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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.
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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?
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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
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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 ?

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Uva.
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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
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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
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