Question
The product of two consecutive natural numbers is 650. The greater of the two numbers is:
The correct answer is
26
Consecutive Natural Numbers Product Problem
Let the two consecutive natural numbers be $n$ and $n+1$.
Algebraic Solution
The problem states that the product of these two numbers is 650.
We can write this as an equation:
$ n(n+1) = 650 $Expand the equation:
$ n^2 + n = 650 $Rearrange into a standard quadratic equation:
$ n^2 + n - 650 = 0 $We need to find two numbers that multiply to -650 and add to +1. We can estimate $\sqrt{650} \approx 25.5$. Let's test numbers around 25 and 26.
Trying $n=25$:
$ 25^2 + 25 - 650 = 625 + 25 - 650 = 650 - 650 = 0 $So, $n=25$ is the smaller natural number.
The two consecutive natural numbers are 25 and $25+1=26$.
The greater of the two numbers is $n+1$, which is 26.
Verification
Check the product:
$ 25 \times 26 = 650 $The product matches the condition given in the question.
Final Answer
The greater of the two consecutive natural numbers is 26.
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Important Questions from Number system (Railways)
- The product of two consecutive natural numbers is 380. The greater of the two numbers is:
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