If a positive integer q is divisible by both 3 and 11, then q must also be divisible by which of the following?
I. 14
II. 33
III. 66
A. I only
B. II only
C. III only
D. I and II
E. II and III
OA B
Source: Princeton Review
If a positive integer q is divisible by both 3 and 11, then
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
I. 14BTGmoderatorDC wrote:If a positive integer q is divisible by both 3 and 11, then q must also be divisible by which of the following?
I. 14
II. 33
III. 66
A. I only
B. II only
C. III only
D. I and II
E. II and III
14 is NOT divisible by 3 or 11
So, statement I is NOT true.
ELIMINATE A and D
III. 66
Integer q COULD equal 33 (which is divisible by 3 and 11)
Since 33 is NOT divisible by 66, statement III is NOT true.
ELIMINATE C and E
By the process of elimination, the correct answer is B
Cheers,
Brent
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
$$q \ge 1\,\,{\mathop{\rm int}} $$BTGmoderatorDC wrote:If a positive integer q is divisible by both 3 and 11, then q must also be divisible by which of the following?
I. 14
II. 33
III. 66
A. I only
B. II only
C. III only
D. I and II
E. II and III
Source: Princeton Review
$${q \over 3} = {\mathop{\rm int}} \,\,\,;\,\,\,\,{q \over {11}} = {\mathop{\rm int}} \,\,\,\,\,\left( * \right)$$
$$?\,\,\,:\,\,\,{q \over {{\rm{altern}}}} = {\mathop{\rm int}} $$
$$\left. \matrix{
{\rm{I}}{\rm{.}}\,\,{\rm{14}}\,\,{\rm{?}}\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\left( {{\rm{Take}}\,\,q = 33} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,A,D\,\,{\rm{refuted}} \hfill \cr
{\rm{II}}{\rm{.}}\,\,{\rm{33}}\,\,{\rm{?}}\,\,\,\,\left( * \right)\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\left( {GCD\left( {3,11} \right) = 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,C\,\,{\rm{refuted}}\,\,\,\, \hfill \cr
{\rm{III}}{\rm{.}}\,\,{\rm{66}}\,\,{\rm{?}}\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\left( {{\rm{Take}}\,\,q = 33} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,E\,\,{\rm{refuted}} \hfill \cr} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{B}} \right)$$
The correct answer is (B).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi All,
We're told that Q is a positive integer that is divisible by BOTH 3 and 11. We're asked which of the following MUST also divisible evenly into Q. This question can be approached in a couple of different ways, including by TESTing VALUES.
With these types of prompts, it often helps to choose the SMALLEST value that fits everything that you're told. Here, the smallest positive value of Q that is divisible by 3 and 11 is 33.
IF.... Q=33...
I. 14
14 does NOT divide evenly into 33.
Eliminate Answers A and D
II. 33
33 DOES divide evenly into 33, so we'll keep this option for now.
III. 66
66 does NOT divide evenly into 33.
Eliminate Answers C and E.
There's only one answer remaining...
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that Q is a positive integer that is divisible by BOTH 3 and 11. We're asked which of the following MUST also divisible evenly into Q. This question can be approached in a couple of different ways, including by TESTing VALUES.
With these types of prompts, it often helps to choose the SMALLEST value that fits everything that you're told. Here, the smallest positive value of Q that is divisible by 3 and 11 is 33.
IF.... Q=33...
I. 14
14 does NOT divide evenly into 33.
Eliminate Answers A and D
II. 33
33 DOES divide evenly into 33, so we'll keep this option for now.
III. 66
66 does NOT divide evenly into 33.
Eliminate Answers C and E.
There's only one answer remaining...
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Since q is divisible by both 3 and 11, it's also divisible by the LCM of 3 and 11 (and all the factors of this LCM). Since the LCM of 3 and 11 is 3 x 11 = 33, q is divisible by 33. (Note: q is not divisible by 14 and 66 since they are not factors of 33.)BTGmoderatorDC wrote:If a positive integer q is divisible by both 3 and 11, then q must also be divisible by which of the following?
I. 14
II. 33
III. 66
A. I only
B. II only
C. III only
D. I and II
E. II and III
OA B
Source: Princeton Review
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews