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:

In a certain sequence, each term, starting with the 3rd term [#permalink]
27 Mar 2013, 21:53

3

This post received KUDOS

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (medium)

Question Stats:

39% (05:10) correct
61% (01:36) wrong based on 218 sessions

In a certain sequence, each term, starting with the 3rd term, is found by multiplying the previous two terms. What is the difference between the 6th and 3rd terms in the sequence?

(1) The 1st term is equal to 8 times the 2nd term. (2) The 4th term is equal to 1.

Re: In a certain sequence, each term, starting with the 3rd term [#permalink]
27 Mar 2013, 22:40

1

This post received KUDOS

Expert's post

mun23 wrote:

In a certain sequence, each term, starting with the 3rd term, is found by multiplying the previous two terms. What is the difference between the 6th and 3rd terms in the sequence?

(1) The 1st term is equal to 8 times the 2nd term.

(2) The 4th term is equal to 1.

Need explanation

From F.S 1, consider this series : 8, 1, 8, 8, 64, 64*8.

Again, consider the series 2, 1/4, 1/2, 1/8, 1/16, 1/(8*16). Clearly, the difference of the 6th and the 3rd term is different for them. Insufficient.

From F.S 2, let the series be a,b,ab,ab^2,a^2b^3,a^3b^5. Now we know that ab^2 = 1. The required difference =a^3b^5 - ab = ab(a^2b^4-1) = ab[(ab^2)^2 -1]= 0.Sufficient.

Re: In a certain sequence, each term, starting with the 3rd term [#permalink]
27 Jun 2013, 22:18

3

This post received KUDOS

mun23 wrote:

In a certain sequence, each term, starting with the 3rd term, is found by multiplying the previous two terms. What is the difference between the 6th and 3rd terms in the sequence?

(1) The 1st term is equal to 8 times the 2nd term. (2) The 4th term is equal to 1.

The question is: 1st term = x 2nd term = y 3rd term = xy 4th term = (xy)*y = xy^2 5th term = (xy^2)*(xy) = x^2y^3 6th term = (x^2y^3)*(xy^2) = x^3y^5

Have equation: 6th term - 3rd term = x^3y^5 - xy = xy(x^2y^4 -1)

Statement 1: The 1st term is equal to 8 times the 2nd term ==> x = 8y Replace back to equation: 6th term - 3rd term = 8yy((8y)^2y^4 -1) = 8y^2(64y^6 - 1) ==> NOT Sufficient because we don't know y

Statement 2: The 4th term is equal to 1 ==> =xy^2 = 1. Replace back to equation: 6th term - 3rd term = xy((xy^2)^2 - 1) = xy(1 - 1) = 0 ==> Sufficient

Hence, B is correct.

Hope it helps.

_________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Re: In a certain sequence, each term, starting with the 3rd term [#permalink]
04 Feb 2014, 04:04

(1) First term is 8 times the second term. could be 8 and 1 or 64 and 8 or 2 and 1/4, which would all lead to different sequences, varying the differences between the 6th and the 3rd term.. IS.

(2) Since the 4th term is 1 and has to be a product of the 3rd and 2nd term, all terms are 1, so the difference will be zero. SUFF.

Hence answer B.

I guess it was a lucky pick for me, but I didn't took long time setting up equations and stuff. Went straight as I described it, took me about 40 seconds!

Re: In a certain sequence, each term, starting with the 3rd term [#permalink]
18 Feb 2014, 16:29

unceldolan wrote:

(1) First term is 8 times the second term. could be 8 and 1 or 64 and 8 or 2 and 1/4, which would all lead to different sequences, varying the differences between the 6th and the 3rd term.. IS.

(2) Since the 4th term is 1 and has to be a product of the 3rd and 2nd term, all terms are 1, so the difference will be zero. SUFF.

Hence answer B.

I guess it was a lucky pick for me, but I didn't took long time setting up equations and stuff. Went straight as I described it, took me about 40 seconds!

Why should all terms be 1? Do we have to assume that all terms are integers here? What if S2 = 1/3 and S3= 3 then S4 = (1/3)(3) = 1

Re: In a certain sequence, each term, starting with the 3rd term [#permalink]
18 Feb 2014, 21:13

1

This post received KUDOS

Expert's post

jlgdr wrote:

unceldolan wrote:

(1) First term is 8 times the second term. could be 8 and 1 or 64 and 8 or 2 and 1/4, which would all lead to different sequences, varying the differences between the 6th and the 3rd term.. IS.

(2) Since the 4th term is 1 and has to be a product of the 3rd and 2nd term, all terms are 1, so the difference will be zero. SUFF.

Hence answer B.

I guess it was a lucky pick for me, but I didn't took long time setting up equations and stuff. Went straight as I described it, took me about 40 seconds!

Why should all terms be 1? Do we have to assume that all terms are integers here? What if S2 = 1/3 and S3= 3 then S4 = (1/3)(3) = 1

Can anyone explain second statement?

Thanks a lot Cheers J

No, you don't have to assume anything. What you say is absolutely possible though it doesn't change our answer.

"S2 = 1/3 and S3= 3 then S4 = (1/3)(3) = 1"

The sequence could be: 9, 1/3, 3, 1, 3, 3, .... But in any case t_6 - t_3 = 0

Note why: Statement 2 tells us that t_4 = 1

t_1, t_2, t_3, 1, what will be t_5? It will be t_3 * 1 = t_3 What will be t_6? It will be 1*t_5 = 1*t_3 = t_3

So in any case the sixth term will be same as the third term. Once you have a 1 in the sequence, all following terms will be equal to the term just preceding 1.