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Which of the following statements is correct?

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Square of any number ending with 5 can be expressed as the sum of two consecutive positive integers.

Square of any number ending with 4 can be expressed as the sum of two consecutive positive integers.

If a number can be expressed as the sum of two consecutive odd numbers, then the number is a perfect square.

If a number can be expressed as the sum of two consecutive even numbers, then the number is a perfect square.

answer is B.

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Detailed Solution

The square of any odd number can be expressed as the sum of two consecutive positive integers. For example, 3² = 9 = 4 + 5, 5² = 25 = 12 +13

Thus, in particular, any number ending with 5 (which is an odd number) can be expressed as the sum of two consecutive positive numbers.

Thus, statement B is correct.

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