GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Which of the following cannot yield an integer when divided by 12? A.
[#permalink]
08 Apr 2022, 06:27
08 Apr 2022, 06:27
Expert Reply
1
Bookmarks
00:00
Question Stats:
11% (01:26) correct
88% (01:33) wrong based on 17 sessions
Hide Show timer Statistics
Which of the following cannot yield an integer when divided by 12?
A. The sum of 5 consecutive integers
B. An integer less than 12
C. The product of three primes
D. The product of two odd integers
E. A multiple of 5
A. The sum of 5 consecutive integers
B. An integer less than 12
C. The product of three primes
D. The product of two odd integers
E. A multiple of 5
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Which of the following cannot yield an integer when divided by 12? A.
[#permalink]
08 Apr 2022, 06:34
08 Apr 2022, 06:34
1
Carcass wrote:
Which of the following cannot yield an integer when divided by 12?
A. The sum of 5 consecutive integers
B. An integer less than 12
C. The product of three primes
D. The product of two odd integers
E. A multiple of 5
A. The sum of 5 consecutive integers
B. An integer less than 12
C. The product of three primes
D. The product of two odd integers
E. A multiple of 5
STRATEGY: Find counter-examples that allow us to eliminate four of the five answer choices.
A. The sum of 5 consecutive integers
10 + 11 + 12 + 13 + 14 = 60, and 60 divided by 12 equals 5 (which is an integer)
B. An integer less than 12
-12 is less than 12, and -12 divided by 12 equals -1 (which is an integer)
C. The product of three primes
(2)(2)(3) = 12, and 12 divided by 12 equals 1 (which is an integer)
D. The product of two odd integers
Unable to find a counterexample for this answer choice. Skip for now.
E. A multiple of 5
60 is a multiple of 5, and 60 divided by 12 equals 5 (which is an integer)
Answer: D
ALTERNATE APPROACH
In order for a number to yield an integer when divided by 12, that number must be a multiple of 12.
Numbers that are multiples of 12 include the following: ...-24, -12, 0, 12, 24, 36,...
You'll notice that, since 12 is an even integer, all multiples of 12 are also EVEN.
Since the product of two odd integers is always ODD, it's impossible for the product of two odd integers to be a multiple of 12.
Answer: D
gmatclubot
Re: Which of the following cannot yield an integer when divided by 12? A. [#permalink]
08 Apr 2022, 06:34
Moderators:
