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# If a positive integer n is divisible by both 5 and 7, the n must also

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If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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02 Jul 2017, 11:17
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15% (low)

Question Stats:

64% (00:27) correct 36% (00:22) wrong based on 166 sessions

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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

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Posts: 243
Concentration: Finance, Accounting
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Re: If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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02 Jul 2017, 11:21
The lowest possible value is 35.

Hence : C
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Re: If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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02 Jul 2017, 11:40
1
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

$$n$$ is divisible by both $$5$$ and $$7$$.

$$n$$ will also be divisible by the LCM of $$5$$ and $$7$$, ie; $$35$$.

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Re: If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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02 Jul 2017, 11:45
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

Since positive integer n is divisible by both 5 and 7 , it must also be divisible by LCM of 5 and 7 i.e 35
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Posts: 1903
If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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03 Jul 2017, 03:04
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.

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that within me there lay an invincible summer.

Director
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Re: If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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06 Apr 2018, 09:03
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.

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:)
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If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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06 Apr 2018, 15:46
1
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.

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

See below for what I learned today.

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 mark
to 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)

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

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Posts: 477
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GPA: 3.68
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Re: If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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07 Apr 2018, 04:13
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 n is divisible by both 5 and 7 , the lowest value of n could be 35, which is LCM of 5 and 7. now, what could be the other values of n. n could be 70, 105, 140, 175. All the mentioned numbers will be evenly divisible by only 35. Thus, The correct answer will be C.
Re: If a positive integer n is divisible by both 5 and 7, the n must also &nbs [#permalink] 07 Apr 2018, 04:13
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