Question

If 1² + 2² + 3² + ….. + 2003² = (2003) (4007) (334) and (1) (2003) + (2) (2002) + (3) (2001) + …+ (2003) (1) = (2003) (334) (x) then x equals –

• A. 2005
• B. 2004
• C. 2003
• D. 2001

Answer 1

Answer: (A)

2005

Answer 2

Let

S = (1) (2003) + (2) (2002) + (3) (2001) + …. + (2003) (1)

and

K = 1² + 2² + 3² + …. + 2003²

Adding, we get

S + K = (2004) [1 + 2 + 3 +…. + 2003]

̃ (2003) (334) (x) + (2003) (4007) (334)

= (2004) (1002) (2003)

̃ x = 2005.