Given that $1 + 2 + 3 + 4 + .... + 10 = 55$, then the sum $6 + 12 + 18 + 24 + .... + 60$ is equal to

### Concept & Logic When evaluating an arithmetic progression, check if the series is simply a scalar multiple of a simpler, known series. Factoring out the greatest common divisor simplifies the calculation entirely. ### Step-by-Step Solution * **Given:** $1 + 2 + 3 + 4 + .... + 10 = 55$ Target Series: $6 + 12 + 18 + 24 + .... + 60$ * **Calculation / Deduction:** Observe the terms in the target series. Each term is an exact multiple of $6$. Factor out the constant multiplier ($6$) from the entire series: $$ 6 \times (1) + 6 \times (2) + 6 \times (3) + .... + 6 \times (10) $$ $$ = 6 \times (1 + 2 + 3 + 4 + .... + 10) $$ The bracketed expression is exactly the series provided in the given statement. Substitute the known value ($55$) into the equation: $$ = 6 \times 55 $$ Calculate the final product: $$ 6 \times 50 = 300 $$ $$ 6 \times 5 = 30 $$ $$ 300 + 30 = 330 $$ ### Exam Strategy & Shortcut **Direct Multiplication:** The core of aptitude tests is pattern recognition. Immediately notice that $6 = 1 \times 6$, and $60 = 10 \times 6$. The whole series is scaled by $6$. You just need to multiply the given total sum by the scalar: $55 \times 6 = 330$. ### Common Pitfall A common time-wasting pitfall is ignoring the given hint ($1$ to $10 = 55$) and manually applying the arithmetic progression sum formula $S = \frac{n}{2}(a + l)$ to the target series. While it yields the right answer, it eats up valuable seconds in an exam environment. ### Final Answer **Therefore, the correct answer is 330.**