# Blog

# Remainders are reminders that quotients don’t just fit, and more.

- May 7, 2017
- Posted by: gmatdudes
- Category: Uncategorized

By Gustavo Luyo

The definition of a remainder is, to the GMAT-untrained eye, something so obvious that very often you could be misled as to how to apply its notion when dealing with Quant problems involving integer variables of unknown value. Consider the following example:

What is the remainder of positive integer N when it is divided by *x ^{2} – y^{2}* , such that

*x*and

*y*are integers and

*x > y*?

(1) The remainder of N when divided by *x + y* equals 17.

(2) *x* and *y* are consecutive integers.

By first inspecting the general statement in the question, you learn it’s all about an integer division and that *x*^{2}* – y*^{2} is simply a positive integer, as it is simply the difference of two integer squares: yet not a hint about the remainder. So, we could now proceed to evaluate the statements.

**Statement 1**. You’re given the remainder of N when divided by *(x + y)*, which is one of the factors of *x*^{2}* – y*^{2}. But this does not mean you know the remainder when N is divided by *(x + y)(x – y)*. For example, if 74 is 17 more than a multiple of 19, this does not mean 74 is 17 more than a multiple of 19 x 2. So, the statement is INSUFFICIENT.

**Statement 2.** At first sight, the statement seems *unrelated* to the key issue here. So, considering it insufficient seems the right choice. Nevertheless, however insufficient it may look like, the statement DOES simplify the question down to: What is the remainder when N is divided by *(x + y)*? If this does not seem obvious, you may think of the meaning of consecutive integers: *x – y = 1*. Therefore, the product , which equals *(x + y)(x – y)*, would equal just *(x + y)*. Here we don’t know the value of the remainder. So, it’s INSUFFICIENT, but not just because the info added by the statement didn’t seem to fit in the problem.

**Statements 1 and 2 together. **Now we realize that the question is simplified to what is the remainder when N is divided by *(x + y)*, and we know for certain the remainder is 17. So the correct answer choice is ( C ).

Investing a few seconds more on thinking intently about the consequences of statement (2) is what really paid off here. So, the key takeaway is:

- NEVER discard a statement just because it seems unrelated or irrelevant to the problem.
- ALWAYS try to connect the dots, by finding a relation with the problem’s question. When the time comes for evaluating the statements together, any boring or indifferent statement might really hold the clue you need to resolve a problem successfully.