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# If positive integer A = m3n2, where m and n are distinct prime numbers

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If positive integer A = m3n2, where m and n are distinct prime numbers  [#permalink]

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09 Oct 2018, 05:33
3
00:00

Difficulty:

65% (hard)

Question Stats:

58% (02:01) correct 42% (03:20) wrong based on 38 sessions

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If positive integer A = $$m^3n^2$$, where m and n are distinct prime numbers, is 54 a factor of A?

(1) 25mn is the least common multiple of 15 and 50
(2) The greatest common factor of $$15m^3$$ and $$14n^2$$ is 6
Math Expert
Joined: 02 Aug 2009
Posts: 7334
If positive integer A = m3n2, where m and n are distinct prime numbers  [#permalink]

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09 Oct 2018, 05:54
1
1
If positive integer A = $$m^3n^2$$, where m and n are distinct prime numbers, is 54 a factor of A?

So 54=3^3*2 only possible if m is 3 and n is 2

(1) 25mn is the least common multiple of 15 and 50
LCM of 15 and 50 is 2*3*5*5=150=25mn......mn=6=2*3
If m=3 and n=2....yes
If n =3 and m=2...no
Insufficient

(2) The greatest common factor of $$15m^3$$ and $$14n^2$$ is 6
HCF/GCD of 15m^3 and 14n^2 is 6..
Only possible if m is a multiple of 2 and n is a multiple of 3
m=2 and n=3
Ans is NO
Sufficient

B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Intern
Joined: 05 Jun 2014
Posts: 9
Re: If positive integer A = m3n2, where m and n are distinct prime numbers  [#permalink]

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10 Oct 2018, 07:24
chetan2u wrote:
If positive integer A = $$m^3n^2$$, where m and n are distinct prime numbers, is 54 a factor of A?

So 54=3^3*2 only possible if m is 3 and n is 2

(1) 25mn is the least common multiple of 15 and 50
LCM of 15 and 50 is 2*3*5*5=150=25mn......mn=6=2*3
If m=3 and n=2....yes
If n =3 and m=2...no
Insufficient

(2) The greatest common factor of $$15m^3$$ and $$14n^2$$ is 6
HCF/GCD of 15m^3 and 14n^2 is 6..
Only possible if m is a multiple of 2 and n is a multiple of 3
m=3 and n=2
Ans is NO
Sufficient

B

While checking point 2 since m is a multiple of 2, shouldn't m be equal to 2 . Similarly since n is a multiple of 3, shouldn't n be equal to 3? Could you please correct me if I am missing something?
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If positive integer A = m3n2, where m and n are distinct prime numbers  [#permalink]

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10 Oct 2018, 07:33
storm1327 wrote:
chetan2u wrote:
If positive integer A = $$m^3n^2$$, where m and n are distinct prime numbers, is 54 a factor of A?

So 54=3^3*2 only possible if m is 3 and n is 2

(1) 25mn is the least common multiple of 15 and 50
LCM of 15 and 50 is 2*3*5*5=150=25mn......mn=6=2*3
If m=3 and n=2....yes
If n =3 and m=2...no
Insufficient

(2) The greatest common factor of $$15m^3$$ and $$14n^2$$ is 6
HCF/GCD of 15m^3 and 14n^2 is 6..
Only possible if m is a multiple of 2 and n is a multiple of 3
m=3 and n=2
Ans is NO
Sufficient

B

While checking point 2 since m is a multiple of 2, shouldn't m be equal to 2 . Similarly since n is a multiple of 3, shouldn't n be equal to 3? Could you please correct me if I am missing something?

Yes, you are correct..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Re: If positive integer A = m3n2, where m and n are distinct prime numbers   [#permalink] 10 Oct 2018, 07:33
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