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

 It is currently 23 Jan 2020, 15:13

### 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

# In a certain sequence, each term beyond the second term is equal to th

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60627
In a certain sequence, each term beyond the second term is equal to th  [#permalink]

### Show Tags

15 May 2018, 02:47
18
00:00

Difficulty:

95% (hard)

Question Stats:

20% (02:53) correct 80% (02:35) wrong based on 148 sessions

### HideShow timer Statistics

In a certain sequence, each term beyond the second term is equal to the average of the previous two terms. If $$A_1$$ and $$A_3$$ are positive integers, which of the following is not a possible value of $$A_5$$?

A. $$-\frac{9}{4}$$

B. 0

C. $$\frac{9}{4}$$

D. $$\frac{75}{8}$$

E. $$\frac{41}{2}$$

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3026
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
In a certain sequence, each term beyond the second term is equal to th  [#permalink]

### Show Tags

15 May 2018, 03:24
1
Bunuel wrote:
In a certain sequence, each term beyond the second term is equal to the average of the previous two terms. If $$A_1$$ and $$A_3$$ are positive integers, which of the following is not a possible value of $$A_5$$?

A. $$-\frac{9}{4}$$

B. 0

C. $$\frac{9}{4}$$

D. $$\frac{75}{8}$$

E. $$\frac{41}{2}$$

Since $$A_1$$ and $$A_3$$ are both Integers so $$A_2$$ must be integer as well

at the same time

$$A_1$$ and $$A_2$$ should both be either even or both should be Odd

$$A_1$$ = Even
$$A_2$$ = Even
$$A_3$$ = Even/Odd
$$A_4$$ = Even/ Odd / Integer2
$$A_5$$ = Even / Odd/ Inteegr/4

i.e. denominator part of $$A_5$$ can never be more than 4 hence

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Senior Manager
Joined: 01 Feb 2017
Posts: 250
Re: In a certain sequence, each term beyond the second term is equal to th  [#permalink]

### Show Tags

15 May 2018, 12:47
4
Let the terms be
a1, a2, a3, a4 and a5

ATS,
a3=(a1+a2)/2 is a positive integer. Therefore, a1+a2 is even. Hence, both a1 and a2 are either even or odd.

Now, a5=(a4+a3)/2=(5*a2+3*a1)/8

As a1 & a2 are both either odd or even, Numerator i.e.(5*a2+3*a1) must be even.

Plugin Ans choices:
A. -9/4
So, (5*a2+3*a1)=-18, possible

B. 0
So, (5*a2+3*a1)=0, possible

C. 9/4
So, (5*a2+3*a1)=18, possible

D. 75/8
So, (5*a2+3*a1)=75, not possible

E. 41/2
So, (5*a2+3*a1)=82, possible

Hence, Ans D

Posted from my mobile device
Manager
Joined: 01 Jan 2019
Posts: 92
Concentration: Finance, Entrepreneurship
GPA: 3.24
Re: In a certain sequence, each term beyond the second term is equal to th  [#permalink]

### Show Tags

18 Jul 2019, 10:49
Hi I need help on this one. Can any of the experts look in to this..

Posted from my mobile device
Manager
Joined: 29 Dec 2018
Posts: 82
Location: India
WE: Marketing (Real Estate)
In a certain sequence, each term beyond the second term is equal to th  [#permalink]

### Show Tags

28 Jul 2019, 09:51
Shef08 wrote:
Hi I need help on this one. Can any of the experts look in to this..

Posted from my mobile device

Please can you explain this one?

I did not understand why A1 & A2 have to be both odd or both even.
_________________
Keep your eyes on the prize: 750
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10008
Location: Pune, India
Re: In a certain sequence, each term beyond the second term is equal to th  [#permalink]

### Show Tags

30 Jul 2019, 04:41
DarkHorse2019 wrote:
Shef08 wrote:
Hi I need help on this one. Can any of the experts look in to this..

Posted from my mobile device

Please can you explain this one?

I did not understand why A1 & A2 have to be both odd or both even.

The question tells you that A3 is a positive integer.

A3 = (A1 + A2)/2 = Integer

This means (A1 + A2) = 2*Integer = Even Integer

When will sum of two numbers be even? When both are even or both are odd.
Even + Even = Even
Odd + Odd = Even

Even + Odd = Odd

So A1 and A2 are both either even or both odd. Anyway, it doesn't matter.

You know that A1, A2 and A3 all are integers. A4 may not be an integer.
A4 = (A2 + A3)/2
A5 = (A3 + A4)/2 = [A3 + (A2 + A3)/2]/2 = (3*A3 + A2)/4

Since A2 and A3 are integers, you cannot have 8 in the denominator.
_________________
Karishma
Veritas Prep GMAT Instructor

Re: In a certain sequence, each term beyond the second term is equal to th   [#permalink] 30 Jul 2019, 04:41
Display posts from previous: Sort by