Problem Solving

grandh01 wrote:If the remainder is 7 when positive
integer n is divided by 18, what is the
remainder when n is divided by 6 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

When positive integer n is divided by 18 the remainder is 7 implies n = 18q + 7 = (18q + 6) + 1 = 6(3q + 1) + 1
It can be seen that the first term is divisible by 6, so the remainder will only be from the second term 1
1 divided by 6 gives 1 as the remainder.

The correct answer is B.

grandh01 wrote:If the remainder is 7 when positive
integer n is divided by 18, what is the
remainder when n is divided by 6 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

grandh01 already showed that we can pick a number that satisfies the given condition. grandh01 chose n=25 and then showed that 25 divided by 6 leaves a remainder of 1.

I just wanted to mention that when we are plugging in possible values, it's often best to plug in the smallest possible value (for each of calculations).

For example, what if the question had said that the remainder is 7 when n is divided by 890? Since n=897 satisfies the given information, we could use that value to determine the remainder when n is divided by 6. However, it would be much easier if we plugged in the value n=7, since it also satisfies the given condition (7 divided by 890 equals zero with remainder 7). Likewise, 7 divided by 18 equals zero with remainder 7. So, we could have also used n=7 in the original question.

In general, we can say that:

If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

Cheers,
Brent

Brent@GMATPrepNow wrote:[
I just wanted to mention that when we are plugging in possible values, it's often best to plug in the smallest possible value (for each of calculations).

For example, what if the question had said that the remainder is 7 when n is divided by 890? Since n=897 satisfies the given information, we could use that value to determine the remainder when n is divided by 6. However, it would be much easier if we plugged in the value n=7

I agree completely that you should just work with the remainder itself if you want to choose a number in a remainders question - that's excellent advice. If you know that, say, "the remainder is 5 when k is divided by 23", then k can be 5 (when you divide 5 by 23, the quotient is 0 and the remainder is 5). If you need to do any arithmetic at all, 5 is going to be a much simpler value to work with than, say, 28, or 51, or 74, etc.

I did just want to quickly point out that in the example you gave above, you might want to change the '890' to a different number (to any multiple of 6), since knowing the remainder when you divide something by 890 isn't enough information to tell you the remainder when you divide by 6. The only reason we can get a unique answer to the question in the original post is because 18 is a multiple of 6.

Ian Stewart wrote: I did just want to quickly point out that in the example you gave above, you might want to change the '890' to a different number (to any multiple of 6), since knowing the remainder when you divide something by 890 isn't enough information to tell you the remainder when you divide by 6. The only reason we can get a unique answer to the question in the original post is because 18 is a multiple of 6.

Excellent point, Ian.
I just pulled that number out of the air. 870 would have been a better choice.

Cheers,
Brent