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)
_________________

At the still point, there the dance is. -- T.S. Eliot

Formerly genxer123