dave13 wrote:
generis wrote:
carcass wrote:
If a positive integer n is divisible by both 5 and 7, the n must also be divisible by which of the following?
I 12
II 35
III 70
(A) None
(B) I only
(C) II only
(D) I and II
(E) II and III
As above, a number divisible by 5 and 7 will also be divisible by the LCM of 5 and 7, i.e., 35.
The trap answer is 70. Per prime factorization, in order to be sure the number were divisible by 70, we would need to know that integer n also had a factor of 2: (5*7*2) = 70. The prompt doesn't indicate that there is a factor of 2.
Answer C
Hello
generis, how is your fantastic life ?
did you learn anything new today
what if question said:
If a positive integer n is divisible by both 5 and 7, the n COULD also be divisible by which of the following? then answer would be 70 ?
i fall in trap, so thats why i am asking this question
happy weekend:)
Hi
dave13 Your good cheer is refreshing.
See below for what I learned today.
In answer to your question
Quote:
If a positive integer n is divisible by both 5 and 7, the n COULD also be divisible by which of the following? then answer would be 70 ?
Yes. Then the answer would include 35 and 70.
In that case, we deal with
this certainty: \(n\) has
one factor of 5 and one factor of 7
There COULD be a factor of 2 in positive integer n.
If a question depends on \(n\),
and we are not told exactly what \(n\) equals,
or exactly what factors \(n\) has,
it can help to draw "\(n\)" with a little tree diagram
of known factors.
_________
n________
____5______7_____
?The key? Put at least one
question markto remind us that we have
no idea what the other factors are.
Hope that helps. You have a great weekend, too.
Today I learned that a 14-year-old girl in the U.S.
saved up all her money to pay for
a "free laundry day" for her classmates and neighbors during spring break.
She didn't want them to feel ashamed.
I read that story originally on
Good News Network (dated April 4 2018)