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

 It is currently 06 Jul 2020, 20:11 ### 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.  # Each term, starting from the third term, of a sequence

Author Message
TAGS:

### Hide Tags

Senior Manager  B
Joined: 28 Jun 2015
Posts: 272
Concentration: Finance
GPA: 3.5
Each term, starting from the third term, of a sequence  [#permalink]

### Show Tags

1
6 00:00

Difficulty:   35% (medium)

Question Stats: 77% (02:48) correct 23% (02:43) wrong based on 121 sessions

### HideShow timer Statistics

Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

(A) 34 : 15
(B) 33 : 16
(C) 30 : 19
(D) 29 : 20
(E) 35 : 14

_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Manager  P
Joined: 14 Oct 2015
Posts: 236
GPA: 3.57
Each term, starting from the third term, of a sequence  [#permalink]

### Show Tags

1
TimeTraveller wrote:
Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

(A) 34 : 15
(B) 33 : 16
(C) 30 : 19
(D) 29 : 20
(E) 35 : 14

It should be B.

If first two terms are Odd, third would be Even, 4th would be E + O = Odd, so sequence becomes.

O O E O

fifth would again be Odd because E + O = O

O O E O O

Now 6th term would be Even because 4th and 5th are both odd and this sequence repeats.

O O E O O E O O E

If this sequence goes on 33 times, terms would be 99 and last term would be even but we have trimmed the last Even term out.

so we have 33 x 2 odd and 32 Even terms.

66:32 = 33:16
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10634
Location: Pune, India
Re: Each term, starting from the third term, of a sequence  [#permalink]

### Show Tags

1
1
TimeTraveller wrote:
Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

(A) 34 : 15
(B) 33 : 16
(C) 30 : 19
(D) 29 : 20
(E) 35 : 14

Use Pattern Recognition:

First two are odd terms.

Odd + Odd = Even
So third term is even. We have Odd, Odd, Even

Odd + Even = Odd
So fourth term is Odd. We have Odd, Odd, Even, Odd

Even + Odd = Odd
So fifth term is Odd. We have Odd, Odd, Even, Odd, Odd

Now, we again have 2 odd terms to the pattern will continue.

Odd, Odd, Even, Odd, Odd, Even, Odd, Odd, Even... and so on
In every 3 terms, 2 are Odd and 1 is Even. So in 99 terms, 66 would be Odd and 33 would be Even,the last one being Even.
If we have only 98 terms, we would have 66 Odd and 32 Even.

Required Ratio = 66/32 = 33/16

_________________
Karishma
Veritas Prep GMAT Instructor

Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2799
Re: Each term, starting from the third term, of a sequence  [#permalink]

### Show Tags

TimeTraveller wrote:
Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

(A) 34 : 15
(B) 33 : 16
(C) 30 : 19
(D) 29 : 20
(E) 35 : 14

Since the first two terms are odd, we have:

1st term: odd

2nd term: odd

3rd term: odd + odd = even

4th term: even + odd = odd

5th term: even + odd = odd

6th term: odd + odd = even

7th term: even + odd = odd

8th term: odd + even = odd

9th term: odd + odd = even

We see that each term that is a multiple of 3 is even and all other terms are odd.

From 1 to 98, there are (96 - 3)/3 + 1 = 32 multiples of 3, and thus there are 32 even terms. So, there are 98 - 32 = 66 odd terms. So, the ratio of odd-valued terms to even-valued terms is 66/32 = 33/16.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

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

VP  D
Joined: 07 Dec 2014
Posts: 1259
Re: Each term, starting from the third term, of a sequence  [#permalink]

### Show Tags

TimeTraveller wrote:
Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

(A) 34 : 15
(B) 33 : 16
(C) 30 : 19
(D) 29 : 20
(E) 35 : 14

for each 3 term cycle, the sequence is odd-odd-even
98/3=32 2/3 cycles
32*1=32 even terms
32*2+2=66 odd terms
66:32=33:16
B
Intern  S
Joined: 14 Oct 2016
Posts: 34
Location: India
WE: Sales (Energy and Utilities)
Re: Each term, starting from the third term, of a sequence  [#permalink]

### Show Tags

1
VeritasPrepKarishma wrote:
TimeTraveller wrote:
Each term, starting from the third term, of a sequence, which has 98 terms, is the sum of the two preceding terms. If the first two terms of the sequence are odd numbers, then what is the ratio of the number of odd valued terms to that of even valued terms?

(A) 34 : 15
(B) 33 : 16
(C) 30 : 19
(D) 29 : 20
(E) 35 : 14

Use Pattern Recognition:

First two are odd terms.

Odd + Odd = Even
So third term is even. We have Odd, Odd, Even

Odd + Even = Odd
So fourth term is Odd. We have Odd, Odd, Even, Odd

Even + Odd = Odd
So fifth term is Odd. We have Odd, Odd, Even, Odd, Odd

Now, we again have 2 odd terms to the pattern will continue.

Odd, Odd, Even, Odd, Odd, Even, Odd, Odd, Even... and so on
In every 3 terms, 2 are Odd and 1 is Even. So in 99 terms, 66 would be Odd and 33 would be Even,the last one being Even.
If we have only 98 terms, we would have 66 Odd and 32 Even.

Required Ratio = 66/32 = 33/16

VeritasPrepKarishma,

Hello,

tried a different approach

98 Numbers can be divided in 14 sets each having 7 numbers. In each set we have 5 odd and 2 Even

Then number of Odd is 14*5= 70 and number of even is 2* 14= 28

Then the ratio is 70:28

Can you help me identify my error?

Thanks
Abhimanyu
_________________
Abhimanyu
Non-Human User Joined: 09 Sep 2013
Posts: 15382
Re: Each term, starting from the third term, of a sequence  [#permalink]

### Show Tags

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.
_________________ Re: Each term, starting from the third term, of a sequence   [#permalink] 02 Jun 2020, 13:03

# Each term, starting from the third term, of a sequence  