onlynk1 wrote:
honchos wrote:
Bunuel wrote:
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
III to be true it should be mentioned that k is a positive integer. For example, 0 is a common multiple of 75, 98, and 140 and is NOT greater than 14,000.
Rare example of flawed question from GMAT.
I was also astonished it was an exam pack questions.
Bunuel, Calculating LCM of 75,98 and 140 is 14700 which is least,so how can you say zero is a common multiple? Please correct me if I am wrong.
Notice that we are told that k is
a common multiple of 75, 98, and 140 NOT
the least common multiple of 75, 98, and 140. By default,
the least common multiple is considered to be
the least common positive multiple, because otherwise it does not make any sense.
For example, the LCM of 2 and 3 is 6, which means that 6 is the least common
positive multiple of 2 and 3. If we were allowed to consider negative multiples too, then there won't be an answer.
Back to the question:
1. 0 is a multiple of every integer, so 0 is a common multiple of every non-zero sets of integers.
2. 0 is not the only common multiple of 75, 98, and 140, less than 14,000, so is -14,700, -2*14,700, -3*14,700, -4*14,700, ...
Hope it's clear.