Let’s start 2015 with a frequently asked question type on the GMAT which is based on our last discussion of remainders.

Many GMAT questions could have a piece of information like

“When positive integer n is divided by 5, the remainder is 1.”

To make use of this information, you will need to find the different possible values of n. To find the different possible values of n, we shall use the relationship between dividend, divisor, quotient and remainder that we discussed in the previous post.

**Dividend = Quotient x Divisor + Remainder**

All we have to do to generate possible values of n is perform two calculations

– multiply 5 by an integer

– add 1 to that product

On doing so, we get the following table.

Dividend (n) |
= |
Quotient (integer) |
x |
Divisor (5) |
+ |
Remainder (1) |

1 |
= |
0 |
x |
5 |
+ |
1 |

6 |
= |
1 |
x |
5 |
+ |
1 |

11 |
= |
2 |
x |
5 |
+ |
1 |

16 |
= |
3 |
x |
5 |
+ |
1 |

Notice that possible values of n follow a pattern: each next value of n is 5 more than the previous value. So we can also generate the values of n by adding 5 at each step, and hence the different values of n form an arithmetic sequence.

As you can see, there will be infinite values of n satisfying the given condition. So, you will have to practice such questions to get an idea of which are the most relevant values of n.

Consider the following example –

Question – A positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. What is the remainder that n leaves after division by 30?

- 3 b. 10 c. 15 d. 20 e. 28

Solution – From the first condition, n could be 4,10,16,22,28,..

From the second condition, n could be 3,8,13,18,23,28,..

We want values of n that satisfy both the conditions; hence the first possible value of n is 28. And when we divide 28 by 30, the remainder is 28. Answer (e)

Here’s another similar question –

When positive integer x is divided by 5, the remainder is 2. When positive integer

y is divided by 4, the remainder is 1. Which of the following values CANNOT be the

sum x+y?

- 12 b. 13 c. 14 d. 16 e. 21

Answer. C

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