Question

The set M consists of p consecutive integers with sum 2p. The set N consists of 2p consecutive integers with sum p. The difference between the largest elements of M and N is 9. Then p is

• A. 17
• B. 36
• C. 9
• D. 21

Answer 1

The correct option is D 21

Let the first term of series M and N be 'a' and 'b' respectively

For the series M we have, (a+1)+...+(a+p) = p(2a+p+1)/2 = 2p

For the series N we have (b+1)+...+(b+2p) = 2p(2b+2p+1)/2 = p

Also- b+p-a=9 or a-b-p=9

Solving we get, p = 21 or - 15 (not possible)

Hence choice (d) is right option.