GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 18 Feb 2020, 09:05

### GMAT Club Daily Prep

#### 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

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

# After the first two terms in a sequence of numbers, each term in the

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61283
After the first two terms in a sequence of numbers, each term in the  [#permalink]

### Show Tags

26 Apr 2019, 01:56
11
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:43) correct 30% (01:43) wrong based on 416 sessions

### HideShow timer Statistics

After the first two terms in a sequence of numbers, each term in the sequence is formed by adding all of the preceding terms. Is 12 the fifth term in the sequence?

(1) The sum of the first 3 terms in the sequence is 6.
(2) The fourth term in the sequence is 6.

DS92602.01
OG2020 NEW QUESTION

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8261
Re: After the first two terms in a sequence of numbers, each term in the  [#permalink]

### Show Tags

26 Apr 2019, 03:44
3
Bunuel wrote:
After the first two terms in a sequence of numbers, each term in the sequence is formed by adding all of the preceding terms. Is 12 the fifth term in the sequence?

(1) The sum of the first 3 terms in the sequence is 6.
(2) The fourth term in the sequence is 6.

DS92602.01
OG2020 NEW QUESTION

After the first two terms in a sequence of numbers, each term in the sequence is formed by adding all of the preceding terms. Is 12 the fifth term in the sequence?

Now, we are just looking at fifth term, so we can write the first five terms, when first two terms are x and y
So, x, y, ... Third term=(x+y)... fourth term=(x+y)+x+y=2(x+y), and fifth term = 4(x+y)..
The general term is $$2^{n-3}(x+y)$$, so fifth term = $$2^{5-3}(x+y)=4(x+y)$$

1. The sum of the first 3 terms in the sequence is 6.
so sum of the first 3 terms in the sequence=4th term = $$2^{4-3}(x+y)=2(x+y)=6.......x+y=3$$
So, 4(x+y)=483=12
suff

2. The fourth term in the sequence is 6.
Same as statement I
Suff
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9426
Location: United States (CA)
Re: After the first two terms in a sequence of numbers, each term in the  [#permalink]

### Show Tags

12 May 2019, 18:08
3
Bunuel wrote:
After the first two terms in a sequence of numbers, each term in the sequence is formed by adding all of the preceding terms. Is 12 the fifth term in the sequence?

(1) The sum of the first 3 terms in the sequence is 6.
(2) The fourth term in the sequence is 6.

DS92602.01
OG2020 NEW QUESTION

If we can determine the 5th term, then we can determine whether it’s 12 or not. To determine the 5th term, we either need to know the first two terms (since once we know those two terms, then we can determine any other terms) or the sum of the first 3 terms and the 4th term (since the 5th term is the sum of the first 4 terms).
Statement One Alone:

The sum of the first 3 terms in the sequence is 6.

Since the 4th term is the sum of the first 3 terms, so the 4th term is also 6 and thus the 5th term = the 4th term + the sum of the first 3 terms = 6 + 6 = 12. Statement one alone is sufficient.

Statement Two Alone:

The fourth term in the sequence is 6.

Since the 4th term is the sum of the first 3 terms, so the sum of the first 3 terms is also 6 and thus the 5th term = the 4th term + the sum of the first 3 terms = 6 + 6 = 12. Statement two alone is sufficient.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16107
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: After the first two terms in a sequence of numbers, each term in the  [#permalink]

### Show Tags

15 May 2019, 19:41
1
Hi All,

We're told that after the first two terms in a sequence of numbers, each term in the sequence is formed by adding ALL of the preceding terms. We're asked if 12 is the fifth term in the sequence? This is a YES/NO question and can be approached with some basic Arithmetic and note-taking.

(1) The sum of the first 3 terms in the sequence is 6.

With the information in Fact 1, we don't know exactly what those three terms are (they could be 0, 3, 3 or 1, 2, 3, for example), but that doesn't matter, since we can now determine how the sequence proceeds from there...
4th term = sum of the first 3 terms = 6
5th term = sum of the first 4 terms = 6+6 = 12
Thus, the answer to the question is YES.
Fact 1 is SUFFICIENT

(2) The fourth term in the sequence is 6.

The information in Fact 2 defines the same pattern we deduced in Fact 1:
4th term = sum of the first 3 terms = 6
5th term = sum of the first 4 terms = 6+6 = 12
Fact 2 is SUFFICIENT

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5931
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: After the first two terms in a sequence of numbers, each term in the  [#permalink]

### Show Tags

27 Apr 2019, 06:57
Bunuel wrote:
After the first two terms in a sequence of numbers, each term in the sequence is formed by adding all of the preceding terms. Is 12 the fifth term in the sequence?

(1) The sum of the first 3 terms in the sequence is 6.
(2) The fourth term in the sequence is 6.

DS92602.01
OG2020 NEW QUESTION

1st term = a
2nd term = b
so 3rd term ; a+b= 6
4th term ; 6+a+b =
5th term ; 6+6+a+b; 12+a+b

#2 to check 5th term = 12 = 4th term + 3rd term + a+b
4th term ; 3rd term + a+b = 6
so 5th term ; 6+3rd term + a+b
sufficient
IMO D
Re: After the first two terms in a sequence of numbers, each term in the   [#permalink] 27 Apr 2019, 06:57
Display posts from previous: Sort by