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Board of Directors P
Joined: 01 Sep 2010
Posts: 3367
If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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Difficulty:   15% (low)

Question Stats: 71% (00:36) correct 29% (00:37) wrong based on 207 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

_________________
Manager  S
Joined: 23 May 2017
Posts: 240
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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1
The lowest possible value is 35.

Hence : C
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Director  V
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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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; $$35$$.

Verbal Forum Moderator V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2234
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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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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The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
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Senior SC Moderator V
Joined: 22 May 2016
Posts: 2558
If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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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.

_________________

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

VP  D
Joined: 09 Mar 2016
Posts: 1277
Re: If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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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:)
Senior SC Moderator V
Joined: 22 May 2016
Posts: 2558
If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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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 Your good cheer is refreshing. 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)

_________________

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

VP  P
Joined: 31 Oct 2013
Posts: 1269
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If a positive integer n is divisible by both 5 and 7, the n must also  [#permalink]

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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   [#permalink] 07 Apr 2018, 04:13
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# If a positive integer n is divisible by both 5 and 7, the n must also

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