Question Bank • QB_GA_ADV_102 NAT • 1 Mark

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

Calculate the sum of all natural numbers between $100$ and $300$ (exclusive) that are exactly divisible by $7$. ________ (answer in integer).

Answer Key:

5586

Step-by-Step Solution & Explanation

**Method 1: Arithmetic Progression Formula** - First term
gt; 100$ divisible by 7: $7 \times 15 = 105$. - Last term
lt; 300$ divisible by 7: $7 \times 42 = 294$. - Number of terms $n = 42 - 15 + 1 = 28$. $\text{Sum } S = \frac{n}{2}(a + l) = \frac{28}{2}(105 + 294) = 14 \times 399 = 5,586$ **Method 2: Multiples Summation** $S = 7 \sum_{k=15}^{42} k = 7 \left[ \frac{42 \times 43}{2} - \frac{14 \times 15}{2} \right] = 7 [903 - 105] = 7 \times 798 = 5,586$
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