Sequence S consists of 24 nonzero integers. If each term in S after the second 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
One important thing to understand is that in GMAT sequence questions there is almost always a pattern. So there is no real need to calculate all 24 integers' signs.
The most difficult part in this question is:
If each term in S after the second is the product of the previous two terms .
It is the same as saying that:
x; y; xy; x(y^2); (x^2)(y^3); (x^3)(y^5); (x^5)(y^8); ...
1 st.) xy is positive. In this case both x and y are negative or they both positive. If both positive all the terms will be positive: (+) (+) (+) (+) (+) (+)... In case both are negative we have: (-) (-) (+) (-) (-) (-) (+).... Two different answers - statement is not sufficient
2 st.) x(y^2) is negative. There are two possible options: x is negative and y is positive, or x is negative and y is negative.
In the 1st option we have the following pattern: (-) (+) (-) (-) (+) (-) (-) (+)...
In the 2nd option we have the follwing pattern: (-) (-) (+) (-) (-) (+) (-) (-)... It starts slightly different but the pattern is the same, so we can conclude that the number of positives and negatives within 24 integers will be the same rerdless of the options. So the answer is B.
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