sequence

[indi999_us]

Sequence S consists of 24 non-zero integers. If each term in S after the second term is the product of the previous two terms, how many terms in S are negative ?

1) The third term in S is positive

2) The fourth term in S is negative

SPOILER: Official Answer B , thought C

[rd_eastbay]

(1)
--+--+...
or
+++++...
Insuff.
(2)
--+--+...
or
-+--+-
One +ve sign for every 2 -ve in either case.
Suff.

Hence B.

[sumeet_rana]

I also thought it is C.
Agree with I being insufficient. But B is also insufficient.
{a,b,a*b, a*b^2, a^2*b^3,...}
II: 4rth term is -ve hence a is - but we cant conclude about b . Therefore B is insufficient also.
But if we take I and II togeather. We get our answer ?

Please explain.

[racsun_81]

I think it should be 'B'.
It is given that 4th term is -ve
this is true only in the following case
Case
a=-ve
b=+ve
a*b=-ve
a*b*b=-ve
Now we can determine the number of -ve terms using rd_eastbay

[Priyadarshi]

B is the correct choice.

1.Stmt 1 not suff , as we can have a sequence with all positive or a seqence with 2 negatives and one positive evry three terms.

2. Stm2 is suff
If the 4th term is -ve either the third is -ve and 2nd is +ve or 3rd is +ve and 2nd is -ve .

case 1 : 3rd -ve , which means the first has to be -ve as thes econd is +ve , so we hv a sequence : - + - - +--+-... so 16 -ve and 8+ve (as in every three terms there is 2 -ve and 1 +ve)

case 2 : 3rd +ve , means 2nd is -ve and so 1st is also -ve , so sequence is : --+--+...

so total 16 -ve and 8 +ve ( same answer as case 1)

therefore B is suff .