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The sum of the squares of two consecutive odd natural numbers is 202. The sum of these two numbers is:
20
24
28
18
20
Let the two consecutive odd natural numbers be x and x+2. The equation x squared + (x+2) squared = 202 simplifies to 2x squared + 4x + 4 = 202, which further reduces to x squared + 2x - 99 = 0. Factoring gives (x+11)(x-9) = 0, meaning the numbers are 9 and 11, and their sum is 20.
Let the two consecutive odd natural numbers be x and x+2. The equation x squared + (x+2) squared = 202 simplifies to 2x squared + 4x + 4 = 202, which further reduces to x squared + 2x - 99 = 0. Factoring gives (x+11)(x-9) = 0, meaning the numbers are 9 and 11, and their sum is 20.
In the context of the Indian Constitution, the number 20 is significant as it relates to the number of members in the Estimates Committee of the Parliament, which was increased from 25 to 30 in 1956, though it originally had 25 members in 1950.
Consecutive odd numbers always maintain a difference of 2.
The square of any odd number always results in an odd value.
Sum of two odd numbers is always an even number.
The numbers satisfying the condition are 9 and 11: 81 + 121 = 202.
Option B (24) is incorrect as the roots for 24 would be 11 and 13, whose squares sum to 290.
Option C (28) is incorrect as the roots for 28 would be 13 and 15, whose squares sum to 394.
Option D (18) is incorrect as the roots for 18 would be 8 and 10, but these are even numbers, not odd.
A is correct — The two consecutive odd natural numbers are 9 and 11, which sum to 20.
In competitive exams like RRB JE, always check for the parity of numbers in the options; since the sum of squares is even and the numbers are odd, the final sum must be an even number, which eliminates odd-numbered distractors.
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