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Question
How many numbers from 1 to 500 can be expressed as a difference of squares in atleast one way?
How many numbers from 1 to 500 can be expressed as a difference of squares in atleast one way?
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Solution
The correct option is C 375
Numbers which cannot be expressed as a 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 numbers cannot be expressed, hence 375 numbers can be expressed. Thus, option (c) is the correct answer.
Numbers which cannot be expressed as a 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 numbers cannot be expressed, hence 375 numbers can be expressed. Thus, option (c) is the correct answer.
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