It is currently 23 Nov 2017, 06:10

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

If a number N is divisible by both 2 and 8 then which of the following

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
User avatar
S
Joined: 17 Oct 2016
Posts: 82

Kudos [?]: 38 [0], given: 17

Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)
Premium Member Reviews Badge
If a number N is divisible by both 2 and 8 then which of the following [#permalink]

Show Tags

New post 12 Aug 2017, 01:33
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

64% (00:24) correct 36% (00:21) wrong based on 36 sessions

HideShow timer Statistics

If a number N is divisible by both 2 and 8, then which of the following statements must be true?

I. N is divisible by 4
II. N is divisible by 6
III. N is divisible by 16

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

_________________

Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.

Dr. Pratik



Kudos [?]: 38 [0], given: 17

Manager
Manager
avatar
B
Joined: 02 Nov 2015
Posts: 176

Kudos [?]: 26 [0], given: 121

GMAT 1: 640 Q49 V29
Premium Member CAT Tests
Re: If a number N is divisible by both 2 and 8 then which of the following [#permalink]

Show Tags

New post 12 Aug 2017, 02:05
Imo 1 only . A is the answer.
Suppose if not=8.
Then it's divisible by 4 but not by 6 or 16.

Thus A wins


Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app

Kudos [?]: 26 [0], given: 121

Manager
Manager
avatar
B
Joined: 07 Jun 2017
Posts: 111

Kudos [?]: 3 [0], given: 454

Re: If a number N is divisible by both 2 and 8 then which of the following [#permalink]

Show Tags

New post 13 Aug 2017, 10:09
I thought C would be correct.. why is it wrong?
can any one explain?

Kudos [?]: 3 [0], given: 454

Manager
Manager
avatar
B
Joined: 02 Nov 2015
Posts: 176

Kudos [?]: 26 [0], given: 121

GMAT 1: 640 Q49 V29
Premium Member CAT Tests
Re: If a number N is divisible by both 2 and 8 then which of the following [#permalink]

Show Tags

New post 13 Aug 2017, 10:39
pclawong wrote:
I thought C would be correct.. why is it wrong?
can any one explain?

Suppose we chose the number 8. It's divisible by both 4 ad 8 but not by 16. So it cannot be C .

Hope it helps.

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app

Kudos [?]: 26 [0], given: 121

Manager
Manager
User avatar
G
Joined: 30 May 2012
Posts: 220

Kudos [?]: 82 [0], given: 151

Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Premium Member
Re: If a number N is divisible by both 2 and 8 then which of the following [#permalink]

Show Tags

New post 13 Aug 2017, 12:19
When N is divisible by 2 and 8 means, N has at least 3 2s in it (because 8 = 2x2x2). With this information given, look at the options:
1. Is N divisible by 4 --- Yes, because 4 = 2x2
2. Is N divisible by 6 --- Don't know for sure, because 6 = 2x3. From the given information, we don't know if N has a 3 in it.
3. Is N divisible by 8 --- Don't know again, because 8 = 2x2x2x2. From the given information again, we don't know if N has 4 2s in it.

Because this is a "Must" question, we know for sure that N is divisible by 4.

Kudos [?]: 82 [0], given: 151

Manager
Manager
avatar
B
Joined: 30 Apr 2013
Posts: 91

Kudos [?]: [0], given: 9

CAT Tests
Re: If a number N is divisible by both 2 and 8 then which of the following [#permalink]

Show Tags

New post 14 Aug 2017, 11:59
Am not sure If I got the correctly. If we assume N=48. Then It would be divisible by 4, 6 and 16. Then options dont make sense. Please help me understand the question. where am going wrong?

Kudos [?]: [0], given: 9

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42326

Kudos [?]: 133106 [0], given: 12411

Re: If a number N is divisible by both 2 and 8 then which of the following [#permalink]

Show Tags

New post 14 Aug 2017, 12:07
Expert's post
1
This post was
BOOKMARKED
santro789 wrote:
Am not sure If I got the correctly. If we assume N=48. Then It would be divisible by 4, 6 and 16. Then options dont make sense. Please help me understand the question. where am going wrong?


If a number N is divisible by both 2 and 8, then which of the following statements must be true?

I. N is divisible by 4
II. N is divisible by 6
III. N is divisible by 16


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

Notice that the question asks "which of the following statements must be true", not "which of the following statements could be true". While N could be divisible by any number, it must be divisible only by some of the numbers.

Generally if a positive integer x is divisible by positive integers a and b, then it will be divisible by the least common multiple of a and b. Thus since N is divisible by both 2 and 8, then it will be divisible by the LCM(2, 8), which is 8. If N is divisible by 8, then it's divisible by every factor of 8: 1, 2, 4, and 8. Therefore, only option A MUST be true.

Answer: A.
_________________

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 [?]: 133106 [0], given: 12411

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42326

Kudos [?]: 133106 [0], given: 12411

Re: If a number N is divisible by both 2 and 8 then which of the following [#permalink]

Show Tags

New post 14 Aug 2017, 12:10
Bunuel wrote:
santro789 wrote:
Am not sure If I got the correctly. If we assume N=48. Then It would be divisible by 4, 6 and 16. Then options dont make sense. Please help me understand the question. where am going wrong?


If a number N is divisible by both 2 and 8, then which of the following statements must be true?

I. N is divisible by 4
II. N is divisible by 6
III. N is divisible by 16


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

Notice that the question asks "which of the following statements must be true", not "which of the following statements could be true". While N could be divisible by any number, it must be divisible only by some of the numbers.

Generally if a positive integer x is divisible by positive integers a and b, then it will be divisible by the least common multiple of a and b. Thus since N is divisible by both 2 and 8, then it will be divisible by the LCM(2, 8), which is 8. If N is divisible by 8, then it's divisible by every factor of 8: 1, 2, 4, and 8. Therefore, only option A MUST be true.

Answer: A.


11. Must or Could be True Questions



For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________

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 [?]: 133106 [0], given: 12411

Director
Director
avatar
P
Joined: 25 Feb 2013
Posts: 567

Kudos [?]: 257 [0], given: 35

Location: India
Schools: Mannheim"19 (S)
GPA: 3.82
GMAT ToolKit User Reviews Badge
If a number N is divisible by both 2 and 8 then which of the following [#permalink]

Show Tags

New post 14 Aug 2017, 20:12
Bunuel wrote:
santro789 wrote:
Am not sure If I got the correctly. If we assume N=48. Then It would be divisible by 4, 6 and 16. Then options dont make sense. Please help me understand the question. where am going wrong?


If a number N is divisible by both 2 and 8, then which of the following statements must be true?

I. N is divisible by 4
II. N is divisible by 6
III. N is divisible by 16


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

Notice that the question asks "which of the following statements must be true", not "which of the following statements could be true". While N could be divisible by any number, it must be divisible only by some of the numbers.

Generally if a positive integer x is divisible by positive integers a and b, then it will be divisible by the least common multiple of a and b. Thus since N is divisible by both 2 and 8, then it will be divisible by the LCM(2, 8), which is 8. If N is divisible by 8, then it's divisible by every factor of 8: 1, 2, 4, and 8. Therefore, only option A MUST be true.

Answer: A.


Adding on to what Bunuel explained, we can write \(N = 8K\)

Now, \(\frac{N}{4} = \frac{8k}{4} =\) Always an Integer

\(\frac{N}{6} = \frac{8k}{6} =\) May or may not be an integer, depending upon the value of k (if \(k=1\), \(\frac{N}{6}\) is not an integer, but if \(k=3\), \(\frac{N}{6}\) is an integer)

\(\frac{N}{16} = \frac{8k}{16} =\) May or may not be an integer, depending upon the value of k (if \(k=1\), \(\frac{N}{16}\) is not an integer, but if \(k=2\), \(\frac{N}{16}\) is an integer)

Hence only I must be true . Option A

Kudos [?]: 257 [0], given: 35

If a number N is divisible by both 2 and 8 then which of the following   [#permalink] 14 Aug 2017, 20:12
Display posts from previous: Sort by

If a number N is divisible by both 2 and 8 then which of the following

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


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®.