How many numbers between 1 and 500 can be expressed as a difference of squares in atleast one way?

125

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250

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375

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none of these

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Solution

The correct option is C 375
option (c)

Numbers which cannot be expressed as difference of squares are all even non-multiples of 4. There are 250 even non-multiples of 4 from 1 to 1000 and 125 such numbers between 1 and 500 (2,6,10......). 125 cannot be expressed hence 375 can be expressed. Hence option c

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