It is currently 14 Dec 2017, 05:31

Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1


Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

S96-09

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42606

Kudos [?]: 135613 [0], given: 12705

S96-09 [#permalink]

Show Tags

New post 16 Sep 2014, 00:50
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (00:49) correct 42% (00:40) wrong based on 53 sessions

HideShow timer Statistics

A geometric sequence is one in which the ratio of any term after the first to the preceding term is a constant. If the letters \(a\), \(b\), \(c\), \(d\) represent a geometric sequence in normal alphabetical order, which of the following must also represent a geometric sequence for all values of \(k\)?

I. \(dk\), \(ck\), \(bk\), \(ak\)

II. \(a + k\), \(b + 2k\), \(c + 3k\), \(d + 4k\)

III. \(ak^4\), \(bk^3\), \(ck^2\), \(dk\)


A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135613 [0], given: 12705

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42606

Kudos [?]: 135613 [0], given: 12705

Re S96-09 [#permalink]

Show Tags

New post 16 Sep 2014, 00:50
Official Solution:


A geometric sequence is one in which the ratio of any term after the first to the preceding term is a constant. If the letters \(a\), \(b\), \(c\), \(d\) represent a geometric sequence in normal alphabetical order, which of the following must also represent a geometric sequence for all values of \(k\)?

I. \(dk\), \(ck\), \(bk\), \(ak\)

II. \(a + k\), \(b + 2k\), \(c + 3k\), \(d + 4k\)

III. \(ak^4\), \(bk^3\), \(ck^2\), \(dk\)


A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III


Our first task is to ensure that we understand the definition of a geometric sequence. Let's use the sequence given to us: \(a\), \(b\), \(c\), \(d\). We are told that the ratio of any term after the first to the preceding term is a constant. In other words, \(\frac{b}{a} = \text{some constant}\), which is the same constant for the other ratios (\(\frac{c}{b}\) and \(\frac{d}{c}\)). Let's name that constant \(r\). Thus, we have the following:
\(\frac{b}{a} = \frac{c}{b} = \frac{d}{c} = r\)

By a series of substitutions, we can rewrite the sequence in terms of just \(a\) and \(r\):

\(a\), \(b\), \(c\), \(d\) is the same as \(a\), \(ar\), \(ar^2\), \(ar^3\)

Rewriting the sequence this way highlights the role of the constant ratio \(r\). That is, to move forward in the sequence one step, we just multiply by a constant factor \(r\). Rewriting also lets us substitute into the alternative sequences and watch what happens.

I. \(dk\), \(ck\), \(bk\), \(ak\)

This sequence is the same as \(ar^3k\), \(ar^2k\), \(ark\), \(ak\). To move forward in the sequence, we divide by \(r\). This is the same thing as multiplying by \(\frac{1}{r}\). Since this factor is constant throughout the sequence, the sequence is geometric.

II. \(a + k\), \(b + 2k\), \(c + 3k\), \(d + 4k\)

This sequence is the same as \(a + k\), \(ar + 2k\), \(ar^2 + 3k\), \(ar^3 + 4k\). To move forward in this sequence, we cannot simply multiply by a constant expression. The presence of the plus sign means that we will not have a constant ratio between successive terms, and this sequence is not geometric.

III. \(ak^4\), \(bk^3\), \(ck^2\), \(dk\)

This sequence is the same as \(ak^4\), \(ark^3\), \(ar^2k^2\), \(ar^3k\). To move forward in the sequence, we multiply by \(r\) and divide by \(k\). In other words, we multiply by \(\frac{r}{k}\), which is a constant factor. This sequence is therefore geometric.

Only sequences I and III are geometric.


Answer: D
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135613 [0], given: 12705

Intern
Intern
avatar
Joined: 16 Oct 2017
Posts: 4

Kudos [?]: 5 [0], given: 1

Location: India
WE: Business Development (Non-Profit and Government)
Re: S96-09 [#permalink]

Show Tags

New post 26 Oct 2017, 07:51
Another method would be to

1. substitute an actual geometric series ex: a,b,c,d as 2,4,6,8
2. give any easy value to k. I chose k =2
3. Substitute these values back in to the answer options and verify

Hope this helps!

Kudos [?]: 5 [0], given: 1

Intern
Intern
avatar
B
Joined: 16 Jul 2013
Posts: 15

Kudos [?]: 2 [0], given: 22

Location: Hungary
Concentration: Entrepreneurship, Marketing
GPA: 3.37
Re: S96-09 [#permalink]

Show Tags

New post 05 Dec 2017, 13:56
vishkatti2005 wrote:
Another method would be to

1. substitute an actual geometric series ex: a,b,c,d as 2,4,6,8
2. give any easy value to k. I chose k =2
3. Substitute these values back in to the answer options and verify

Hope this helps!


I also solved this by substitution / picking numbers, however, 2, 4, 6 and 8 is NOT a geometric sequence as 8/6 does not equal 6/4 does not equal 4/2

I tried 1 2 4 8 and k=2. For the last one (III.) I got 16 16 16 16, so just to make sure, I also tried k=3, which gave 81 54 36 (constant or r=3/2).

Kudos [?]: 2 [0], given: 22

Re: S96-09   [#permalink] 05 Dec 2017, 13:56
Display posts from previous: Sort by

S96-09

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: chetan2u, Bunuel



GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.