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

It is currently 16 Aug 2018, 18:31

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

Which of the following could be true of at least some of the terms of

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47946
Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 12 Mar 2015, 07:05
1
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (01:50) correct 40% (01:44) wrong based on 154 sessions

HideShow timer Statistics

Which of the following could be true of at least some of the terms of the sequence defined by \(b_n = (2n - 1)(2n + 3)\)

I. divisible by 15
II. divisible by 18
III. divisible by 27

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

Kudos for a correct solution.

_________________

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

Manager
Manager
User avatar
Joined: 04 Oct 2013
Posts: 173
Concentration: Finance, Leadership
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 12 Mar 2015, 07:50
2n denotes an even integer when n is an integer. So 2n-1 and 2n+3 are two odd integers. Looking at the answer choices II. is out of place since it's a multiple of two.

Answer is D.
_________________

learn the rules of the game, then play better than anyone else.

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6535
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 12 Mar 2015, 09:01
gmat6nplus1 wrote:
2n denotes an even integer when n is an integer. So 2n-1 and 2n+3 are two odd integers. Looking at the answer choices II. is out of place since it's a multiple of two.

Answer is D.


hi gmat6nplus1,

it is very important to answer the question very deliberately pertaining to a variable....
please remember ,it can take a value of a fraction, integer , 0 ,-ive or +ive unless specified otherwise...
here we are trying to find 'atleast' so we look for any value which can satisfy the given properties..
remember 2n is not even when n =19/2.. (2n-1)=18... so ll is satisfied..
l and lll is satisfied by integer values and ll by fraction..

any value is possible with (2n-1)(2n+3)..
ans E
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Manager
Manager
User avatar
Joined: 04 Oct 2013
Posts: 173
Concentration: Finance, Leadership
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 13 Mar 2015, 01:00
chetan2u wrote:
gmat6nplus1 wrote:
2n denotes an even integer when n is an integer. So 2n-1 and 2n+3 are two odd integers. Looking at the answer choices II. is out of place since it's a multiple of two.

Answer is D.


hi gmat6nplus1,

it is very important to answer the question very deliberately pertaining to a variable....
please remember ,it can take a value of a fraction, integer , 0 ,-ive or +ive unless specified otherwise...
here we are trying to find 'atleast' so we look for any value which can satisfy the given properties..
remember 2n is not even when n =19/2.. (2n-1)=18... so ll is satisfied..
l and lll is satisfied by integer values and ll by fraction..

any value is possible with (2n-1)(2n+3)..
ans E


Hey chetan2u, you're right. I misread that n was an integer, my brain did all the rest :)
_________________

learn the rules of the game, then play better than anyone else.

Manager
Manager
User avatar
Status: Kitchener
Joined: 03 Oct 2013
Posts: 91
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Premium Member
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 13 Mar 2015, 06:32
the answer is E
where N could be any positive number, negative number or zero
_________________

Click +1 Kudos if my post helped

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47946
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 15 Mar 2015, 21:56
Bunuel wrote:
Which of the following could be true of at least some of the terms of the sequence defined by \(b_n = (2n - 1)(2n + 3)\)

I. divisible by 15
II. divisible by 18
III. divisible by 27

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

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

First of all, if n = 8, then \(b_8 = (16 - 1)(16 + 3) = 15*19\)

We don’t have to calculate that: clearly, whatever it is, it is divisible by 15. Similarly, if n = 12, then \(b_{12} = (24 - 1)(24 + 3) = 23*27\)

Whatever that equals, it must be divisible by 27. Thus, I & III are true. Notice that, for any integer, 2n must be even, so both (2n – 1) and (2n + 3) are odd numbers, and their product must be odd. Every term in this sequence is an odd number. Now, no odd number can be divisible by an even number, because there is no factor of 2 in the odd number. Therefore, no terms could possibly be divisible by 18. Statement II is absolutely not true.

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

Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 560
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post Updated on: 21 Mar 2015, 09:10
Bunuel wrote:
Bunuel wrote:
Which of the following could be true of at least some of the terms of the sequence defined by \(b_n = (2n - 1)(2n + 3)\)

I. divisible by 15
II. divisible by 18
III. divisible by 27

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

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

First of all, if n = 8, then \(b_8 = (16 - 1)(16 + 3) = 15*19\)

We don’t have to calculate that: clearly, whatever it is, it is divisible by 15. Similarly, if n = 12, then \(b_{12} = (24 - 1)(24 + 3) = 23*27\)

Whatever that equals, it must be divisible by 27. Thus, I & III are true. Notice that, for any integer, 2n must be even, so both (2n – 1) and (2n + 3) are odd numbers, and their product must be odd. Every term in this sequence is an odd number. Now, no odd number can be divisible by an even number, because there is no factor of 2 in the odd number. Therefore, no terms could possibly be divisible by 18. Statement II is absolutely not true.

Answer = (D).


Hi Magoosh Team ,
The question stem does not say that N is an integer . (snippet from official explaination : ' Notice that, for any integer, 2n must be even' ) i think the question is not complete. for example at \(N= \frac{1}{2}\) 15,27,18 or any other number will be able to divide \(b_n = (2n-1)*(2n+3)\)

thanks
lucky
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)


Originally posted by Lucky2783 on 21 Mar 2015, 09:00.
Last edited by Lucky2783 on 21 Mar 2015, 09:10, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47946
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 21 Mar 2015, 09:04
Lucky2783 wrote:
Bunuel wrote:
Bunuel wrote:
Which of the following could be true of at least some of the terms of the sequence defined by \(b_n = (2n - 1)(2n + 3)\)

I. divisible by 15
II. divisible by 18
III. divisible by 27

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

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

First of all, if n = 8, then \(b_8 = (16 - 1)(16 + 3) = 15*19\)

We don’t have to calculate that: clearly, whatever it is, it is divisible by 15. Similarly, if n = 12, then \(b_{12} = (24 - 1)(24 + 3) = 23*27\)

Whatever that equals, it must be divisible by 27. Thus, I & III are true. Notice that, for any integer, 2n must be even, so both (2n – 1) and (2n + 3) are odd numbers, and their product must be odd. Every term in this sequence is an odd number. Now, no odd number can be divisible by an even number, because there is no factor of 2 in the odd number. Therefore, no terms could possibly be divisible by 18. Statement II is absolutely not true.

Answer = (D).


Hi Magoosh Team ,
The question stem does not say that N is an integer . (snippet from official explaination : ' Notice that, for any integer, 2n must be even' ) i think the question is not complete. for example at N= 1/2 15,27,18 or any other number will be able to divide \(b_n = (2n-1)*(2n+3)\)

thanks
lucky


\(b_n\) is n-th term in the sequence, so n must be an integer.
_________________

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

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6535
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 21 Mar 2015, 09:07
Lucky2783 wrote:
Bunuel wrote:
Bunuel wrote:
Which of the following could be true of at least some of the terms of the sequence defined by \(b_n = (2n - 1)(2n + 3)\)

I. divisible by 15
II. divisible by 18
III. divisible by 27

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

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

First of all, if n = 8, then \(b_8 = (16 - 1)(16 + 3) = 15*19\)

We don’t have to calculate that: clearly, whatever it is, it is divisible by 15. Similarly, if n = 12, then \(b_{12} = (24 - 1)(24 + 3) = 23*27\)

Whatever that equals, it must be divisible by 27. Thus, I & III are true. Notice that, for any integer, 2n must be even, so both (2n – 1) and (2n + 3) are odd numbers, and their product must be odd. Every term in this sequence is an odd number. Now, no odd number can be divisible by an even number, because there is no factor of 2 in the odd number. Therefore, no terms could possibly be divisible by 18. Statement II is absolutely not true.

Answer = (D).


Hi Magoosh Team ,
The question stem does not say that N is an integer . (snippet from official explaination : ' Notice that, for any integer, 2n must be even' ) i think the question is not complete. for example at N= 1/2 15,27,18 or any other number will be able to divide \(b_n = (2n-1)*(2n+3)\)

thanks
lucky


hi lucky,
although i too thought the same but i think since bn is a term in a sequence so n has to be an integer
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 560
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 21 Mar 2015, 09:12
\(b_n\) is n-th term in the sequence, so n must be an integer.[/quote]


i see. thanks Bunuel .
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 560
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 21 Mar 2015, 09:15
chetan2u wrote:
hi lucky,
although i too thought the same but i think since bn is a term in a sequence so n has to be an integer



yeah , we have to be very careful in reading the question.
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12183
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 21 Mar 2015, 11:44
Hi All,

Sequence questions are always based on a pattern of some kind, but there might be more to the pattern than you might initially realize. It often helps to "map out" the first few terms in a sequence question, so you can "see" the numbers and spot any hidden patterns involved.

Here, we're given the 'equation' for the sequence: bN = (2N-1)(2N+3) where N is the Nth term in the sequence....

1st term = (2-1)(2+3) = (1)(5) = 5
2nd term = (4-1)(4+3) = (3)(7) = 21
3rd term = (6-1)(6+3) = (5)(9) = 45
4th term = (8-1)(8+3) = (7)(11) = 77
Etc.

From this, we can deduce a number of details:
1) EVERY term will be an ODD INTEGER
2) The sequence of "products" will work through EVERY positive odd integer (notice the 1, the 3, the 5, the 7, etc).

This helps us to prove that Roman Numerals I and III COULD be true and that II is false.

Final Answer:

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!***********************

Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2717
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 11 Mar 2016, 20:16
Bunuel wrote:
Which of the following could be true of at least some of the terms of the sequence defined by \(b_n = (2n - 1)(2n + 3)\)

I. divisible by 15
II. divisible by 18
III. divisible by 27

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

Kudos for a correct solution.


since it's a COULD be and not a MUST be true question...we can find ways for I and III to work.
look at the sequence..we have 2 odd numbers multiplied. since neither of them has a factor of 2, we can eliminate choices with II right away - B, C, and E - out.

now..
for (2n-1)(2n+3), we can find values so that it would be divisible by 15 and by 27
suppose 2n+3=15. 2n=12. n=6
(12-1)(12+3)=11*15 - so yes, possible

suppose 2n+3=27
2n=24
n=12
(24-1)(24+3)=23x27 - so yes, possible.

D
Retired Moderator
User avatar
P
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 533
GMAT ToolKit User
Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 21 Dec 2017, 00:07
Bunuel wrote:
Lucky2783 wrote:
Hi Magoosh Team ,
The question stem does not say that N is an integer . (snippet from official explaination : ' Notice that, for any integer, 2n must be even' ) i think the question is not complete. for example at N= 1/2 15,27,18 or any other number will be able to divide \(b_n = (2n-1)*(2n+3)\)

thanks
lucky


\(b_n\) is n-th term in the sequence, so n must be an integer.

Could n be a negative integer? May not be, I think.:suspect
_________________

Hasan Mahmud

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47946
Re: Which of the following could be true of at least some of the terms of  [#permalink]

Show Tags

New post 21 Dec 2017, 00:48
Mahmud6 wrote:
Bunuel wrote:
Lucky2783 wrote:
Hi Magoosh Team ,
The question stem does not say that N is an integer . (snippet from official explaination : ' Notice that, for any integer, 2n must be even' ) i think the question is not complete. for example at N= 1/2 15,27,18 or any other number will be able to divide \(b_n = (2n-1)*(2n+3)\)

thanks
lucky


\(b_n\) is n-th term in the sequence, so n must be an integer.

Could n be a negative integer? May not be, I think.:suspect


n is an index number which indicates the position of the term in the sequence, it cannot be negative.
_________________

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

Re: Which of the following could be true of at least some of the terms of &nbs [#permalink] 21 Dec 2017, 00:48
Display posts from previous: Sort by

Which of the following could be true of at least some of the terms of

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.