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In a sequence of 13 consecutive integers, all of which are [#permalink]
18 Jun 2006, 21:58

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Difficulty:

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Question Stats:

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In a sequence of 13 consecutive integers, all of which are less than 100, there are exactly 3 multiples of 6. How many integers in the sequence are prime?

(1) Both of the multiples of 5 in the sequence are also multiples of either 2 or 3.

(2) Only one of the two multiples of 7 in the sequence is not also a multiple of 2 or 3.

St1:
1-13: Out. Only two multiple of 6
6-18: 3 multiples of 6, two multiples of 5 are also multiples of 2 or 3. --> 4 primes
12-24: 3 multiples of 6, 2 multiples of 5 are also multiples of 2 or 3 --> 4 primes

Should always end up with 4 primes. Sufficient.

St2:
6-18: 3 multiples of 6, two muliples of 7, and one is not a multiple of 2/3 --> 4 primes

Can't think of any other series that satisfies the criteria set in st2. Should be be just 6-18. In any case, the number of primes integers in this set = 4. Sufficient.

Re: DS - Mixed Bag [#permalink]
19 Jun 2006, 08:02

shobhitb wrote:

In a sequence of 13 consecutive integers, all of which are less than 100, there are exactly 3 multiples of 6. How many integers in the sequence are prime?

(1) Both of the multiples of 5 in the sequence are also multiples of either 2 or 3.

(2) Only one of the two multiples of 7 in the sequence is not also a multiple of 2 or 3.

Is this a plugging problem? this could take time. Any way to use number theory here to shorten the time? (for e.g. divisibility of last 2 digits, prime factors etc.) _________________

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