Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

68% (02:22) correct
32% (02:38) wrong based on 37 sessions

Veritas Prep 10 Year Anniversary Promo Question #3

One quant and one verbal question will be posted each day starting on Monday Sept 17th at 10 AM PST/1 PM EST and the first person to correctly answer the question and show how they arrived at the answer will win a free Veritas Prep GMAT course ($1,650 value). Winners will be selected and notified by a GMAT Club moderator. For more questions and details please check here: veritas-prep-10-year-anniversary-giveaway-138806.html

To participate, please make sure you provide the correct answer (A,B,C,D,E) and explanation that clearly shows how you arrived at it. Winners will be announced the following day at 10 AM Pacific/1 PM Eastern Time.

A sequence is given by the rule a_{n} = |a_{(n-2)}| - |a_{(n-1)}| for all n\geq{3}, where a_1 = 0 and a_2 = 3.

A function s_{n} is defined as the sum of all the terms of the sequence from its beginning through a_n. For instance, s_{4} = a_1 + a_2 + a_3 + a_4. What is s_{101}?

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:

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}. _________________

Ans=C, i have considered first upto a12, and observed that s1=0, s2=3, s3=0 and the cycle repeats.. by this we can divide 101 as 99+2 i.e., s99 would be 0 and s100 =0 and s101=3.

Last edited by chetanachethu on 18 Sep 2012, 10:05, edited 2 times in total.

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

If we use the above formula we get a repetitve series of 3,0,-3 as follows a3 = |a2|- |a1| = 3-0 = 3 a4 = |a3| - |a2| = 3-3 =0 a5 = |a4|-|a3| = 0 - 3 = -3 a6 = |a5| - |a4| = |-3| - 0 = 3-0 =3 a7 = |a6| - |a5| = |3| - |-3| = 3 -3 = 0 And this trend will continue as follows a8 = -3 , a9 = 3 ....and so on until a101 = -3 If we observe there is a pattern emerging starting a3 .If we sum a particular triplet,say a3 + a4+ a5 = 3+0+-3 = 0. Our sum will be 0 Similiarly if we keep adding triplets a6 + a7 + a8 =0 a9 + a10 + a11 = 0 . . . a99 + a100 + a101 = 3 + 0 + -3 = 0. So we can conclude the sum of all the triplets is 0. a3 + .a4 + a5 + .......a101 = 0.

S101 = a1 + a2 + (sum of all the triplets present ) = 0 + 3 + 0 Hence S101 = 3.

A sequence is given by the rule a_{n} = |a_{(n-2)}| - |a_{(n-1)}| for all n\geq{3}, where a_1 = 0 and a_2 = 3.

A function s_{n} is defined as the sum of all the terms of the sequence from its beginning through a_n. For instance, s_{4} = a_1 + a_2 + a_3 + a_4. What is s_{101}?

(A) -3 (B) 0 (C) 3 (D) 201 (E) 303

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.)

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

A sequence is given by the rule a_{n} = |a_{(n-2)}| - |a_{(n-1)}| for all n\geq{3}, where a_1 = 0 and a_2 = 3.

A function s_{n} is defined as the sum of all the terms of the sequence from its beginning through a_n. For instance, s_{4} = a_1 + a_2 + a_3 + a_4. What is s_{101}?[/b]

So the series is 0, 3, -3, 0, 3, -3, for a(1), a(2), a(3), a(4), a(5) and a(6) respectively. If you look at the series carefully, S(3) = 0 + 3 + (-3) = 0 this trend will continue and hence S(3), S(6), S(9)..... S(99) = 0 S(101) = S(99) + a(100) + a(101) = 0 + 0 + 3 = 3 S(101) = 3

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:

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}. _________________

It’s been a long time, since I posted. A busy schedule at office and the GMAT preparation, fully tied up with all my free hours. Anyways, now I’m back...

Ah yes. Funemployment. The time between when you quit your job and when you start your MBA. The promised land that many MBA applicants seek. The break that every...