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

Question

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.

M36-131

Bunuel · Accepted Answer

Official Solution:

Is the positive integer  n  divisible by 8? 
 
(1)  n  is divisible by the product of three consecutive integers.
 
If these three consecutive integers are 1, 2, and 3, then the product is 6 and the answer is NO;
 
If these three consecutive integers are 2, 3, and 4, then the product is 24 and the answer is YES.
 
Not sufficient.
 
(2)  n  is divisible by the product of two consecutive even integers.
 
Out of any two consecutive EVEN integers, one will be disable by 4. So, the product will be divisible by  2*4=8 .
 
Sufficient.

Answer: B

PKN · Answer

Hi  Bunuel  Sir,

Question subject is not matching with Question stem. Could you please re-check?

Bunuel · Answer

_______________
Edited. Thank you.

PKN · Answer

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)

Bunuel · Answer

There was another typo in the statements. It's edited now. Sorry.

sidsst · Answer

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

GYANENDRA88 · Answer

sidsst 
As per statement 2
What if first no. is 0 and second is 2

Posted from my mobile device

sidsst · Answer

As you must know, division by 0 is not mathematically allowed.

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

sahuiitd · Answer

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

gvij2017 · Answer

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?

PKN · Answer

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.

Posted from my mobile device

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

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