2iim cat question from number system.

1. Number Theory

2. Number Theory
n2 + 5n + 6 is a multiple of 6. n is natural number less than 100. How
many values can n take?
(a) 33 (b) 65
(c) 66 (d) 67

3. Number Theory
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 ....
n2 + 5n + 6 is a multiple of 6. n is natural number less than 100. How
many values can n take?

4. Number Theory
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.
Answer choice (c)
n2 + 5n + 6 is a multiple of 6. n is natural number less than 100. How
many values can n take?

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