GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 06 Dec 2019, 20:27 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In the sequence S of numbers, each term after the first two terms is

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59587
In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

2
51 00:00

Difficulty:   55% (hard)

Question Stats: 66% (02:08) correct 34% (02:25) wrong based on 1179 sessions

### HideShow timer Statistics

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

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

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

10
11
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.

_________________
Manager  Joined: 25 Sep 2012
Posts: 228
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31 GMAT 2: 680 Q48 V34 Re: In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

4
2
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
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India
Re: In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

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

_________________
Karishma
Veritas Prep GMAT Instructor

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

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.
_________________
Senior Manager  P
Joined: 22 Feb 2018
Posts: 312
Re: In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

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?
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

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;
...
_________________
Intern  B
Joined: 03 Dec 2017
Posts: 31
Re: In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

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 ?
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

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.
_________________
Intern  B
Joined: 05 Jan 2019
Posts: 18
Location: Spain
GMAT 1: 740 Q49 V42 Re: In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

Hi,

I am not able to understand why is not d).

When I first read the problem, the Fibonacci sequence instantly came to my mind: 0,1,2,3,5,8,13,21...
The only way I found to start the sequence having the 6th and 7th terms summing up 21 is starting by 0. Therefore I know that 5 is my solution as it is the 5th term.

That (probably incorrect) logic also validates the first statement.

Where am I making the mistake?

Please Bunuel help me! I want to be like you!
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

1
BunuelWannabe wrote:
Hi,

I am not able to understand why is not d).

When I first read the problem, the Fibonacci sequence instantly came to my mind: 0,1,2,3,5,8,13,21...
The only way I found to start the sequence having the 6th and 7th terms summing up 21 is starting by 0. Therefore I know that 5 is my solution as it is the 5th term.

That (probably incorrect) logic also validates the first statement.

Where am I making the mistake?

Please Bunuel help me! I want to be like you!

That's not the only sequence satisfying the stem and the second statement. For example, check 1, 1, 2, 3, 5, 8, 13, ...
_________________
Manager  B
Joined: 31 Mar 2019
Posts: 58
Re: In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

Bunuel wrote:
BunuelWannabe wrote:
Hi,

I am not able to understand why is not d).

When I first read the problem, the Fibonacci sequence instantly came to my mind: 0,1,2,3,5,8,13,21...
The only way I found to start the sequence having the 6th and 7th terms summing up 21 is starting by 0. Therefore I know that 5 is my solution as it is the 5th term.

That (probably incorrect) logic also validates the first statement.

Where am I making the mistake?

Please Bunuel help me! I want to be like you!

That's not the only sequence satisfying the stem and the second statement. For example, check 1, 1, 2, 3, 5, 8, 13, ...

Still the answer will be 5, the 5th term is 5 only in both the sequence

So, why can’t we say D ?

Posted from my mobile device
Manager  B
Joined: 31 Mar 2019
Posts: 58
In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

Bunuel wrote:
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;
...

Can’t we form the sequence by taking some good numbers and then solve this question ?

For eg , Sequence S could be (1,1,2,3,5,8,13) ??

We are getting 5th term as 5 and 6th term + 7th term =8+13 = 21 ,satisfying both the statements

Is it sufficient or I am missing something ? M

Posted from my mobile device

Originally posted by LeenaSai on 14 Nov 2019, 20:56.
Last edited by LeenaSai on 14 Nov 2019, 21:23, edited 1 time in total.
Manager  B
Joined: 31 Mar 2019
Posts: 58
In the sequence S of numbers, each term after the first two terms is  [#permalink]

### Show Tags

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

Can’t we assume the sequence based on the provided pattern to answer this question ?
For eg, Sequence S could be (1,1,2,3,5,8,13..)
5th term is 5 and 6th term + 7th term is 21

So, can’t we say the answer is D ?

Kindly help

Posted from my mobile device In the sequence S of numbers, each term after the first two terms is   [#permalink] 14 Nov 2019, 21:00
Display posts from previous: Sort by

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