
E) 40%


Any multiple of 6 is even.
Any two-digit prime number is odd.

(even+odd)/2 is not an integer. Thus # does not yield an integer at all.

Therefore P=0.

Answer: A.
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Re: Operation "#" is defined as adding a randomly selected two  [#permalink]

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New post 30 Mar 2018, 10:52
registerincog wrote:
Operation "#" is defined as adding a randomly selected two digit multiple of 6 to a randomly selected two digit prime number and reducing the result by half. If operation "#" is repeated 10 times, what is the probability that it will yield at least two integers?

A) 0%
B) 10%
C) 20%
D) 30%
E) 40%


All two-digit multiples of 6 are even, and all two-digit prime numbers are odd. Thus, we are adding even + odd, which always yields an odd number. When that odd number is divided by 2, the result is a non-integer. If operation “#” is repeated, we will again obtain a non-integer, and, in fact, operation “#” will never yield an integer. Thus, the probability of yielding at least 2 integers is zero.

Answer: A
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Re: Operation "#" is defined as adding a randomly selected two   [#permalink] 30 Mar 2018, 10:52
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