It is currently 23 Nov 2017, 06:10

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

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

Author Message
Manager
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)
If a number N is divisible by both 2 and 8 then which of the following [#permalink]

Show Tags

12 Aug 2017, 01:33
00:00

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
Joined: 02 Nov 2015
Posts: 176

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

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

Show Tags

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
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

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
Joined: 02 Nov 2015
Posts: 176

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

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

Show Tags

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

Show Tags

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
Joined: 30 Apr 2013
Posts: 91

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

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

Show Tags

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

Math Expert
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

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.

_________________

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

Math Expert
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

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.

11. Must or Could be True Questions

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________

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

Director
Joined: 25 Feb 2013
Posts: 567

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

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

Show Tags

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.

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

 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®.