QB_PH_GA_019: Quantitative Aptitude

Find the sum of all two-digit natural numbers that are exactly divisible by 7.

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Identify the Terms in the Range [10, 99]**: - Smallest two-digit multiple of 7: $a = 14$ - Largest two-digit multiple of 7: $l = 98$ - Common difference: $d = 7$ 2. **Number of Terms ($n$)**: $l = a + (n - 1)d \implies 98 = 14 + (n - 1)7$ $84 = (n - 1)7 \implies n - 1 = 12 \implies n = 13$ 3. **Sum of Arithmetic Progression**: $S_n = \frac{n}{2}(a + l) = \frac{13}{2}(14 + 98) = \frac{13}{2}(112) = 13 \times 56 = 728$ 4. **Official Integer Answer**: 728.