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Math Expert V
Joined: 02 Sep 2009
Posts: 58449
Integer m has 4 different prime factors and n has 3 different prime  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 66% (01:25) correct 34% (01:37) wrong based on 146 sessions

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Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

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Senior Manager  G
Joined: 19 Apr 2016
Posts: 269
Location: India
GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5
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Integer m has 4 different prime factors and n has 3 different prime  [#permalink]

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Bunuel wrote:
Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Since m has 4 different prime factors and n has 3 different prime factors

let the prime factors of m be a,b,3 and 5
let the prime factors of n be c,3 and 5

Since the GCD(m,n)=15, both m and n will have 3 and 5 as common prime factors

now m*n will have the following prime factors a,b,c,3 and 5 which are 5 in number.

Hence option B is correct.
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Re: Integer m has 4 different prime factors and n has 3 different prime  [#permalink]

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Bunuel wrote:
Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

If m and n have a GCF of 15, they both share a prime of 3 and 5. Thus, m has 2 prime factors that differ from those of n and n has 1 other prime factor that differs from those of m.

Since mn has 2 common prime factors and 3 uncommon prime factors, mn has a total of 5 different prime factors.

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Intern  B
Joined: 17 May 2016
Posts: 17

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I guess that 3 and 5 are common to both m and n.
Besides that m has 2 unique prime factors and n has 1 unique factor making a total of 5 prime factors
IMO answer is B

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Intern  B
Joined: 27 May 2016
Posts: 1
Re: Integer m has 4 different prime factors and n has 3 different prime  [#permalink]

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Answer should be B as the there will be 3 prime numbers in addition, so in total we will have 5 different prime numbers,
Intern  Joined: 21 Mar 2017
Posts: 3
Re: Integer m has 4 different prime factors and n has 3 different prime  [#permalink]

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I have a doubt my answer is coming out to be 4

Like I took m to be 210 which has 4 prime factors-2,3,5,7 and n to be 30 which has 3 prime factors-2,3,5

now mn is 6300 which has 4 prime factors-2,3,5,7
Intern  B
Joined: 25 Aug 2016
Posts: 4
Integer m has 4 different prime factors and n has 3 different prime  [#permalink]

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johncath wrote:
I have a doubt my answer is coming out to be 4

Like I took m to be 210 which has 4 prime factors-2,3,5,7 and n to be 30 which has 3 prime factors-2,3,5

now mn is 6300 which has 4 prime factors-2,3,5,7

Hello, I took the same approach as yours i.e. by listing 2 sets of integers which have only prime factors. The answer must be B.

The error in the numbers you chose is as follows,
210 = 2x3x5x7
30 = 2x3x5
GCF of 210 and 30 is 2x3x5 = 30 and not 3 x 5 = 15.

Thus the numbers you selected should have been:
210 = 2x3x5x7 and
165 = 3x5x11 such that
GCF = 3 x 5 = 15.
With this combination now, Number of prime factors of mn = Count(2, 3, 5, 7, 11) = 5. Correct AC is B

Hope that helps.
Intern  Joined: 21 Mar 2017
Posts: 3
Re: Integer m has 4 different prime factors and n has 3 different prime  [#permalink]

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ThePhDAspirant wrote:
johncath wrote:
I have a doubt my answer is coming out to be 4

Like I took m to be 210 which has 4 prime factors-2,3,5,7 and n to be 30 which has 3 prime factors-2,3,5

now mn is 6300 which has 4 prime factors-2,3,5,7

Hello, I took the same approach as yours i.e. by listing 2 sets of integers which have only prime factors. The answer must be B.

The error in the numbers you chose is as follows,
210 = 2x3x5x7
30 = 2x3x5
GCF of 210 and 30 is 2x3x5 = 30 and not 3 x 5 = 15.

Thus the numbers you selected should have been:
210 = 2x3x5x7 and
165 = 3x5x11 such that
GCF = 3 x 5 = 15.
With this combination now, Number of prime factors of mn = Count(2, 3, 5, 7, 11) = 5. Correct AC is B

Hope that helps.

Ah Got it! Thanks alot mate:)
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Re: Integer m has 4 different prime factors and n has 3 different prime  [#permalink]

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Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Now M has 4 prime factors and n has 3.

the GCF is the greatest comman factore since it is 15 we see the prime factors for 15 and they are 3*5

so 2 of the Ms prime factor are 3 and 5 and left 2 other prime factors, 2 of the Ns prime factor are 3 and 5 left 1 other prime factor

2+(2)+1=5
Senior Manager  G
Joined: 06 Jul 2016
Posts: 358
Location: Singapore
Concentration: Strategy, Finance
Re: Integer m has 4 different prime factors and n has 3 different prime  [#permalink]

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Bunuel wrote:
Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

The Answer should be B.

m = A*B*C*D
n = X*Y*Z
Both have powers >= 1.

GCD (M,N) = 3*5 => 3 and 5 are common prime factors.
=> 2 + 3 additional factors so a total of 5 factors.

Correct?
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Manager  B
Joined: 06 Dec 2016
Posts: 231
Re: Integer m has 4 different prime factors and n has 3 different prime  [#permalink]

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M has 4 different prime factors
M - 2 x 3 x 5 x 7 = 210

N has 3 different prime factors
N - 3 x 5 x 11 = 165

MN = 210 x 165 = 34650

34650 has 5 different prime factors (2, 3, 5, 7 and 11).

The answer is B
Non-Human User Joined: 09 Sep 2013
Posts: 13271
Re: Integer m has 4 different prime factors and n has 3 different prime  [#permalink]

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_________________ Re: Integer m has 4 different prime factors and n has 3 different prime   [#permalink] 19 Mar 2019, 07:10
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