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

 It is currently 23 Apr 2019, 03:07

### 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

# Is integer x divisible by 21? (1) x is divisible by 14.

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

### Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 416
Is integer x divisible by 21? (1) x is divisible by 14.  [#permalink]

### Show Tags

24 Mar 2014, 03:45
1
00:00

Difficulty:

(N/A)

Question Stats:

88% (00:47) correct 12% (00:41) wrong based on 137 sessions

### HideShow timer Statistics

Is integer x divisible by 21?

(1) x is divisible by 14.
(2) x is divisible by 12.

OE:
(1): x can be 14, which is indivisible by 21, or by 14*21, in which case it is divisible by 21.
Insufficient
(2): x can be 12, which is indivisible by 21, or by 12*21, in which case it is divisible by 21.
Insufficient
Combined: x is divisible by 14 and by 12
x must be divisible by the prime factors of 14=2*7 and by those of 12=2*2*3, thus x is divisible by 7 and by 3
-> x is divisible by 7*3=21.
Sufficient
Math Expert
Joined: 02 Sep 2009
Posts: 54462
Re: Is integer x divisible by 21? (1) x is divisible by 14.  [#permalink]

### Show Tags

24 Mar 2014, 03:57
1
1
goodyear2013 wrote:
Is integer x divisible by 21?

(1) x is divisible by 14.
(2) x is divisible by 12.

OE:
(1): x can be 14, which is indivisible by 21, or by 14*21, in which case it is divisible by 21.
Insufficient
(2): x can be 12, which is indivisible by 21, or by 12*21, in which case it is divisible by 21.
Insufficient
Combined: x is divisible by 14 and by 12
x must be divisible by the prime factors of 14=2*7 and by those of 12=2*2*3, thus x is divisible by 7 and by 3
-> x is divisible by 7*3=21.
Sufficient

Is integer x divisible by 21?

(1) x is divisible by 14 --> if x=42, then YES but if x=14, then NO. Not sufficient.

(2) x is divisible by 12 --> if x=84, then YES but if x=12, then NO. Not sufficient.

(1)+(2) From (1) x is divisible by 7 and from (2) x is divisible by 3, thus x must be divisible by the least common multiple of 7 and 3, which is 21. Sufficient.

Hope it's clear.
_________________
Intern
Joined: 15 Jul 2014
Posts: 2
Re: Is integer x divisible by 21? (1) x is divisible by 14.  [#permalink]

### Show Tags

23 Jul 2014, 21:18
goodyear2013 wrote:
Is integer x divisible by 21?

(1) x is divisible by 14.
(2) x is divisible by 12.

OE:
(1): x can be 14, which is indivisible by 21, or by 14*21, in which case it is divisible by 21.
Insufficient
(2): x can be 12, which is indivisible by 21, or by 12*21, in which case it is divisible by 21.
Insufficient
Combined: x is divisible by 14 and by 12
x must be divisible by the prime factors of 14=2*7 and by those of 12=2*2*3, thus x is divisible by 7 and by 3
-> x is divisible by 7*3=21.
Sufficient

I just want to try to explain my thinking (a little different method than Bunuel) so in case it's helpful to others..
Question asks: is x divisible by 21.. I factored out 21 = 7*3
s1. x is divisible by 14 14 = 7*2 --> not sufficient no 3 here.
s2. x is divisible by 12 12= 2*2*3 --> no 7 here so insuff.
s1+s2 we have 2,3,7 hence x is divisible by 21 (C).

I'm very new here and trying to get better with math. using this to express my method (also in case if it's wrong somebody can correct me) and hope it help to other people.
Cheers
Intern
Joined: 27 Aug 2012
Posts: 4
Is integer x divisible by 21? (1) x is divisible by 14.  [#permalink]

### Show Tags

23 Jul 2014, 21:59
prime factors of 21 are 3,7
So to x be divisible 21 it should have 3 and 7 in its prime box
Prime factors of 14(2,7)
so statement 1 is not sufficient, it shows that there is 2,7 present in the prime box of x, but we dont know what x is, So we are not sure if we have 3 present in the prime box of X

prime factors of 12 (2,2,3)
statement 2 is not sufficient, because we dont know if 7 is present in the prime box of x

now consider both the statements together
x is having following factors in its prime box(2,2,7,3) or (2,2,2,7,3) because one of the 2 could be common or different.
So from the above statemnts together we can say that x is divisible by 21, because (3,7) are present in its prime box.

Cheers,
Navjot
Director
Joined: 12 Nov 2016
Posts: 725
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: Is integer x divisible by 21? (1) x is divisible by 14.  [#permalink]

### Show Tags

17 Jul 2017, 20:24
goodyear2013 wrote:
Is integer x divisible by 21?

(1) x is divisible by 14.
(2) x is divisible by 12.

OE:
(1): x can be 14, which is indivisible by 21, or by 14*21, in which case it is divisible by 21.
Insufficient
(2): x can be 12, which is indivisible by 21, or by 12*21, in which case it is divisible by 21.
Insufficient
Combined: x is divisible by 14 and by 12
x must be divisible by the prime factors of 14=2*7 and by those of 12=2*2*3, thus x is divisible by 7 and by 3
-> x is divisible by 7*3=21.
Sufficient

We can use properties of LCM and prime factorization to solve

Statement 1
x= 7 x 2 x some integer K

insufficient because X could be a small number like 14

Statement 2

x= 3 x 2 x 2 x some integer K

insufficient x could be some small number like 24

Statement 1 & 2

We should find the LCM of both numbers - which can be done through prime factorization

LCM (14, 12) = 7 x 3 x 2 x 2

https://www.khanacademy.org/math/algebr ... e-exercise - he does GMAT stuff now lol

C
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5807
Location: United States (CA)
Re: Is integer x divisible by 21? (1) x is divisible by 14.  [#permalink]

### Show Tags

30 Jul 2017, 17:39
goodyear2013 wrote:
Is integer x divisible by 21?

(1) x is divisible by 14.
(2) x is divisible by 12.

We need to determine whether x/21 = integer

Statement One Alone:

x is divisible by 14.

Statement one alone is not sufficient to answer the question. If x = 14, then x/21 is not an integer; however, if x = 42, then x/21 is an integer.

Statement Two Alone:

x is divisible by 12.

Statement two alone is not sufficient to answer the question. If x = 12, then x/21 is not an integer; however, if x = 84, then x/21 is an integer.

Statements One and Two Together:

Using statements one and two, we see that x is a multiple of 14 and 12, and thus it is a multiple of their least common multiple, which is 84. Since all multiples of 84 are divisible by 21, x/21 = integer.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Re: Is integer x divisible by 21? (1) x is divisible by 14.   [#permalink] 30 Jul 2017, 17:39
Display posts from previous: Sort by

# Is integer x divisible by 21? (1) x is divisible by 14.

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

 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®.