Sequence S consists of 24 nonzero integers. If each term in

Check the statements not the OA (placement of negative/positive in 1 and 2). There is nothing wrong with the question.

you were right......I AM going mental.... just edited my post....hope this makes more sense

One final question:
I misinterpreted the If each term in S after the second part....thought that the "formula"/instructions (\(An= An-1 * An-2\) is only for the third onwards, thus we know nothing for the first two terms thus it is not possible to answer the question.....is that a valid conclusion....?

You interpreted correctly: \(a_n=a_{n-1}*a_{n-2}\), for \(n>2\).

But you are not right about the first two terms for the following statements:


(2) The fourth term in S is negative --> \(a_4=negative=a_3*a_2\) --> second and third term must have opposite signs, so third term is either positive or negative. Now, case 1: if third term is positive then first and second terms must be both negative (for first and second it's not possible to be both positive as in this case fourth term would be positive too and we know that it's negative) and case 2: if third term is negative then first and second terms must have opposite signs. So there are only 2 cases possible:

--+--+--+...
OR
-+--+--+-...

In both cases there is a repeated pattern of three terms in which 2 are negative and 1 positive (--+ or -+-) so in both cases out of 24 terms 2/3 will be negative, so there will be 16 negative terms. Sufficient.

Answer: B.

I also get B. You can establish a pattern at 4 and each combination to get negative (- * + or + * -) gets to the same number of negative numbers. I must admist that I did this the long way, without a formula - prorbably took a little over 2 minutes.

If you write out the options resulting from b

T3 below will be T1T2
T1 ---------- T2--------- T3--------------T4
-ve -ve +ve -ve
-ve +ve -ve -ve

For both these cases expand out the first 8 terms and you will see the ratio of 2:1 for negative to positive!

I classify these types of questions as torturous; because we need to count them out to be sure.

1. We can easily rule this out because the 3rd term is +ve; first two can either be -ve or all can be positive. Not sufficient.

2. This statement is little hairy.

X-------\(|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|\). 16 -ves

Y-------\(|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|\). 16 -ves

Sufficient.

Well after some thought; you may recognize the pattern that there are two negatives after every +ve; but I would rather write them all out and count them.

As you see for X; first position is -ve and the 2nd +ve. 3rd and 4th are negative and 5th +ve and the pattern continues. You may now count -ves. Likewise for Y.


Ans: "B"

Bunuel you are awesome ! If I had seen this question on test day I would have marked C and move on ! But then I took numbers and yes it answered. So - its imperative to find the first negative term. That is the key for the pattern ? Right?

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

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.

Even though OA is B and is right, # of negative terms is 17 and not 16. The first term has to be negative in both the scenarios of B.

There are 24 numbers and 2/3 are negative, thus 16 numbers are negative not 17.

Yes 16, I over worked on the final answer

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 --> either all terms are positive, so zero negatives or +--... and not all terms are positive, so more than zero negatives. Not sufficient.

(2) The fourth term in S is negative --> again two cases:

--+--+--+...
OR
-+--+--+-...

The same here: in both cases there is a repeated pattern of three terms in which 2 are negative and 1 positive (--+ or -+-) so in both cases out of 24 terms 2/3 will be negative, so there will be 16 negative terms. Sufficient.

Answer: B.
tnx for this

1st term x
2nd term y
S={x,y,xy,xy^2.........}

since 4th term is -ve , xY^2 is -ve i.e. x is -ve since y^2 cannot be -ve.
Now since 1st term is -ve there can be 2 different pattern for the sequence assuming 2nd term to be either +ve or -ve.

S={-,-,+,-,-,+,......}
or
S={-,+,-,-,+,-,......}

So its clear that either 2nd term is +ve or -Ve the # of -ve terms is equal for 24 terms(since # of terms is a product of 3).

Why isn't fourth term x^2y^2

Each term in S after the second is the product of the previous two terms.
x
y
xy
y*xy = xy^2
xy*xy^2 = x^2y^3
...

Hope it's clear now.