Out of six consecutive natural numbers if the sum of first three is $27$, what is the sum of the other three?

### Concept & Strategy For consecutive natural numbers, every number in the sequence increases by exactly $1$. This predictable difference allows us to compare two subsets of a sequence mathematically without necessarily finding the individual numbers. ### Step-by-Step Solution * **Given:** We have six consecutive natural numbers. Let's call them $x$, $x+1$, $x+2$, $x+3$, $x+4$, $x+5$. * **Given:** The sum of the first three is $27$. * Formulate the equation for the first three: $$x + (x+1) + (x+2) = 27$$ $$3x + 3 = 27$$ * Solve for $x$: $$3x = 24$$ $$x = 8$$ * The first three numbers are $8, 9, 10$. * The next three numbers are $11, 12, 13$. * Calculate the sum of the other three: $$11 + 12 + 13 = 36$$ ### Exam Strategy & Shortcut Use relational mapping for an instant answer. Compare the first three terms with the next three terms: Term 1 vs Term 4: Difference is $+3$ Term 2 vs Term 5: Difference is $+3$ Term 3 vs Term 6: Difference is $+3$ Since there are $3$ terms, the second set is exactly $3 \times 3 = 9$ greater than the first set. New Sum = Old Sum $+ 9$ New Sum = $27 + 9 = 36$. This solves the problem mentally in $3$ seconds. ### Common Pitfall Students often spend unnecessary time writing out the full algebraic equation ($3x + 3 = 27$) and solving for the exact terms, which eats up the clock. Always look for relative differences between groups when dealing with consecutive series. ### Final Answer **Therefore, the correct answer is 36.**