# CAT Practice : Number System

You are here: Home  CAT Questionbank   CAT Quant  Number System  Question 5
Product of two consecutive integers is always even. When will this be a multiple of 3 as well.

## Multiples

Q.5: n2 + 5n + 6 is a multiple of 6. n is natural number less than 100. How many values can n take?
1. 33
2. 65
3. 66
4. 67

Choice C. 66

Click to watch video solution
Click to view the explanation as a slide show

## Detailed Solution

n2 + 5n + 6
(n + 2) (n + 3)
(n + 2) and (n + 3) are two consecutive numbers.
One of (n + 2) or (n + 3) has to be even.

We need n such that (n + 2) (n + 3) is a multiple of 3.
(n + 2) or (n + 3) should be a multiple of 3.
n leaves a remainder of 0 or 1 when divided by 3.
n could be 1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18 ....
So, from among the first 99 natural numbers, N cannot take 2, 5, 8, 11, 14…….98.

There are 33 numbers in this list – we are effectively listing all numbers {3 × 0 + 2, 3 × 1 + 2, 3 × 3 + 2, ….3 × 32 + 2}.

So, N can take 99 – 33 = 66 values.

## Our Online Course, Now on Google Playstore!

### Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

### Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

## More questions from Number System

This idea is so good that it comes with an exclamation mark. N! holds marvels that you might not have noticed before. Enter here to see those.