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If a, b, and c are consecutive integers and 0 < a < b < c, is the prod

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If a, b, and c are consecutive integers and 0 < a < b < c, is the prod [#permalink]

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If a, b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8 ?

(1) The product ac is even.

(2) The product bc is a multiple of 4.
[Reveal] Spoiler: OA

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Kudos [?]: 9510 [0], given: 1203

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Kudos [?]: 6128 [0], given: 121

If a, b, and c are consecutive integers and 0 < a < b < c, is the prod [#permalink]

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New post 27 Jul 2017, 07:31
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carcass wrote:
If a, b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8 ?

(1) The product ac is even.

(2) The product bc is a multiple of 4.



hi,

If a, b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8
TWO cases..
A) a and c are even AND b is ODD.... abc will always be multiple of 8 or rather 24.. ans will be YES
B) a and c are ODD and b is even.. if b is multiple of 8.. YES otherwise NO


lets see the statements
(1) The product ac is even.
this MEANS a and c are even..
falls under category A above..
always YES
sufficient

(2) The product bc is a multiple of 4

either b is multiple of 4, ans can be YES or NO case B
OR c is multiple of 4, ans will be YES.. case A
different answers possible
insuff

A
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6128 [0], given: 121

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Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod [#permalink]

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New post 27 Jul 2017, 07:34
I Think answer is A

Statement 1:
ac is even -> a and c are even and b is odd, minimum possible values of abc is 2*3*4.
Sufficient

Statement 2:
bc multiple of 4 --> b can be 4.. c can be 5.... so a can be 3, which gives abc=60
not sufficient

Answer A

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Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod [#permalink]

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New post 01 Dec 2017, 14:58
I don't get why a and c are even AND b is ODD.... abc will always be multiple of 8 or rather 24, could you explain me please

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Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod [#permalink]

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New post 01 Dec 2017, 19:38
analuisa wrote:
I don't get why a and c are even AND b is ODD.... abc will always be multiple of 8 or rather 24, could you explain me please


Hi analuisa

as the numbers are consecutive, so \(a\), \(b\), \(c\) can take two options -

Case 1: Even, Odd, Even OR

Case 2: Odd, Even, Odd

Statement 1: as \(ac\) is even, so it has to be Case 1

Now let \(a=2k\) (even number) so \(b=2k+1\) and \(c=2k+2=2(k+1)\), where \(k\) is any number greater than \(0\) (because \(0<a<b<c\))

Hence \(ac=2k*2(k+1)=4k(k+1)\)

so if \(k\) is odd then \(k+1=even\), hence \(4k(k+1)\) will be a multiple of \(8\)

if \(k\) is even then \(4k\) will be a multiple of \(8\). Therefore \(abc\) is a multiple of \(8\) because \(ac\) is a multiple of \(8\). Sufficient

Statement 2: \(bc\) is a multiple of \(4\). so it could be multiple of \(8\) such as \(16,24,32\) etc. or it could not be a multiple of \(8\) such as \(20, 28\) etc.. Insufficient

Option A

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Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod [#permalink]

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New post 01 Dec 2017, 20:29
carcass wrote:
If a, b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8 ?

(1) The product ac is even.

(2) The product bc is a multiple of 4.


The Best would be to plug in by numbers.

Let b = n, a = n-1, c = n+1

Stmnt 1: ac = even, \(n^2\) - 1 =even, Here n can be only a odd number starting from 3,5,7,9,11 etc.. So abc will be Divisible by 8.
Stmnt 2: n(n+1) = 4m.. Here, n can be 3,4,7,8,9,11,13,14.. etc. when n = 3, abc Divisible by 8 but n= 4, abc not divisible by 8.

Hope this Helps.

Kudos [?]: 17 [0], given: 333

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Kudos [?]: 6128 [0], given: 121

Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod [#permalink]

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New post 01 Dec 2017, 20:48
analuisa wrote:
I don't get why a and c are even AND b is ODD.... abc will always be multiple of 8 or rather 24, could you explain me please


Hi...
Three consecutive integers and two even means even, odd, even...
Now since three are consecutive, one of them would surely be a MULTIPLE of 3.
Two of them even means one will be MULTIPLE of 2 and other will be MULTIPLE of atleast 4 so product will be MULTIPLE of atleast 3*2*4=24
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6128 [0], given: 121

Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod   [#permalink] 01 Dec 2017, 20:48
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