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
8Example-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 8When 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)
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine