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

 It is currently 21 Oct 2018, 09:52

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

A certain sequence consist of alternating positive and negative number

Author Message
TAGS:

Hide Tags

Manager
Joined: 13 Sep 2016
Posts: 120
A certain sequence consist of alternating positive and negative number  [#permalink]

Show Tags

Updated on: 18 Sep 2016, 02:49
00:00

Difficulty:

15% (low)

Question Stats:

86% (01:29) correct 14% (00:50) wrong based on 49 sessions

HideShow timer Statistics

A certain sequence consist of alternating positive and negative numbers. If the sequence begins with a negative number and contains K numbers, where K is odd, how many positive numbers are in the set?

a) (k+1)/2
b) (k-1)/2
c) k/(2+1)
d) k/(2-1)
e) k/2

Originally posted by alanforde800Maximus on 18 Sep 2016, 02:45.
Last edited by Bunuel on 18 Sep 2016, 02:49, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 24 Aug 2016
Posts: 68
Location: India
WE: Information Technology (Computer Software)
Re: A certain sequence consist of alternating positive and negative number  [#permalink]

Show Tags

18 Sep 2016, 03:19
Every even digit of the sequence will be positive number and kth digit will be odd.

The position of last positive digit will be (k-1)

So, total number of digits= $$\frac{(k-1)}{2}$$ ==> Ans. B
_________________

"If we hit that bullseye, the rest of the dominos will fall like a house of cards. Checkmate."

Current Student
Joined: 08 Jun 2013
Posts: 33
Re: A certain sequence consist of alternating positive and negative number  [#permalink]

Show Tags

18 Sep 2016, 05:13
1
this question can also be solved with putting values for k, say k=7 since it's odd
and first number is neg so sequence will be {neg,pos,neg,pos,neg,pos,neg} we can see that it has 3 positive terms
so putting K=7 in the options, option b = (k-1)/2 => 7-1/2 = 3 , the number of positive integers

Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3622
Re: A certain sequence consist of alternating positive and negative number  [#permalink]

Show Tags

18 Sep 2016, 05:33
Take K = 5 and see how many are +ve and how many are -ve.

Substitute the value of K in options, you will get only one option satisfied, which is option B.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.

Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

Check our new About Us Page here.

CEO
Joined: 12 Sep 2015
Posts: 3021
Re: A certain sequence consist of alternating positive and negative number  [#permalink]

Show Tags

18 Sep 2016, 06:37
Top Contributor
alanforde800Maximus wrote:
A certain sequence consist of alternating positive and negative numbers. If the sequence begins with a negative number and contains K numbers, where K is odd, how many positive numbers are in the set?

a) (k+1)/2
b) (k-1)/2
c) k/(2+1)
d) k/(2-1)
e) k/2

Another approach it to look for a pattern...

k = 1
NEGATIVE
0 positive numbers

k = 3
NEGATIVE, POSITIVE, NEGATIVE
1 positive number

k = 5
NEG, POS, NEG, POS, NEG
2 positive numbers
Notice that if we examine the first 4 numbers, HALF are positive (and the last number is negative).

k = 7
NEG, POS, NEG, POS, NEG, POS, NEG
3 positive numbers
Notice that if we examine the first 6 numbers, HALF are positive (and the last number is negative).

k = 9
NEG, POS, NEG, POS, NEG, POS, NEG, POS, NEG
4 positive numbers
Notice that if we examine the first 8 numbers, HALF are positive (and the last number is negative).

In general, if we examine the first k-1 numbers, HALF will be positive (and the last number is negative).
So, the number of positive numbers = HALF of (k-1)
= (k-1)/2
_________________

Brent Hanneson – GMATPrepNow.com

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12687
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A certain sequence consist of alternating positive and negative number  [#permalink]

Show Tags

28 Jan 2018, 14:35
Hi All,

TESTing VALUES is a great approach for this type of question. You can also solve it with a bit of logic (and paying careful attention to how the answer choices are written).

We're told that we have an ODD number of terms in a sequence (represented by the variable "K"), the first term is NEGATIVE and the sequence alternates between negatives and positives. By definition, this means that there will be one more negative term than the total number of positive terms. The question asks for the number of POSITIVE terms.

Notice how all of the answers are written are written as fractions. Based on the description of the sequence, a little less than half of the K terms will be positive. So we should be dividing the total (K) by a little more than 2.

Answer C divides the total by 3, answer D divides the total by 1 and answer E divides the total by exactly 2. None of these answers matches what we're looking for, so they can all be eliminated. Between A and B, answer A INCREASES the total before halving it while Answer B DECREASES the total before halving it. With those two options, the only one that would logically end up with a 'net decrease' leading to a little less than half of the terms is B.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Re: A certain sequence consist of alternating positive and negative number &nbs [#permalink] 28 Jan 2018, 14:35
Display posts from previous: Sort by