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13 consecutive integers

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13 consecutive integers

by Vemuri » Mon May 18, 2009 9:53 am
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 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 also not a multiple of 2 or 3?
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Re: 13 consecutive integers

by iamcste » Mon May 18, 2009 10:32 am
Vemuri 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 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 also not a multiple of 2 or 3?
IMO E
Last edited by iamcste on Sun May 24, 2009 6:59 am, edited 1 time in total.
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by cramya » Mon May 18, 2009 3:01 pm
6-18-> 4 primes

42-54-> 3 primes

72-84-> 3 primes

I would say E

This was one time consuming number picking prob. I am sure Ian may have a better solution....

Regards,
CR
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by Ian Stewart » Mon May 18, 2009 3:47 pm
It's not a well-written question. As written, the answer is clearly E; the integers can be negative (they don't say in the question that the integers are positive). Even if you look only at positive integers, the answer is E anyway, but it's a bit tedious to see why. I posted a solution here:

www.beatthegmat.com/please-help-me-t17777.html

It's a more interesting problem if you disallow the set 6, 7, 8, ..., 17, 18, and I solved that version of the problem in the above post as well. Regardless, I don't find the question all that similar to real GMAT questions, so it isn't worth spending much time on.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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by cramya » Mon May 18, 2009 5:27 pm
Saw ur post, Ian. Simply awesome!!!

Thank u.

Regards,
Cramya
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