Definitions

Expert replies

kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Mon Nov 18, 2013 9:53 am

Hello,

I simply wanted to get consensus on the following:

x is a multiple of 5 if and only if x/5 is an integer.
Thus -5 and 0 are both multiples of 5.

x is a common multiple of 6 and 4 if and only if x is a multiple of both 4 and 6. Thus -12, 0, and 24 are all common multiples of 4 and 6.

The least common multiple of 4 and 6 is the smallest positive number that is a multiple of both 4 and 6. Thus the least common multiple of 4 and 6 is 12.

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

Like this post

Source: Beat The GMAT — Problem Solving | Mon Nov 18, 2013 9:53 am

GMAT/MBA Expert

Mike@Magoosh: GMAT Instructor; Posts: 768; Joined: Wed Dec 28, 2011 4:18 pmFollowed by: 140 members; Location: Berkeley, CA; Thanked: 387 times

by Mike@Magoosh » Mon Nov 18, 2013 10:41 am

kevincanspain wrote:Hello,

I simply wanted to get consensus on the following:

x is a multiple of 5 if and only if x/5 is an integer.
Thus -5 and 0 are both multiples of 5.

x is a common multiple of 6 and 4 if and only if x is a multiple of both 4 and 6. Thus -12, 0, and 24 are all common multiples of 4 and 6.

The least common multiple of 4 and 6 is the smallest positive number that is a multiple of both 4 and 6. Thus the least common multiple of 4 and 6 is 12.

Kevin,
That's my understanding.

(a) negative and zero are included in multiples; in particular, zero is a multiple of every integer.
(b) common multiples would include zero and negatives, but in practice, the only common multiples about we care are the LCM
(c) the LCM is a positive number, the smallest positive number that is a multiple of both individual numbers.

Points (a) & (c) are true and very important for GMAT students to understand. Point (b) is technically true, but is not necessarily a helpful focus for GMAT students.

Does all this make sense?
Mike

Magoosh GMAT Instructor
https://gmat.magoosh.com/

Like this post

kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Mon Nov 18, 2013 4:31 pm

Here is a question from the GMATPrep Exam Pack

If k is a common multiple of 75, 98, and 140, which of the following statements are true?

I. k is divisible by 9
II. k is divisible by 49
III. k is greater than 14,000

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

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

Like this post

Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Mon Nov 18, 2013 7:24 pm

kevincanspain wrote:Here is a question from the GMATPrep Exam Pack

If k is a common multiple of 75, 98, and 140, which of the following statements are true?

I. k is divisible by 9
II. k is divisible by 49
III. k is greater than 14,000

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

Since,k is a common multiple of 75, 98, and 140
K should be of the form,
K = n*75*98*140
K = n*(3*5*5)*(2*7*7)*(2*2*5*7) = n*14700

Case 1 :k is divisible by 9
Let N = 1
K = 14700/9 is not divisible
Hence Not sufficient.(You can also notice there is only one 3 in the above, so it is not always divisible.)

Case 2 :k is divisible by 49
Let N = 1
K = 14700/49 = 3*49*100/49
Hence Divisible
It is also divisible for all n's
Hence Sufficient.

Case 3 : k is greater than 14,000
Yes K = 14700*n
It will always be greater than 14,00
Hence sufficient.

So Answer is D

Is OA D ?

Regards,
Uva.

Known is a drop Unknown is an Ocean

Like this post

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Nov 18, 2013 8:49 pm

+1 for [spoiler]{D}[/spoiler]
75 = 5 x 5 x 3
98 = 7 x 7 x 2
140 = 7 x 5 x 2 x 2
A common multiple will have atleast = (5)^2 x (3) x (7)^2 x (2)^2 == 25 x 3 x 49 x 4 == 300 x 49 = 14700
I. k is divisible by 9 = NO (we have only one "3")
II. k is divisible by 49 == YES (we have two "7"s)
III. k is greater than 14,000 == YES (the minimum resultant is greater than 14000)

Answer [spoiler]{D}[/spoiler]

kevincanspain wrote:Here is a question from the GMATPrep Exam Pack

If k is a common multiple of 75, 98, and 140, which of the following statements are true?

I. k is divisible by 9
II. k is divisible by 49
III. k is greater than 14,000

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

R A H U L

Like this post

kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Mon Nov 18, 2013 11:19 pm

The correct answer is indeed D. From this question we can deduce that all common multiples of 4 and 6 are positive, at least for the purposes of the GMAT

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review