Divisibility concerns

[drajkhowa]

When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder when N is divided by 30?

1. 13
2. 3
3. 11
4. 6.
5. 17

Would like to know if there is any algebraic approach to such problems.

[drajkhowa]

Any takers from the Instructor's team. ?? Any help will be greatly appreciated.

[RonPurewal]

is this problem from the GMATPREP SOFTWARE?

the ordering of the answer choices suggests otherwise; GMATPREP problems' answer choices are pretty much always in numerical order, unless there's a very, very good reason for them not to be (e.g., the problem asks something like "which of the following numbers is third greatest?")

if this problem is NOT from the GMATPREP software, then please tell us, and we'll move this thread to the appropriate section of the forum.

When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder when N is divided by 30?

1. 13
2. 3
3. 11
4. 6.
5. 17

Would like to know if there is any algebraic approach to such problems.

i don't know of a simple algebraic approach.
taken one at a time, the statements admit easy algebraic translations, if you know how to do them:
* the first statement translates to N = 10k + 1, where k is some integer;
* the second statement translates to N = 3m + 2, where m is some (other) integer.
however, i don't know of any particularly simple way to combine these statements, nor do i suspect that one exists.

instead, you should just GENERATE LISTS OF NUMBERS THAT SATISFY THE STATEMENTS, and look for a number that's in both lists.

as soon as you find any such number, you're golden; since the answer choices are pure numbers, you can tell that you're going to get the same remainder every time.

TAKEAWAY:
to generate lists of NUMBERS THAT HAVE REMAINDER "R" UPON DIVISION BY "D":
just take MULTIPLES OF "D" and ADD "R" to them.

so:
numbers that have remainder = 1 upon division by 10:
1, 11, 21, 31, 41, 51, ...
numbers that have remainder = 2 upon division by 3:
2, 5, 8, 11, 14, 17, ...

you don't have to go very far (11) to find the first example.
the remainder when you divide 11 by 30 is 11**, so the answer is (c) 11.

(alternatively, you could just make one of the lists, and then perform the other division to see whether you get the appropriate remainder.
for instance, take the first list. dividing 1 by 3 doesn't give a remainder of 2. dividing 11 by 3 does, so, 11 is the number you want.

if you don't know, or don't remember, how to take remainders when you divide a smaller number by a larger number, you can go to the next number that satisfies both statements, namely, 41.
dividing 41 by 30 gives the same remainder, 11.

--

**if you divide a number SMALLER than "D" by "D", then the remainder is the original number.
for instance, dividing 11 by 30 gives a remainder of 11.