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)
_________________
And above all, watch with glittering eyes the whole world around you
because the greatest secrets are always hidden in the most unlikely places.
Those who don't believe in magic will never find it. —Roald Dahl