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## Veritas Prob

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klmehta03 Rising GMAT Star
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Veritas Prob Mon Apr 02, 2012 5:13 pm
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The inifinite sequence a1,a2,a3.....an.. is such that a1=X,a2=y, a3=Z,a4=3, and an=a(n-4) (<--subscript) for n>4. what is the sum of first 98 terms of sequence?

1) x=5
2) y+Z=2

OA later

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Mon Apr 02, 2012 9:11 pm
klmehta03 wrote:
The inifinite sequence a1,a2,a3.....an.. is such that a1=X,a2=y, a3=Z,a4=3, and an=a(n-4) (<--subscript) for n>4. what is the sum of first 98 terms of sequence?

1) x=5
2) y+Z=2

OA later
Our sum is X + Y + Z + 3 + X + Y + Z + 3 +... We can see that we have a pattern of 4 terms. WIth a total of 98 terms in the sequence, we know how many complete patterns (one set of all 4 terms) we have: 98/4 = 24 R 2. We have 24 sets of 4, and 2 extra terms (which must be X and Y). We can rewrite our equation as:

=24(X + Y + Z + 3) + X + Y

To solve, we'll need a way to fill in each variable.

Statement 1 provides X, but Y and Z are still unknown. Insufficient.

Statement 2 provides Y + Z, but X is still unknown. Insufficient.

Put together, we have values for each variable. However, the problem is that we only have Y and Z together. If we fill in our equation, we're still left with a lone Y:

24(5 + 2 + 3) + 5 + Y

Y could have many values. It could be 1 if Z is 1, 0 if Z is 2, 2 if Z is 0, etc. Thus, we could end up with many different sums, so the correct answer is E

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