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Sequence

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by acorra » Sun Nov 09, 2008 10:00 am
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


Please explain in details,
thanks
Andrew
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Source: — Data Sufficiency |
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by cramya » Sun Nov 09, 2008 10:19 am
I would go wiht B) OA?
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by acorra » Sun Nov 09, 2008 10:23 am
yes it is, please explain now....

thanks
Andrew
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by cramya » Sun Nov 09, 2008 10:36 am
Stmt I

Given: x1 x2 x3 x4 ...... x24

The third term in S is positive i.e x3 is positive

x1 and x2 could bothe be positive or x1 and x2 could both be negative. This does not lead us to a 1 definite answer for the number of negative terms

INSUFF

Stmt II


The fourth term in S is negative i.e x4 is negative

This means either x3 is negative x2 positive
(OR)
x3 is POSITIVE x2 NEGATIVE

Case 1
x1 x2 x3 x4 x5 x6
+ve - ve -ve +ve -ve

or

Case2

x1 x2 x3 x4 x5 x6
-ve +ve -ve -ve +ve

If u notice after x5 the signs alternate and there are 20 left of which 10 will be negative and 10 positive

We now have to figure out x1-x4 signs

Case 1
x1 x2 x3 x4
-ve +ve - ve -ve

If its case1 then x1 has to be -ve


Case2

x1 x2 x3 x4
-ve -ve +ve -ve

If its case2 then x1 still has to be -ve since x2 is neagtive and x3 is positive

So whether its case 1 or case 2 we know in x1-x4 ther's 3 nagatives and 1 positive

1 DEFINITE ANSWER for the number of negative terms

SUFF

Let me know if u still have questions (m hoping the format came out right for the x's)

Good luck!
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by cramya » Sun Nov 09, 2008 10:39 am
The formatting dint come out as expected so reposting it (removing x1)

Stmt II


The fourth term in S is negative i.e x4 is negative

This means either x3 is negative x2 positive
(OR)
x3 is POSITIVE x2 NEGATIVE

Forget x1 for the time being
Case 1
x2 x3 x4 x5 x6
+ve - ve -ve +ve -ve

or

Case2

x2 x3 x4 x5 x6
-ve +ve -ve -ve +ve

If u notice after x5 the signs alternate and there are 20 left of which 10 will be negative and 10 positive

We now have to figure out x1-x4 signs

Case 1
x1 x2 x3 x4
-ve +ve - ve -ve

If its case1 then x1 has to be -ve


Case2

x1 x2 x3 x4
-ve -ve +ve -ve

If its case2 then x1 still has to be -ve since x2 is neagtive and x3 is positive

So whether its case 1 or case 2 we know in x1-x4 ther's 3 nagatives and 1 positive

1 DEFINITE ANSWER for the number of negative terms

SUFF

Let me know if u still have questions (m hoping the format came out right for the x's)

Good luck!
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