Winner:

yogeshwar007

Official Explanation:

Answer is C

While we spend a lot of time honing the skill of translating English into algebra, there is sometimes great comfort to be gained in a sequence problem through doing precisely the reverse. The general rule for this sequence is that we derive each term based on the two terms that precede it – specifically by subtracting the absolute value of the previous term from the absolute value of the “pre-previous” one.

So a_3 = |a_1| - |a_2|, and a_4 = |a_2| - |a_3|, and a_5 = |a_3| - |a_4|, and so on. We are told that the sequence begins 0, 3, ..., so we can derive that:

a_3 = |a_1| - |a_2| = |0| - |3| = 0 - 3 = -3.
Then a_4 = |a_2| - |a_3| = |3| - |-3| = 3 - 3 = 0.
Then a_5 = |a_3| - |a_4| = |-3| - |0| = 3 - 0 = 3.

As soon as we’ve seen a_4 and a_5 turn out to be 0 and 3 consecutively, we know that the next number to show up in the sequence will be identical to the number that showed up after the last time we saw 0 and 3 appear consecutively (i.e. as a_1 and a_2) — so a_6 will be identical to a_3, so -3. So we have established the pattern 0, 3, -3, 0, 3, -3, ... for our sequence.

Every time we finish a complete cycle within the sequence, the sum returns to 0 (since 0 + 3 + -3 = 0). We finish a cycle after every third entry (i.e. after the third, the sixth, the ninth, and so on), so we will have done so (and returned our running sum to 0) with a_{99}. a_{100} will then add itself (0) to that sum, and a_{101} will add itself (3) onto that. So we will land at a sum of 3 for s_{101}.
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first 8 terms 0,3,-3,0,3,-3,0,3

sum of every four terms is 0+3-3+0 = 0 sum of S100 = 0 sum of s101 = 0+3 =3

Answer is 3 (C)

ANswer C.


S101 = a1+ a2+ .....+ a101

a3=|a1|-|a2|= -3
a4=0

Follwoing the pattern,,

0,3,-3,0,3,-3,....

S99 = 0

A100=0

A101=3

Hence,S101=3

IMo - C

pattern
0,3,-3, ...
sum of 3 terms = 0
sum of 99 terms = 0
100 th = 0
101st = 3

sum = 3
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CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned

Considering the rule of Cyclicity,we can conclude that the pattern repeat itself after 3 units i.e a1=0,a2=3,a3=-3 ; again a4=0,a5=3,a6=-3 and so on...

Now 101/3 [as the pattern repeat itself after 3 units as above] gibes a quotient 99 and thus sum of a1+a2+..a99=0 [as every 3 units having sum 0]and a100+a101=|0|+|3|=3

So, S101=a1+a2+..a99+a100+a101=3.

So Answer is 3.
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UPDATED : AWA compilations-109 Analysis of Argument Essays

a3 = |a1| - |a2|
a4 = |a2| - |a3|
a5 = |a3| - |a4|
..
..
..
..
a100 = |a98| - |a99|
a101 = |a99| - |a100|
----------------------
Summing together both sides
a3+a4+a5+.......+a101 = |a1| - |a100| ( because all other values will be cancelled out in right hand side. For example, |a2| from 1st equation will be cancelled out from |a2| from 2nd equation, and so on.)

adding a1 + a2 both sides
a1 + a2 +a3 .............. + a101 = S101 = a1+a2+|a1| - |a100|
=> 0 + 3 + |0| - |a100|

Now these terms follow a pattern as follows:
a3 = -3
a4 = 0
a5 = -3
..
..
..
So, EVEN indexed "a" will be zero.
Thus, => 0+3+|0|+0 = 3

Hence, answer is C.
_________________

FOCUS..this is all I need!

Ku-Do!

So I figured out the sequence first
a1=0, a2=3, a3=-3, a4=0, a5=3, a6=-3, a7=0, a8=3, a9=-3, a10=0.......
Every third term is a -3 for a3, a6, a9, a12, a15, a18, a21, a, 24....... They are all -3.
So s102 = -3 therefore s101 = 3
Another is that the sum of the first 10 is 0 s10= s1 + s2 +s3 + s4....... is 0 so every tenth interval is 0, therefore s100=0
The answer is 3 which is option C

Answer is C!

The pattern is 0,3,-3,0,3,-3,0,3,-3...

101/3=99 R2

0+3=3

Answer is C:

Explaination:
a(1) = 0 (given)
a(2) = 3 (given)
a(3) = |a(1)| - |a(2)| = |0| - |3| = 0 - 3 = -3
a(4) = |a(2)| - |a(3)| = |3| - |-3| = 3 - 3 = 0
a(5) = |a(3)| - |a(4)| = |-3| - |0| = 3 - 0 = 3
a(6) = |a(4)| - |a(5)| = |0| - |3| = 0 - 3 = -3

However the question asks for S(101). So we have to find a series for S(n).
S(1) = a(1) = 0
S(2) = a(1) + a(2) = 0 + 3 = 3
S(3) = a(1) + a(2) + a(3) = 0 + 3 - 3 = 0
S(4) = a(1) + a(2) + a(3) + a(4) = 0 + 3 - 3 + 0 = 0
s(5) = a(1) + a(2) + a(3) + a(4) + a(5) = 0 + 3 - 3 + 0 + 3 = 3
s(6) = a(1) + a(2) + a(3) + a(4) + a(5) +a(6) = 0 + 3 - 3 + 0 + 3 - 3 = 0

So the real series is 0, 3, 0, 0, 3, 0, for s(1), s(2), s(3), s(4), s(5) and s(6) respectively.

If you divide 101/3 you get 33 remainder 2, which tells us the correct answer should be the 2nd term of the series,
hence S(101) = 3

We have a winner!

Winner:

yogeshwar007

Official Explanation:

Answer is C

While we spend a lot of time honing the skill of translating English into algebra, there is sometimes great comfort to be gained in a sequence problem through doing precisely the reverse. The general rule for this sequence is that we derive each term based on the two terms that precede it – specifically by subtracting the absolute value of the previous term from the absolute value of the “pre-previous” one.

So a_3 = |a_1| - |a_2|, and a_4 = |a_2| - |a_3|, and a_5 = |a_3| - |a_4|, and so on. We are told that the sequence begins 0, 3, ..., so we can derive that:

a_3 = |a_1| - |a_2| = |0| - |3| = 0 - 3 = -3.
Then a_4 = |a_2| - |a_3| = |3| - |-3| = 3 - 3 = 0.
Then a_5 = |a_3| - |a_4| = |-3| - |0| = 3 - 0 = 3.

As soon as we’ve seen a_4 and a_5 turn out to be 0 and 3 consecutively, we know that the next number to show up in the sequence will be identical to the number that showed up after the last time we saw 0 and 3 appear consecutively (i.e. as a_1 and a_2) — so a_6 will be identical to a_3, so -3. So we have established the pattern 0, 3, -3, 0, 3, -3, ... for our sequence.

Every time we finish a complete cycle within the sequence, the sum returns to 0 (since 0 + 3 + -3 = 0). We finish a cycle after every third entry (i.e. after the third, the sixth, the ninth, and so on), so we will have done so (and returned our running sum to 0) with a_{99}. a_{100} will then add itself (0) to that sum, and a_{101} will add itself (3) onto that. So we will land at a sum of 3 for s_{101}.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates