What is the remainder when the positive integer x is divided by 6?
1) When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0.
2) When x is divided by 12, the remainder is 3.
OA D
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From 1:
X=2n+1 and X=3m, where m and n are integers. So basically X takes values which are odd multiples of 3 e.g. 3,9,15 etc
when divided by 6 remainder is always 3
SUFFICIENT
FROM 2:
X=12n+3 So basically X take values like 15, 27 etc (12n is always divisible by 6 leaving 3 as remainder)
when divided by 6 remainder is always 3
SUFFICIENT
IMO answer D
X=2n+1 and X=3m, where m and n are integers. So basically X takes values which are odd multiples of 3 e.g. 3,9,15 etc
when divided by 6 remainder is always 3
SUFFICIENT
FROM 2:
X=12n+3 So basically X take values like 15, 27 etc (12n is always divisible by 6 leaving 3 as remainder)
when divided by 6 remainder is always 3
SUFFICIENT
IMO answer D
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if the remainder is 1 when divided by 2 then we know that x is odd - becuase when you divide by 2 you either get a remainder of 0 (for an even number) or a remainder of 1 (for an odd number) so the first part says that x is odd. If the remainder is 0 when divided by three that means that the number is divisible by three. So stmt 1 says that x is an odd multiple of three - odd multiples of three are 6 numbers apart which means they will all have the same remainder when divided by 6 (incidentally it is 3 in this case)
AD
Stmt 2 says that x is three more than a multiple of 12 - therefore it is also 3 more than a multiple of 6 (because 12 is a multiple of 6) Therefore sufficient.
D.
AD
Stmt 2 says that x is three more than a multiple of 12 - therefore it is also 3 more than a multiple of 6 (because 12 is a multiple of 6) Therefore sufficient.
D.
Becky
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from (1) you can not have x=3(2n+1)liferocks wrote:from 1 we get x=3(2n+1) where n is any integerduongthang wrote:How do you know (1) is sufficient?
only by plugging specific numbers?
or x=6n+3..so when x is divided by 6 reminder is 3
from (1) you can have x=3m(2n+1)= 6mn+3m with m is odd
so when x is divided by 6, remainder is 3m-with m is odd
so 3m=3.(2a+1)=6a+3
only now you can say that remainder is 3.
I see this problem is hard. and plugging number is ok. we should not solve above way.
any idea of this problem. pls, remember , we have only 2 minutes for this problem
HItpr-becky wrote:if the remainder is 1 when divided by 2 then we know that x is odd - becuase when you divide by 2 you either get a remainder of 0 (for an even number) or a remainder of 1 (for an odd number) so the first part says that x is odd. If the remainder is 0 when divided by three that means that the number is divisible by three. So stmt 1 says that x is an odd multiple of three - odd multiples of three are 6 numbers apart which means they will all have the same remainder when divided by 6 (incidentally it is 3 in this case)
AD
Stmt 2 says that x is three more than a multiple of 12 - therefore it is also 3 more than a multiple of 6 (because 12 is a multiple of 6) Therefore sufficient.
D.
If we consider the 1st statement i.e
"X=2n+1 and X=3m, where m and n are int ... always 3 "
We need to consider first X=3,in that case 3 divided by 6 gives a reminder different from ,the reminder whenX=9 is divded by 6.So how the statement 1 is sufficient.
Thanks.