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Positive integer n is a multiple of 18, and positive integer m is a mu

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Positive integer n is a multiple of 18, and positive integer m is a mu  [#permalink]

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27 Apr 2016, 10:21
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35% (medium)

Question Stats:

82% (02:03) correct 18% (02:17) wrong based on 81 sessions

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Positive integer n is a multiple of 18, and positive integer m is a multiple of 30. Is mn a multiple of 120?

(1) n is a multiple of 12.
(2) m is a multiple of 40.

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Joined: 02 Aug 2009
Posts: 7095
Positive integer n is a multiple of 18, and positive integer m is a mu  [#permalink]

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27 Apr 2016, 10:36
1
1
Bunuel wrote:
Positive integer n is a multiple of 18, and positive integer m is a multiple of 30. Is mn a multiple of 120?

(1) n is a multiple of 12.
(2) m is a multiple of 40.

Hi,
mn will be multiple of 18 * 30 = 540,which is not a multiple of 120..

lets see the statements--

(1) n is a multiple of 12.
n is also a multiple of 18, so n has to be amultiple of LCM of 12 and 18 = 36..
we know m is a multiple of 30..
so mn will be a multiple of 30 * 36 = 1080 = 120*9..
suff

(2) m is a multiple of 40.
m is also a multiple of 30..
so m will be multiple of LCM of 30 and 40 =120
so mn will be a multiple of 120 irrespective of value of n..
Suff

D
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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

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Re: Positive integer n is a multiple of 18, and positive integer m is a mu  [#permalink]

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27 Apr 2016, 10:49
1
chetan2u wrote:
Bunuel wrote:
Positive integer n is a multiple of 18, and positive integer m is a multiple of 30. Is mn a multiple of 120?

(1) n is a multiple of 12.
(2) m is a multiple of 40.

Hi,
mn will be multiple of LCM of 18 and 30 = 90..
what is required..
since m is a multiple of 30, if n is multiple of 8, the LCM will be 120 and ans will be YES
Also since n is a multiple of 18, if m is a multiple of 40, the LCM will be 360 and ans will be YES

lets see the statements--

(1) n is a multiple of 12.
n is also a multiple of 18, so n has to be amultiple of LCM of 12 and 18 = 36..
we know m is a multiple of 30..
so mn will be a multiple of LCM of 30 and 36 = 180..
180 is not a multiple of 120
so Insuff

(2) m is a multiple of 40.
m is also a multiple of 30..
so m will be multiple of LCM of 30 and 40 =120
so mn will be a multiple of 120 irrespective of value of n..
Suff

B

n is a multiple of 36: n = 36x;
m is a multiple of 30: m = 30y;

mn = 36x*30y = 1080xy = 120*9xy = multiple of 120. So, the first statement is sufficient too. The correct answer is D.
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Posts: 7095
Re: Positive integer n is a multiple of 18, and positive integer m is a mu  [#permalink]

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27 Apr 2016, 10:54
Bunuel wrote:
chetan2u wrote:
Bunuel wrote:
Positive integer n is a multiple of 18, and positive integer m is a multiple of 30. Is mn a multiple of 120?

(1) n is a multiple of 12.
(2) m is a multiple of 40.

Hi,
mn will be multiple of LCM of 18 and 30 = 90..
what is required..
since m is a multiple of 30, if n is multiple of 8, the LCM will be 120 and ans will be YES
Also since n is a multiple of 18, if m is a multiple of 40, the LCM will be 360 and ans will be YES

lets see the statements--

(1) n is a multiple of 12.
n is also a multiple of 18, so n has to be amultiple of LCM of 12 and 18 = 36..
we know m is a multiple of 30..
so mn will be a multiple of LCM of 30 and 36 = 180..
180 is not a multiple of 120
so Insuff

(2) m is a multiple of 40.
m is also a multiple of 30..
so m will be multiple of LCM of 30 and 40 =120
so mn will be a multiple of 120 irrespective of value of n..
Suff

B

n is a multiple of 36: n = 36x;
m is a multiple of 30: m = 30y;

mn = 36x*30y = 1080xy = 120*9xy = multiple of 120. So, the first statement is sufficient too. The correct answer is D.

Hi Bunuel,
I realized the moment I saw my answer again. It is MN, WHY should I even talk of LCM ..
If n is multiple of 12 and m is a multiple of 30, mn is a multiple of 12*30, and I must have been dreaming that I started talking of LCM..
Its 12:30 in the night , seems sleep is taking its toll on me..
Thanks
_________________

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

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Re: Positive integer n is a multiple of 18, and positive integer m is a mu  [#permalink]

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27 Apr 2016, 10:55
Positive integer n is a multiple of 18, and positive integer m is a multiple of 30. Is mn a multiple of 120?

(1) n is a multiple of 12.
(2) m is a multiple of 40.[/quote]

Answer to this question is D as both statements are alone sufficient.
to find whether mn is multiple of 120, first take lcm of 120. that will come 2*2*2*5*3.
from the given information n has 3*2 in it and m has 5*2 in it. you need one 2 to find the answer which each statement is providing.
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Re: Positive integer n is a multiple of 18, and positive integer m is a mu  [#permalink]

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07 Nov 2017, 00:58
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Re: Positive integer n is a multiple of 18, and positive integer m is a mu &nbs [#permalink] 07 Nov 2017, 00:58
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