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In a sequence of 13 consecutive integers, all of which are

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shobhitb
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In a sequence of 13 consecutive integers, all of which are [#permalink] New post   18 Jun 2006, 22:58
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E

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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.



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Re: In a sequence of 13 consecutive integers, all of which are [#permalink] New post   18 Jun 2006, 23:57
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.

I am going with D
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Re: In a sequence of 13 consecutive integers, all of which are [#permalink] New post   19 Jun 2006, 00:50
66-78 satisfy stmt. 1 ( 3 primes )

48-60 satisfy stmt. 2 ( 3 primes )


So taken alone they are not sufficient
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Re: In a sequence of 13 consecutive integers, all of which are [#permalink] New post   19 Jun 2006, 01:00
Gandalf if right. OA is C.
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Re: In a sequence of 13 consecutive integers, all of which are [#permalink] New post   19 Jun 2006, 01:05
shobhitb wrote:
Gandalf if right. OA is C.


shobhitb

please use my login name for references.
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Re: In a sequence of 13 consecutive integers, all of which are [#permalink] New post   19 Jun 2006, 01:50
deowl wrote:
shobhitb wrote:
Gandalf if right. OA is C.


shobhitb

please use my login name for references.


Sure deowl. Sorry if you were offended.
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Re: In a sequence of 13 consecutive integers, all of which are [#permalink] New post   19 Jun 2006, 07:38
Although I could find hte answer, but is there any trick for such questions.. these questions really take time.
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Re: In a sequence of 13 consecutive integers, all of which are [#permalink] New post   19 Jun 2006, 09:02
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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Re: In a sequence of 13 consecutive integers, all of which are [#permalink]
19 Jun 2006, 09:02
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