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

Question

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.

Bunuel · Accepted Answer

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.

Answer: A.

b2bt · Answer

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

Answer - A
Difficulty - 650
Time taken - 1:59

KarishmaB · Answer

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

Answer (A)

Raxit85 · Answer

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?

Bunuel · Answer

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;
...

gmatns2018 · Answer

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 ?

Bunuel · Answer

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.

BunuelWannabe · Answer

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!

Bunuel · Answer

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

AndrewN · Answer

I also thought of the Fibonacci sequence, but you left out a crucial number in the beginning: 0, 1,  1 , 2, 3, 5, 8, 13, 21... After the first two terms, the sum of the two previous terms is the value of the next term, just as we see in the question above, only this sequence starts with the first 1 instead of 0. I am guessing the question-writer had some fun with this one.

(Love the Feynman photo, by the way.)

- Andrew

Purnank · Answer

isn't x = y = 1 satisfies 2nd condition? Please correct me if anything is wrong?

Bunuel · Answer

Have you cheked this post? https://gmatclub.com/forum/in-the-seque ... l#p2210535

Purnank · Answer

Thanks, i was assuming x and y can only be integers. I was wrong there.

Bunuel · Answer

Even then there are more solutions:
y = 9 and x = -12
y = 17 and x = -25
y = 25 and x = -38
...

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards