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505-555 Level|   Multiples and Factors|                  
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Bunuel
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Bunuel
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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(1) n=36
gcd=12
(2) 12 divides n
gcd=12

It must be D. Each statement alone is sufficient
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Bunuel
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.
D is the answer.
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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.

Answer: D
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anuj04
Bunuel
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.
D is the answer.


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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dave13
anuj04
Bunuel
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.
D is the answer.


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
help you understand what the Greatest Common divisor is.

Hope this helps you!
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Bunuel
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.

Answer: D
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given n is an integer

we need to find the HCF of 12 and n.
remember that we need to find the HCF, not the "n".

Statement 1 gives straight answer
1) 12 * n =432
n can be found and HCF of 12 and n can also be found.
there ends the matter
Sufficient

Statement 2 says
the HCF of 24 and n is 12.
means that n is a multiple of 12

Let n =12p, where p is an integer
So HCF of 12 and 12p has to be 12 itself
Sufficient
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Bunuel
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)

1) 12n = 432
n = 36
two numbers are 12, 36
So the greatest common divisor is 12
Statement 1 is Sufficient.

2) 12 is divisor of n and 24, then surely it will be a divisor of 12.
Statement 2 is sufficient.

Ans. D
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Bunuel
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)

Wanna make solving the Official Questions interesting???


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Answer: Option D

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Video solution from Quant Reasoning:
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