In the sequence A, A1 = 43, A2 = 47,..............., Ak =

Question

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 100 terms in sequence A. 
(2) There are more than 50 terms in sequence A.

nocilis · Answer

Ak = k^2 + k + 41
or 
 = k(k+1) + 41

If k or k+1 is 41, 41 will be a factor of k^2 + k + 41, and it will not be prime
So if k=40 or k=41 it is not prime

1) There are fewer than 100 terms in sequence A. 

Some are prime some are not.

2) There are more than 50 terms in sequence A.

Some are prime some are not.

E

banerjeea_98 · Answer

"D".

Same approach as above but both r sufficient to ans the qestion, both have same ans "no" to the ques if every term is prime. OA ?

Bhimsen · Answer

Ans is B.

as fewer than 100 can be any number say k eq 1 or 41 in which case answer is yes ans no.

but taking B answer is definite yes.

so answer is B

nocilis · Answer

There are more than 50 terms in sequence A. This means our series is not all primes for sure. Yup the answer is B. I guess I need to spend more time reading the actual question!! :wall

banerjeea_98 · Answer

I don't undestand. Let's take statement 2 again. For more than 50 terms, we can see that some r primes and some r not just like statement 1. Let's take 82nd term.

k(k+1) + 41 , for k = 82 or 81

82(83) + 41 this is divisible by 41, so not prime. Again for k = 80 we have 

80(81) + 41 which is prime. So this is just as statement 1 is , some prime some not.


Am I missing something here ??? Plz explain how B is the ans. Thx

jinino · Answer

I am too confused here. Anyone pls explain, thanks! :oops:

MA · Answer

Banerjee,

you missed the question is: is every term in the series a prime?
from statement ii, the answer is: no.

banerjeea_98 · Answer

Isn't the ans "No" for statement 1 also. As shown by many ppl that using the statement 1 you get some prime some not e.g. k = 40 is not prime., which means not all numbers r prime in the sequence consisting lesser than 100 numbers.

Shudn't ans be "D" then ? I don't see how statement 1 is any diff than statement 2.....???? Someone plz explain.

kayser1soze · Answer

i'm confused about the OA.i also think the answer should be D since both statments by themselves are sufficient to answer the question. whether its yes or no there is no difference, we have enough info to answer it. if anyone has a better explanation of B or any other choice all of us would really appreciate it.

jinino · Answer

I got it from MA's reply for another thread. Take a look https://www.gmatclub.com/phpbb/viewtopic.php?t=12769 8-)

MA · Answer

from i,
suppose, 
if k=1, then A1= 1+1+41 = 43...... prime
if k=2, then A2= 4+2+41 = 47...... prime
if k=3, then A3= 9+3+41 = 53...... prime
.
.
.

if k=41, then A41= 41^2+41+41 = 41(41+1+1)=41(43) ...... not prime

but we do not know how many terms are there in the sequence A. the number of terms in sequence A coud be 1 or 2 or 40 or 41 or 82. so if number of terms in the sequence are fewer than 41, then every term in the sequence are prime otherwise not. from this the answer is no because we do not know the exact number of the terms in the sequence A.

from ii, there are more than 50 terms or at least 51 terms and one term in the sequence is A41, which is not prime as under:

k=1, then A1= 1+1+41 = 43...... prime
k=2, then A2= 4+2+41 = 47...... prime
k=3, then A3= 9+3+41 = 53...... prime
.
.
.
k=41, then A41= 41^2+41+41 = 41(41+1+1)=41(43) ...... not prime
.
.
.
k=51 .......... could or could not be prime (because i have not tested. )

from ii, we can surely say that every term in the sequence is not prime.

therefore the answer is B.

In the sequence A, A1 = 43, A2 = 47,..............., Ak =

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