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# If b is the product of three consecutive positive integers

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Senior Manager
Joined: 25 Jun 2009
Posts: 285
If b is the product of three consecutive positive integers  [#permalink]

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03 Aug 2009, 00:04
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If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24 ?

(1) b is a multiple of 3,
(2) c is odd.

OA is A

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CEO
Joined: 17 Nov 2007
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 01:16
I agree, OA is incorrect.
First statement is "empty", because b is always divisible by 3.
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Manager
Joined: 07 Apr 2009
Posts: 143
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 09:15
Quote:
I agree, OA is incorrect.
First statement is "empty", because b is always divisible by 3.

Hey I agree that A is a empty statemetn, as we know that product of n consequtive numbers is always divisible by n, but how does it answer the question is the product multiple of 24 ? IMO it can or cannot right ?

Should the answer be 'E' ?
Senior Manager
Joined: 25 Jun 2009
Posts: 285
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 10:22
skpMatcha wrote:
Quote:
I agree, OA is incorrect.
First statement is "empty", because b is always divisible by 3.

Hey I agree that A is a empty statemetn, as we know that product of n consequtive numbers is always divisible by n, but how does it answer the question is the product multiple of 24 ? IMO it can or cannot right ?

Should the answer be 'E' ?

Yes, the answer should be E.
Senior Manager
Joined: 18 Jun 2009
Posts: 349
Location: San Francisco
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 10:57
Manager
Joined: 16 Apr 2009
Posts: 212
Schools: Ross
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 11:35
Quote:
If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24 ?

(1) b is a multiple of 3,
(2) c is odd.

IMO OA is B

b is the product of three consecutive positive integers c, c + 1, and c + 2
b can be a multiple of 24 only when c is even.

let say c is 2
2 x 2+1 x 2+2 =2x3x4

let say c is 3
3 x 3+1 x 3+2 =3x4x5

let say c is 4
4 x 4+1 x 4+2 =4x5x6
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Senior Manager
Joined: 25 Jun 2009
Posts: 285
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 11:46
vannu wrote:
Quote:
If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24 ?

(1) b is a multiple of 3,
(2) c is odd.

IMO OA is B

b is the product of three consecutive positive integers c, c + 1, and c + 2
b can be a multiple of 24 only when c is even.

let say c is 2
2 x 2+1 x 2+2 =2x3x4

let say c is 3
3 x 3+1 x 3+2 =3x4x5

let say c is 4
4 x 4+1 x 4+2 =4x5x6

What if C= 1 then the product becomes 6 !. Hence Insuff !
Senior Manager
Joined: 18 Jun 2009
Posts: 349
Location: San Francisco
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 11:52
vannu wrote:
Quote:
If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24 ?

(1) b is a multiple of 3,
(2) c is odd.

IMO OA is B

b is the product of three consecutive positive integers c, c + 1, and c + 2
b can be a multiple of 24 only when c is even.

let say c is 2
2 x 2+1 x 2+2 =2x3x4

let say c is 3
3 x 3+1 x 3+2 =3x4x5

let say c is 4
4 x 4+1 x 4+2 =4x5x6

if c = 1

then
b = 1 X 1+1 X 1+2 = 6 which is a multiple of 24 so C can be odd

so B cannot be the answer
Manager
Joined: 16 Apr 2009
Posts: 212
Schools: Ross
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 11:59
is 6 a multiple or factor of 24?
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Senior Manager
Joined: 18 Jun 2009
Posts: 349
Location: San Francisco
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 12:06
Both are same

Like The prime factors of 24 are
2^3 and 3
Manager
Joined: 16 Apr 2009
Posts: 212
Schools: Ross
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 12:11
a multiple is when you multiply numbers by a number
example: multiples of 5 are 5, 10, 15, 20 etc

(5*1=5, 5*2=10, 5*3=15, 5*4=20)

a factor is the numbers that divide evenly into another number
example: factors of 6 are 1, 2, 3

(6 divided by 1=6, 6 divided by 2= 3, 6 divided by 3=2)

---------------------
if b has to be a multiple, it should be 48,72,96 etc;

6 is one of the factor of 24..
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Senior Manager
Joined: 18 Jun 2009
Posts: 349
Location: San Francisco
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 13:03
vannu wrote:
a multiple is when you multiply numbers by a number
example: multiples of 5 are 5, 10, 15, 20 etc

(5*1=5, 5*2=10, 5*3=15, 5*4=20)

a factor is the numbers that divide evenly into another number
example: factors of 6 are 1, 2, 3

(6 divided by 1=6, 6 divided by 2= 3, 6 divided by 3=2)

---------------------
if b has to be a multiple, it should be 48,72,96 etc;

6 is one of the factor of 24..

Yep you are right ... my bad
Senior Manager
Joined: 18 Jun 2009
Posts: 349
Location: San Francisco
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 13:08
vannu wrote:
Quote:
If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24 ?

(1) b is a multiple of 3,
(2) c is odd.

IMO OA is B

b is the product of three consecutive positive integers c, c + 1, and c + 2
b can be a multiple of 24 only when c is even.

let say c is 2
2 x 2+1 x 2+2 =2x3x4

let say c is 3
3 x 3+1 x 3+2 =3x4x5

let say c is 4
4 x 4+1 x 4+2 =4x5x6

what about when c = 7 ?

7*8*9 = 504

it is a multiple of 24
Manager
Joined: 30 May 2009
Posts: 204
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 13:14
I think answrer should be E.

Take c=1, then b = 1*2*3 = 3
3 is a multiple of 3 but not a multiple of 24.

Take c=7, then b= 7*8*9 = 504
504 is a multiple of 3 as well as a multiple of 24.

Hence E
Manager
Joined: 16 Apr 2009
Posts: 212
Schools: Ross
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 13:50
I agree.
Need to be cautious while picking numbers!
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Senior Manager
Joined: 17 Jul 2009
Posts: 259
Concentration: Nonprofit, Strategy
GPA: 3.42
WE: Engineering (Computer Hardware)
Re: Not in agreement with OA  [#permalink]

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03 Aug 2009, 16:30
agree, OA is wrong here..should be E
Manager
Joined: 18 Jul 2009
Posts: 166
Location: India
Schools: South Asian B-schools
Re: Not in agreement with OA  [#permalink]

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06 Aug 2009, 03:48
i accept ans should be E

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: Not in agreement with OA &nbs [#permalink] 06 Aug 2009, 03:48
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