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# In the sequence S of numbers, each term after the first two

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In the sequence S of numbers, each term after the first two  [#permalink]

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26 Feb 2014, 01:21
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55% (hard)

Question Stats:

66% (02:09) correct 34% (02:27) wrong based on 1074 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

In the sequence S of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of S?

(1) The 6th term of S minus the 4th term equals 5.
(2) The 6th term of S plus the 7th term equals 21.

Data Sufficiency
Question: 111
Category: Arithmetic Sequences
Page: 161
Difficulty: 650

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Re: In the sequence S of numbers, each term after the first two  [#permalink]

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26 Feb 2014, 01:22
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SOLUTION

In the sequence S of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of S?

$$s_n=s_{n-1}+s_{n-2}$$, for $$n>2$$.

(1) The 6th term of S minus the 4th term equals 5 --> $$s_6-s_4=5$$ --> $$(s_5+s_4)-s_4=5$$ --> $$s_5=5$$. Sufficient.

(2) The 6th term of S plus the 7th term equals 21 --> $$s_6+s_7=21$$ --> $$s_6+(s_6+s_5)=21$$. Since we don't know $$s_6$$ we cannot find $$s_5$$. Not sufficient.

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Re: In the sequence S of numbers, each term after the first two  [#permalink]

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27 Feb 2014, 21:17
4
1
Lets assume the first two terms to be x and y
Then rest of the numbers in the series will be x, y, x+y, x+2y, 2x+3y, 3x+5y, 5x+8y, ...

A.) (3x+5y) - (x+2y) = 5
2x+3y = 5 which is indeed the fifth term

SUFFICIENT

B.) (3x+5y) +(5x+8y) = 21
8x+13y = 21
its the 8th term

INSUFFICIENT

Difficulty - 650
Time taken - 1:59
##### General Discussion
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Re: In the sequence S of numbers, each term after the first two  [#permalink]

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27 Feb 2014, 21:47
3
b2bt wrote:
Lets assume the first two terms to be x and y
Then rest of the numbers in the series will be x, y, x+y, x+2y, 2x+3y, 3x+5y, 5x+8y, ...

A.) (3x+5y) - (x+2y) = 5
2x+3y = 5 which is indeed the fifth term

SUFFICIENT

B.) (3x+5y) +(5x+8y) = 21
8x+13y = 21
its the 8th term

INSUFFICIENT

Difficulty - 650
Time taken - 1:59

Or you can simply say that the terms are t1, t2, ....

(1) The 6th term of S minus the 4th term equals 5.
t6 - t4 = 5
But t6 = t4 + t5
t6 - t4 = t5 = 5
Sufficient

(2) The 6th term of S plus the 7th term equals 21.
t6 + t7 = 21
t6 + t6 + t5 = 21
We don't know t6 and hence we cannot find t5.
Not sufficient

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Re: In the sequence S of numbers, each term after the first two  [#permalink]

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01 Mar 2014, 04:47
SOLUTION

In the sequence S of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of S?

$$s_n=s_{n-1}+s_{n-2}$$, for $$n>2$$.

(1) The 6th term of S minus the 4th term equals 5 --> $$s_6-s_4=5$$ --> $$(s_5+s_4)-s_4=5$$ --> $$s_5=5$$. Sufficient.

(2) The 6th term of S plus the 7th term equals 21 --> $$s_6+s_7=21$$ --> $$s_6+(s_6+s_5)=21$$. Since we don't know $$s_6$$ we cannot find $$s_5$$. Not sufficient.

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Re: In the sequence S of numbers, each term after the first two  [#permalink]

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18 May 2014, 09:07
1.The 6th term of S minus the 4th term equals 5.

i.e S6 = S5+S4 (from question as given)
thus S6 - S4 = S5 = 5

A) sufficient

2.The 6th term of plus the 7th term equals 21.

It gives no value of any term in the sequence. Therefore impossible to determine S5.
Not sufficient.
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In the sequence S of numbers, each term after the first two  [#permalink]

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18 Jul 2015, 09:11
Let the 1st and 2nd term of the series S be a & b. Than from question stem S= {a , b, a+b, a+2b, 2a+3b, 3a+5b, 5a+8b,....}
We need to find 5th term i.e value of 2a+3b;

from(1): 6th term -4th term = 5=> (3a+5b)-(a+2b)=5=>2a+3b=5 Hence Sufficient
alternatively from question stem 6th Term = 4th term+5th term=>5th term = 6th term -4th term : same as option 1

from(2): At best you can find out value of 8th term Not Sufficient

P.S. This type of series is called fibonacci series: https://en.wikipedia.org/wiki/Fibonacci_number

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Re: In the sequence S of numbers, each term after the first two  [#permalink]

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18 Dec 2015, 07:12
Let say that the first term is called a, the second term is called b, and so on...

(1) Given equation f - d = 5
From the question stem, you realize that d + e = f, or in other words, f - d = e. Combining the information, you yield e = 5.
Sufficient.

(2) Insufficient.
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Re: In the sequence S of numbers, each term after the first two  [#permalink]

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19 Dec 2015, 04:33
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In the sequence S of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of S?

(1) The 6th term of S minus the 4th term equals 5.
(2) The 6th term of S plus the 7th term equals 21.

When you modify the original condition and the question, they become S_n=S_(n-1)+S_(n-2). When you substitute n=5, or S_5=S_4+S_3 or n=6, S_6=S_5+S_4 becomes S_5=S_6-S_4. (The reason why you substitute n=5,6 is S_5=?) Therefore, in 1), S_5-S_4=5 and this is S_5=5, which is sufficient. Therefore, the answer is A.

-> Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: In the sequence S of numbers, each term after the first two  [#permalink]

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30 Jun 2017, 13:42
I find it easy to write the sequence before proceeding.

Given:S= a, b, c, d, e, f , g, h, i.........
c=a+b , we need to find e.

We know that e=c+d

Statement 1: 6th term - 4th term = 5
or f-d=5 which is a fancy way of saying e =5 because f=d+e ...........Sufficient......AD BCE

Statement 2: Terms 6 and 7 add up to 21
or g+h=21
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In the sequence S of numbers, each term after the first two  [#permalink]

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23 May 2018, 18:47
Bunuel wrote:
SOLUTION

In the sequence S of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of S?

$$s_n=s_{n-1}+s_{n-2}$$, for $$n>2$$.

(1) The 6th term of S minus the 4th term equals 5 --> $$s_6-s_4=5$$ --> $$(s_5+s_4)-s_4=5$$ --> $$s_5=5$$. Sufficient.

(2) The 6th term of S plus the 7th term equals 21 --> $$s_6+s_7=21$$ --> $$s_6+(s_6+s_5)=21$$. Since we don't know $$s_6$$ we cannot find $$s_5$$. Not sufficient.

Can anyone please explain how S7 = S6+S5 as i did not get it?

Instead of x, y, x+y, x+2y, 2x+3y, 3x+5y, 5x+8y, ..., Can i consider x,y, x+y, 2x+y, 2x+2y, 4x+3y,4x+4y?
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Re: In the sequence S of numbers, each term after the first two  [#permalink]

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23 May 2018, 21:01
Raxit85 wrote:
Bunuel wrote:
SOLUTION

In the sequence S of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of S?

$$s_n=s_{n-1}+s_{n-2}$$, for $$n>2$$.

(1) The 6th term of S minus the 4th term equals 5 --> $$s_6-s_4=5$$ --> $$(s_5+s_4)-s_4=5$$ --> $$s_5=5$$. Sufficient.

(2) The 6th term of S plus the 7th term equals 21 --> $$s_6+s_7=21$$ --> $$s_6+(s_6+s_5)=21$$. Since we don't know $$s_6$$ we cannot find $$s_5$$. Not sufficient.

Can anyone please explain how S7 = S6+S5 as i did not get it?

Instead of x, y, x+y, x+2y, 2x+3y, 3x+5y, 5x+8y, ..., Can i consider x,y, x+y, 2x+y, 2x+2y, 4x+3y,4x+4y?

The stem says that each term after the first two terms is the sum of the two immediately preceding terms. So, the seventh term $$s_7$$ equals to the sum of the two immediately preceding terms, which are $$s_5$$ and $$s_6$$: $$s_7=s_6+s_5$$.

If you consider the first term to be x and the second term to be y, then:
1st term = x;
2nd term = y;
3rd term = x + y;
4th term = y + (x + y) = 2y + x;
5th term = (x + y) + (2y + x) = 3y + 2x;
...
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In the sequence S of numbers, each term after the first two  [#permalink]

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19 Jan 2019, 00:21
Bunuel wrote:

The stem says that each term after the first two terms is the sum of the two immediately preceding terms. So, the seventh term $$s_7$$ equals to the sum of the two immediately preceding terms, which are $$s_5$$ and $$s_6$$: $$s_7=s_6+s_5$$.

If you consider the first term to be x and the second term to be y, then:
1st term = x;
2nd term = y;
3rd term = x + y;
4th term = y + (x + y) = 2y + x;
5th term = (x + y) + (2y + x) = 3y + 2x;
...

okay so i did this
6th term = 3x + 5y
7th term = 5x + 8y

St1 -- 6th - 4th = 5
3x + 5y - x - 2y => 2x + 3y = 5 --looks like x n y should be 1

St2 -- 6th + 7th = 21
3x + 5y +v5x + 8y => 8x + 13y = 21 --looks like x n y should be 1

could you please let me know why above is wrong ?
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Re: In the sequence S of numbers, each term after the first two  [#permalink]

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19 Jan 2019, 00:39
gmatns2018 wrote:
Bunuel wrote:

The stem says that each term after the first two terms is the sum of the two immediately preceding terms. So, the seventh term $$s_7$$ equals to the sum of the two immediately preceding terms, which are $$s_5$$ and $$s_6$$: $$s_7=s_6+s_5$$.

If you consider the first term to be x and the second term to be y, then:
1st term = x;
2nd term = y;
3rd term = x + y;
4th term = y + (x + y) = 2y + x;
5th term = (x + y) + (2y + x) = 3y + 2x;
...

okay so i did this
6th term = 3x + 5y
7th term = 5x + 8y

St1 -- 6th - 4th = 5
3x + 5y - x - 2y => 2x + 3y = 5 --looks like x n y should be 1

St2 -- 6th + 7th = 21
3x + 5y +v5x + 8y => 8x + 13y = 21 --looks like x n y should be 1

could you please let me know why above is wrong ?

2x + 3y = 5 has INFINITELY MANY solutions. It's an equation with TWO unknowns. For example, x = 0 and y =5/3.
8x + 13y = 21 has INFINITELY MANY solutions. It's an equation with TWO unknowns. For example, x = 0 and y =21/3.
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Re: In the sequence S of numbers, each term after the first two  [#permalink]

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19 Jan 2019, 04:37
a1=x
a2=y
a3=x+y
a4=x+2y
a5=2x+3y
a6=3x+5y
a7=5x+8y
#1
a6-a4=5
3x+5y-x-2y=5
2x+3y=5
sufficient

#2
3x+5y+5x+8y=21
8x+13y=21
not sufficient

IMO A

Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

In the sequence S of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of S?

(1) The 6th term of S minus the 4th term equals 5.
(2) The 6th term of S plus the 7th term equals 21.

Data Sufficiency
Question: 111
Category: Arithmetic Sequences
Page: 161
Difficulty: 650

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

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Re: In the sequence S of numbers, each term after the first two   [#permalink] 19 Jan 2019, 04:37
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