What is the remainder when the positive integer x is divided by 6?
a) When x is divided by 2, the remainder is 1; when x is divided by 3, the remainder is 0.
b) when x is divided by 12, the remainder is 3.
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Side questionif you pick 3 for x after reading statement 1, is the remainder 3 when 3 is divided by 6? That sounds fishy to me, but that's the answer I got after looking it up on the internet.
GMAT PrepRemainder
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a)
When x is divided by 2, the remainder is 1
=> x is of the form: 2k+1. possible values : 3, 5, 7, 9, 11, 13,15.....
when x is divided by 3, the remainder is 0
=> x is a multiple of 3. possible values: 3, 6, 9, 12, 15......
satisfying both the above conditions, possible values of x=3,9,15,21...
in all these, x leaves a remainder of 3 when divided by 6. sufficient
b)when x is divided by 12, the remainder is 3
=> x is of the form 12k+3. possible values: 15, 27, 39...
in all these, x leaves a remainder of 3 when divided by 6. sufficient
hence, D
yes if the numerator is less than the denominator, then the numerator is the remainder.
When x is divided by 2, the remainder is 1
=> x is of the form: 2k+1. possible values : 3, 5, 7, 9, 11, 13,15.....
when x is divided by 3, the remainder is 0
=> x is a multiple of 3. possible values: 3, 6, 9, 12, 15......
satisfying both the above conditions, possible values of x=3,9,15,21...
in all these, x leaves a remainder of 3 when divided by 6. sufficient
b)when x is divided by 12, the remainder is 3
=> x is of the form 12k+3. possible values: 15, 27, 39...
in all these, x leaves a remainder of 3 when divided by 6. sufficient
hence, D
yes if the numerator is less than the denominator, then the numerator is the remainder.