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# Is a*b*c divisible by 24 ? 1. a, b, and c are consecutive

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Senior Manager
Joined: 05 Oct 2008
Posts: 267
Is a*b*c divisible by 24 ? 1. a, b, and c are consecutive [#permalink]

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03 Nov 2008, 00:18
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is a*b*c divisible by 24 ?

1. a, b, and c are consecutive even integers
2. a*b is divisible by 12
Manager
Joined: 24 Sep 2008
Posts: 187
Schools: MIT / INSEAD / IIM - ABC
Re: No. Properties [#permalink]

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03 Nov 2008, 00:37
1
KUDOS
IMO A

Option A: a,b,c consecutive even integers: 2n, 2n+2, 2n+4
a*b*c= 8 X n X n+1 X n+2 so SUFF

Option: a*b divisible by 12 but c could be anything so INSUFF
Senior Manager
Joined: 05 Oct 2008
Posts: 267
Re: No. Properties [#permalink]

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03 Nov 2008, 06:24
if you take 0, 2 and 4
0*2*4=0

wouldn't the answer choice be C considering 0 as even?
VP
Joined: 30 Jun 2008
Posts: 1026
Re: No. Properties [#permalink]

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03 Nov 2008, 06:46
1
KUDOS
study wrote:
if you take 0, 2 and 4
0*2*4=0

wouldn't the answer choice be C considering 0 as even?

you are right study ....
study wrote:
Is a*b*c divisible by 24 ?

1. a, b, and c are consecutive even integers
2. a*b is divisible by 12

24 = 2*2*2*3 .. so we need at least one 3 and three 2s for abc to be divisible by 24 ...

(1) You proved that statement 1 is insuff
(2) a*b is divisible by 12 ... ab could be 12 or 24 or any 12x (where x is an integer)
to ensure abc is divisible by 24, we need to make sure that c is some even number. However statement 2 does not restrict the value of C. it can be ANYTHING (even some random fraction). Statement 2 is insuff...

Combined .... a,b,c are consecutive even numbers and a,b is divisible by 12 ...
so a*b can be ==> 2*6 ( that would make c =4) ===> abc is divisible by 24
so a*b can be ==> 4*6 ( that would make c =2 or c=8) ===> abc is divisible by 24

there is no case where c could be 0.

Answer has to be C.
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Current Student
Joined: 28 Dec 2004
Posts: 3342
Location: New York City
Schools: Wharton'11 HBS'12
Re: No. Properties [#permalink]

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03 Nov 2008, 07:05
1
KUDOS
0 is an even integer and all numbers 0/24 is 0 i.e divisible..

Ans is A

amitdgr wrote:
study wrote:
if you take 0, 2 and 4
0*2*4=0

wouldn't the answer choice be C considering 0 as even?

you are right study ....
study wrote:
Is a*b*c divisible by 24 ?

1. a, b, and c are consecutive even integers
2. a*b is divisible by 12

24 = 2*2*2*3 .. so we need at least one 3 and three 2s for abc to be divisible by 24 ...

(1) You proved that statement 1 is insuff
(2) a*b is divisible by 12 ... ab could be 12 or 24 or any 12x (where x is an integer)
to ensure abc is divisible by 24, we need to make sure that c is some even number. However statement 2 does not restrict the value of C. it can be ANYTHING (even some random fraction). Statement 2 is insuff...

Combined .... a,b,c are consecutive even numbers and a,b is divisible by 12 ...
so a*b can be ==> 2*6 ( that would make c =4) ===> abc is divisible by 24
so a*b can be ==> 4*6 ( that would make c =2 or c=8) ===> abc is divisible by 24

there is no case where c could be 0.

Answer has to be C.
VP
Joined: 30 Jun 2008
Posts: 1026
Re: No. Properties [#permalink]

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03 Nov 2008, 07:19
fresinha12 wrote:
0 is an even integer and all numbers 0/24 is 0 i.e divisible..

Ans is A

amitdgr wrote:
study wrote:
if you take 0, 2 and 4
0*2*4=0

wouldn't the answer choice be C considering 0 as even?

you are right study ....
study wrote:
Is a*b*c divisible by 24 ?

1. a, b, and c are consecutive even integers
2. a*b is divisible by 12

24 = 2*2*2*3 .. so we need at least one 3 and three 2s for abc to be divisible by 24 ...

(1) You proved that statement 1 is insuff
(2) a*b is divisible by 12 ... ab could be 12 or 24 or any 12x (where x is an integer)
to ensure abc is divisible by 24, we need to make sure that c is some even number. However statement 2 does not restrict the value of C. it can be ANYTHING (even some random fraction). Statement 2 is insuff...

Combined .... a,b,c are consecutive even numbers and a,b is divisible by 12 ...
so a*b can be ==> 2*6 ( that would make c =4) ===> abc is divisible by 24
so a*b can be ==> 4*6 ( that would make c =2 or c=8) ===> abc is divisible by 24

there is no case where c could be 0.

Answer has to be C.

whoops ..... Properties of 0
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Senior Manager
Joined: 05 Oct 2008
Posts: 267
Re: No. Properties [#permalink]

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03 Nov 2008, 10:03
Thanks all...
OA isA

Kudos given...
Re: No. Properties   [#permalink] 03 Nov 2008, 10:03
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# Is a*b*c divisible by 24 ? 1. a, b, and c are consecutive

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