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Is the positive integer n divisible by 8? (1) n is divisible by three

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Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 15 Jul 2018, 21:32
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Re: Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 15 Jul 2018, 22:33
Bunuel wrote:

GMAT CLUB TESTS FRESH QUESTION:



Is the positive integer n divisible by 8?

(1) n is divisible by three consecutive integers.
(2) n is divisible by two consecutive even integers.


Hi Bunuel Sir,

Question subject is not matching with Question stem. Could you please re-check?
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Re: Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 15 Jul 2018, 22:51
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Re: Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 16 Jul 2018, 00:07
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Bunuel wrote:

GMAT CLUB TESTS FRESH QUESTION:



Is the positive integer n divisible by 8?

(1) n is divisible by three consecutive integers.
(2) n is divisible by two consecutive even integers.


Statement-1:-

Let the three consecutive numbers are a,b, and c.
n is divisible by three consecutive integers, which implies n=LCM(a,b,c)
And LCM(a,b,c) is divisible by 8 when only one of a,b, and c is 8 or multiple of 8.
In all other cases, n is not divisible by 8.

Example-1:- (a,b,c)=(6,7,8)
n=LCM(6,7,8)=168 is divisible by 6,7,and 8.

Example-2:- (a,b,c)=(16,17,18)
n=LCM(16(=2*8),17,18)=2*8*9*17 is divisible by 16,17,18, and 8

Example-3:- (a,b,c)=(2,3,4)
n=LCM(2,3,4)=12 is divisible by 3,4,5 but not divisible by 8.

Insufficient.

Statement-2:-Same reasoning, n=LCM(x,y), where m and n are consecutive even integers.
When x=2, y=4; n=LCM(2,4)=4 is divisible by 2 and but not divisible by 8
When x=6, y=8; n=LCM(6,8)=24 is divisible by 6 and 8.
Insufficient.

(1)+(2),
case-1
n=168 is divisible by three consecutive integers(6,7 and 8) ,
n=168 is divisible by two consecutive even integers (6 and 8), and
n=168 is divisible by 8 too.

n=12 is divisible by three consecutive integers(2,3 and 4) ,
n=12 is divisible by two consecutive even integers (2 and 4), and
n=12 is not divisible by 8.

Hence, insufficient.

Ans (E)
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Re: Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 16 Jul 2018, 00:22
PKN wrote:
Bunuel wrote:

GMAT CLUB TESTS FRESH QUESTION:



Is the positive integer n divisible by 8?

(1) n is divisible by three consecutive integers.
(2) n is divisible by two consecutive even integers.


Statement-1:-

Let the three consecutive numbers are a,b, and c.
n is divisible by three consecutive integers, which implies n=LCM(a,b,c)
And LCM(a,b,c) is divisible by 8 when only one of a,b, and c is 8 or multiple of 8.
In all other cases, n is not divisible by 8.

Example-1:- (a,b,c)=(6,7,8)
n=LCM(6,7,8)=168 is divisible by 6,7,and 8.

Example-2:- (a,b,c)=(16,17,18)
n=LCM(16(=2*8),17,18)=2*8*9*17 is divisible by 16,17,18, and 8

Example-3:- (a,b,c)=(2,3,4)
n=LCM(2,3,4)=12 is divisible by 3,4,5 but not divisible by 8.

Insufficient.

Statement-2:-Same reasoning, n=LCM(x,y), where m and n are consecutive even integers.
When x=2, y=4; n=LCM(2,4)=4 is divisible by 2 and but not divisible by 8
When x=6, y=8; n=LCM(6,8)=24 is divisible by 6 and 8.
Insufficient.

(1)+(2),
case-1
n=168 is divisible by three consecutive integers(6,7 and 8) ,
n=168 is divisible by two consecutive even integers (6 and 8), and
n=168 is divisible by 8 too.

n=12 is divisible by three consecutive integers(2,3 and 4) ,
n=12 is divisible by two consecutive even integers (2 and 4), and
n=12 is not divisible by 8.

Hence, insufficient.

Ans (E)


There was another typo in the statements. It's edited now. Sorry.
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Re: Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 16 Jul 2018, 02:00
Statement 1 :

N is divisible by the product of three consecutive integers.

Let the set of integers be : {1,2,3} product = 6.

Now 12 is divisible by 6 but not by 8.
24 is divisible by 6 and by 8 as well.

Thus statement not sufficient.

Statement 2 :

N is divisible by the product of two consecutive even integers.

for two consecutive even integers : the product will be of the form : 2^t * 2^(t+1)

Minimum t=1, Thus minimum value of index on 2 =3 . Thus product is always of the form = 8k.

hence N is divisible.


ANSWER = B
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Re: Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 16 Jul 2018, 02:27
sidsst
As per statement 2
What if first no. is 0 and second is 2

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Re: Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 16 Jul 2018, 02:31
As you must know, division by 0 is not mathematically allowed.
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Re: Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 24 Dec 2018, 01:39
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Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 03 Jan 2019, 10:56
Bunuel wrote:

GMAT CLUB TESTS FRESH QUESTION:



Is the positive integer n divisible by 8?

(1) n is divisible by the product of three consecutive integers.
(2) n is divisible by the product of two consecutive even integers.



For n to be divisible by 8, n should contain min. power of 2 as 3.
Statement 1
Case A: 3 consecutive integers can be 2 Odd & 1 Even....if this is the case then n is may be or may be not divisible by 8 as the even integer has to be multiple of 8.
Case B: 3 consecutive integers can be 1 Odd & 2 Even....if this is the case then n is may be divisible by 8 as the min. even integers can be 2 & 4.
Insufficient info.

Statement 2
Min. even integers can be 2 & 4, hence n will be divisible by 8.
Sufficient info.

Option B
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Re: Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 03 Jan 2019, 18:22
I don't understand why folks are ignoring "0" in statement B while considering two consecutive even integers.

(0, 2) can be one pair for which statement 2 is not valid.
Can anyone tell me why 0 is not considered by others?
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Re: Is the positive integer n divisible by 8? (1) n is divisible by three  [#permalink]

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New post 03 Jan 2019, 18:53
gvij2017 wrote:
I don't understand why folks are ignoring "0" in statement B while considering two consecutive even integers.

(0, 2) can be one pair for which statement 2 is not valid.
Can anyone tell me why 0 is not considered by others?


Note:-
1. No number in the number system is divisible by zero.
2. 0/0 is undefined.
3. Any number/0 is an absurd.

Hope it helps.

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Re: Is the positive integer n divisible by 8? (1) n is divisible by three   [#permalink] 03 Jan 2019, 18:53
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