NIMCET 2009 — Reasoning PYQ

To find the sum of numbers from 1 to 100 that are not divisible by 3 and 5, we use the principle of inclusion-exclusion.

Step 1: Calculate the sum of all numbers from 1 to 100.

The sum of the first $n$ natural numbers is given by $S=\frac{n(n+1)}{2}$.

Step 2: Find the sum of numbers divisible by 3.

The numbers are $3,6,9,\dots ,99$. This is an A.P. where $a=3,l=99,n=33$.

Step 3: Find the sum of numbers divisible by 5.

The numbers are $5,10,15,\dots ,100$. This is an A.P. where $a=5,l=100,n=20$.

Step 4: Find the sum of numbers divisible by both 3 and 5 (i.e., divisible by 15).

The numbers are $15,30,45,60,75,90$. Here $a=15,l=90,n=6$.

Step 5: Calculate the sum of numbers divisible by 3 or 5.

Using the formula $S(3\cup 5)=S_3+S_5-S_{15}$:

Step 6: Final Calculation.

The sum of numbers not divisible by 3 and 5 is:

Correct Option:

(c) 2632