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# If n is an integer, what is the greatest common divisor of 12 and n ?

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
If n is an integer, what is the greatest common divisor of 12 and n ? [#permalink]

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25 Jun 2018, 20:29
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79% (00:53) correct 21% (00:58) wrong based on 124 sessions

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If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

NEW question from GMAT® Official Guide 2019

(DS05377)

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Re: If n is an integer, what is the greatest common divisor of 12 and n ? [#permalink]

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25 Jun 2018, 20:47
(1) n=36
gcd=12
(2) 12 divides n
gcd=12

It must be D. Each statement alone is sufficient
Manager
Joined: 25 Jul 2017
Posts: 73
Re: If n is an integer, what is the greatest common divisor of 12 and n ? [#permalink]

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25 Jun 2018, 20:51
Bunuel wrote:
If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

NEW question from GMAT® Official Guide 2019

(DS05377)

From Statement 1: "The product of 12 and n is 432" i.e. n=432/12= 36.
So Greatest common divisor of 12, 36 can be derived. - Sufficient

From Statement 2: "The greatest common divisor of 24 and n is 12.".
that is n could be, 12, 36, 60, 84.... and so on. And, in each case, the Greatest common divisor for 12 & n will be 12. - Sufficient.
Math Expert
Joined: 02 Aug 2009
Posts: 6219
Re: If n is an integer, what is the greatest common divisor of 12 and n ? [#permalink]

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25 Jun 2018, 21:10
1
Bunuel wrote:
If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

NEW question from GMAT® Official Guide 2019

(DS05377)

GCD means the largest number which has both 12 and n as its multiple..
So you require to know the value of n or some relationship between 12 and n or some property of n..

1) 12 * n =432...
n can be found and GCD of 12 and n can also be found..
Sufficient

2) GCD of 24 and n is 12.
This tells us that n is multiple of 12...
Let n =12x, where X is an integer
So GCD of 12 and 12x has to be 12 itself
Sufficient

D
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If n is an integer, what is the greatest common divisor of 12 and n ? [#permalink]

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25 Jun 2018, 21:55

Solution

Given:
• n is an integer

To find:
• The greatest common divisor of 12 and n

Analysing Statement 1
• As per the information given in statement 1, the product of 12 and n is 432
o Therefore, we can find the value of n = $$\frac{432}{12}$$
• As we can find n, we can also find the greatest common divisor of 12 and n

Hence, statement 1 is sufficient to answer the question

Analysing Statement 2
• As per the information given in statement 2, the greatest common divisor of 24 and n is 12
o So, the number n must be a multiple of 12
o Therefore, the greatest common divisor of 12 and n will be 12

Hence, statement 2 is sufficient to answer the question

Hence, the correct answer is option D.

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Re: If n is an integer, what is the greatest common divisor of 12 and n ? [#permalink]

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05 Jul 2018, 03:05
3
Bunuel wrote:
If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

Statement 1:
12n = 432.
Since we can solve for n, the GCF of 12 and n can be determined.
SUFFICIENT.

Statement 2:
24 = 2*2*2*3.
Since the GCF of n and 24 is the blue product (12) without the red factor (2), n must be a multiple of 12 that does NOT include an additional factor of 2.
In other words:
n = 12a, where a is an ODD positive integer.
Options for n:
12*1, 12*3, 12*5, 12*7, 12*9...
In every case, the GCF of n and 12 is the value in green (12).
SUFFICIENT.

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Re: If n is an integer, what is the greatest common divisor of 12 and n ? [#permalink]

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07 Jul 2018, 05:10
anuj04 wrote:
Bunuel wrote:
If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

NEW question from GMAT® Official Guide 2019

(DS05377)

From Statement 1: "The product of 12 and n is 432" i.e. n=432/12= 36.
So Greatest common divisor of 12, 36 can be derived. - Sufficient

From Statement 2: "The greatest common divisor of 24 and n is 12.".
that is n could be, 12, 36, 60, 84.... and so on. And, in each case, the Greatest common divisor for 12 & n will be 12. - Sufficient.

hey pushpitkc,

i dont get if the product of 12 and n is 432" it means n = 36

and the question asks: If n is an integer, what is the greatest common divisor of 12 and n ?

how can 36 be divisor of 12

Also From Statement 2: "The greatest common divisor of 24 and n is 12.".

i dont get how greatest common divisor of 24 can be 12, 36, 60, 84 ?

any ideas ?

thanks and have a great day
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Re: If n is an integer, what is the greatest common divisor of 12 and n ? [#permalink]

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07 Jul 2018, 05:34
1
dave13 wrote:
anuj04 wrote:
Bunuel wrote:
If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

NEW question from GMAT® Official Guide 2019

(DS05377)

From Statement 1: "The product of 12 and n is 432" i.e. n=432/12= 36.
So Greatest common divisor of 12, 36 can be derived. - Sufficient

From Statement 2: "The greatest common divisor of 24 and n is 12.".
that is n could be, 12, 36, 60, 84.... and so on. And, in each case, the Greatest common divisor for 12 & n will be 12. - Sufficient.

hey pushpitkc,

i dont get if the product of 12 and n is 432" it means n = 36

and the question asks: If n is an integer, what is the greatest common divisor of 12 and n ?

how can 36 be divisor of 12

Also From Statement 2: "The greatest common divisor of 24 and n is 12.".

i dont get how greatest common divisor of 24 can be 12, 36, 60, 84 ?

any ideas ?

thanks and have a great day

Hey dave13

For the first statement, it says which is the greatest divisor the two integers, n and 12.
The greatest common divisor (GCD) of a set of integers is the largest integer that divides
each integer in the set. So, if n=36, the greatest common divisor is 12.

As for the second statement, the number n and 24 have a greatest common divisor of 12.
So, n can be any multiple of 12 - 12,12*2 = 24,12*3 = 36, and so on. This link should

Hope this helps you!
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Re: If n is an integer, what is the greatest common divisor of 12 and n ? [#permalink]

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13 Jul 2018, 14:26
Bunuel wrote:
If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

We need to determine the greatest common divisor or the greatest common factor (GCF) of 12 and n. If we can determine the value of n, then we can determine the GCF of 12 and n.

Statement One Alone:

The product of 12 and n is 432

Since 12n = 432, n = 432/12 = 36. So the GCF of 12 and 36 is 12.

Statement one alone is sufficient.

Statement Two Alone:

The greatest common divisor of 24 and n is 12.

Since the GCF of 24 and n is 12, that means n itself is a multiple of 12. Therefore, the GCF of 12 and n must be also 12.

Statement two is sufficient.

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Re: If n is an integer, what is the greatest common divisor of 12 and n ?   [#permalink] 13 Jul 2018, 14:26
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