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In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41

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MA
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In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41 [#permalink] New post   Updated on: 03 Jan 2005, 15:22
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(a) In the sequence A, A1 = 43, A2 = 47,..............., Ak = k^2 + k + 41.
Is every term in sequence A a prime number?

(1) There are fewer than 999 terms in sequence A.
(2) There are more than 99 terms in sequence A.



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Originally posted by MA on 02 Jan 2005, 23:22.
Last edited by MA on 03 Jan 2005, 15:22, edited 1 time in total.
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Re: In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41 [#permalink] New post   03 Jan 2005, 10:39
If I undestand the problem right then Ak=2*k+k+41. So A2=2*2+2+41=4+2+41=6+41=47.

Wouldn't A5=2*5+5+41, so A5=10+5+41=15+41=56.

Since 56 is divisible by 2 it is not prime and I don't need the statements to tell me that every number in the set is not prime. Am I reading the problem wrong?
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Re: In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41 [#permalink] New post   03 Jan 2005, 11:33
I believe the answer is D, that is if it K^2. all numbers are prime!

I checked for the first 10 numbers, and then figure that the sequence repeats itself so in an infintite chain there are infinite prime numbers, either statement can be used!


MA wrote:
(a) In the sequence A, A1 = 43, A2 = 47,.................., Ak = k2 + k + 41.
Is every term in sequence A a prime number?

(1) There are fewer than 999 terms in sequence A.
(2) There are more than 99 terms in sequence A.
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Re: In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41 [#permalink] New post   03 Jan 2005, 15:23
banerjeea_98 wrote:
I believe it is k^2 and not 2*k.


I have edited the problem. k2 = k square
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Re: In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41 [#permalink] New post   09 Jan 2005, 10:07
can somebody elaborate how to approach such problems. i have difficulty in doing these..
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Re: In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41 [#permalink] New post   09 Jan 2005, 12:58
vprabhala wrote:
can somebody elaborate how to approach such problems. i have difficulty in doing these..



vprabhala,

this my understanding.

from i, number of terms can 1,2,3,4,5,6, ............... 999.
if the number of terms in the series is 1, then
A1= 1+1+41= 43. the answer is yes.
if the number of terms in the series is 41, then
A41= 41^2+41+41=41(43). then answer is no because A41 is devided by 41 and 43.

from ii, the number of terms in series is more than 99 means, the series is A1, A2, ....., A41, ........, A82, .........An
the terms A41 and A82 are at least not prime. therefore, the answer is B.
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Re: In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41 [#permalink] New post   09 Jan 2005, 16:55
MA wrote:
vprabhala wrote:
can somebody elaborate how to approach such problems. i have difficulty in doing these..



vprabhala,

this my understanding.

from i, number of terms can 1,2,3,4,5,6, ............... 999.
if the number of terms in the series is 1, then
A1= 1+1+41= 43. the answer is yes.
if the number of terms in the series is 41, then
A41= 41^2+41+41=41(43). then answer is no because A41 is devided by 41 and 43.

from ii, the number of terms in series is more than 99 means, the series is A1, A2, ....., A41, ........, A82, .........An
the terms A41 and A82 are at least not prime. therefore, the answer is B.


From i), there are fewer than 999 items in the series, and since A40, A41 are not prime, and other numbers can be prime, so from i) alone we can say 'no' to the question asked.

From ii), there are more than 99 items in series, and again A40, A41, A82 are not prime, and other numbers can be prime, so again from ii) we can say 'no' to the question asked.

Can you clarify your answer, MA? Thanks.
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Re: In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41 [#permalink] New post   09 Jan 2005, 22:15
jinino,
statement (i) is insufficient to answer the question because if the term in the series is only 1, then every term in the series is prime, but if the terms in the series are 41 or 82, then every term in the series is not prime.

statement (ii) is sufficient to answer the question because there are more than 99 terms in the series means there are at least 100 terms in the series. this series includes terms 41 and 82 and these terms in the series are not prime.

if we read the question stem carefully, it is clearly mentioned that every term in the series. this is the clue to the solution.
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Re: In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41 [#permalink] New post   09 Jan 2005, 23:27
I got it now, MA. :thanks



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Re: In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41 [#permalink]
09 Jan 2005, 23:27
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