What is the remainder when positive integer x is divided by

[Guest]

What is the remainder when 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 then the remainder is 0.

(2)When x is divided by 12, the remainder is 3.

The OA is D.

I just have one doubt. What if x is 3 according to statement 1 then how do you treat it ?

[Guest]

The source is GMAT-PREP.

[Guest]

as per y=qx+r rule, when u divide 3 by 6, the reminder is 3..

[Guest]

When you divide 3 by 6 you get a decimal/ Can you explain how x equals 3?
Thanks

[RonPurewal]

I just have one doubt. What if x is 3 according to statement 1 then how do you treat it ?

if you divide a quantity by a larger quantity, then the integer quotient is 0, and the remainder is exactly the dividend (the smaller number) that you started with.
so, when you divide 3 by 6, the quotient is 0 and the remainder is 3.

although this will look weird at first, it should become obvious in the context of a word problem. first, a "normal" word problem, to set the tone:
what's the remainder when 17 is divided by 6? --> if you have 17 cans of beer and you're assembling complete six-packs, how many cans of beer will be left over?
answer: you'll have 5 (remainder) cans of beer left over, after making 2 (quotient) six-packs.
and now for the main event:
what's the remainder when 3 is divided by 6? --> if you have 3 cans of beer and you're assembling complete six-packs, how many cans of beer will be left over?
answer: you'll have 3 (remainder) cans of beer left over, after making 0 (quotient) six-packs.

--

When you divide 3 by 6 you get a decimal/ Can you explain how x equals 3?
Thanks

when you divide a number by something that isn't a factor, you have to CHOOSE ONE INTERPRETATION: either a decimal / fractional part, or a remainder. you can't have it both ways. (remember that remainders were something that you conjured up in grade school because you had no idea what a fraction was yet.)

illustration:
12 divided by 5 = 2.4, or 2 2/5 (the interpretation with a fractional part)
12 divided by 5 = 2 with a remainder of 2 (notice that the remainder equals the numerator of the UNREDUCED fractional part).
you have to choose one of these interpretations; you can't say, for instance, that it's 2 2/5 with a remainder of 2. that would be not only redundant, but technically incorrect.

[RonPurewal]

there's more on this problem here.

[Joey Z.]

(1) When x is divided by 2, the remainder is 1 and when x is divided by 3 then the remainder is 0.

This means x is a multiple of 3. A multiple of 3 is either an odd number (3, 9, 15, ......) which is a multiple of 6 plus 3 or an even number that can be divided by 6. Given that x is not an even number, when it is divided by 6, the remainder has to be 3. -- Sufficient

(2)When x is divided by 12, the remainder is 3.
This means x=12n+3, where n is an integer. Hence, x/6 = 2n+.5, which can never be an integer. In other words, when x is divided by 6, the remainder is 3. -- Sufficient

[RonPurewal]

(2)When x is divided by 12, the remainder is 3.
This means x=12n+3, where n is an integer. Hence, x/6 = 2n+.5, which can never be an integer. In other words, when x is divided by 6, the remainder is 3. -- Sufficient

not quite a correct explanation.

the reason the remainder is 3 here is because the ".5" part is 3/6.
if you want to convert a decimal remainder into a standard remainder, you have to convert that decimal into a fraction whose denominator is identical to the number you're dividing by.
in this case, this means to write the quotient above as 2n + 3/6, so that the remainder is 3.

if the remainder were 1, 2, 4, or 5, you'd also have a case where the quotient would "never be an integer", so that observation alone isn't enough to ensure that the remainder will be 3 (as ascertained from a literal reading of what you wrote above).