Question

$(a+b+c+d+e)(v+w+x+y+z)=N,$ where a, b, c, d, e are five consecutive even integers and v, w, x, y, z are five consecutive odd integers. If $v=a+1$ and n represents natural numbers, then which of the following is the most suitable value of N?

• A. $(n+4)(n+5)$
• B. $(n+3)(n+4)$
• C. $(n+2)/(n+3)$
• D. $100(n+2)(n+2.5)$

Answer 1

The correct option is D $100(n+2)(n+2.5)$

$Giventhatv=a+1\because visodd\Rightarrow aiseven.Sowecanreplaceaby2nwhennisnaturalnumber.\therefore v=2n+1.\therefore Thegivenproductis(a+b+c+d+e)(v+w+x+y+z)=NAsperthegivenconditionwecanwriteN=(a+a+2+a+4+a+6+a+8)\times (a+1+a+3+a+5+a+7+a+9)=(5a+20)(5a+25)Replacingaby2nN=(5\times 2n+20)(5\times 2n+25)=100(n+2)(n+2.5)\therefore AnswerDiscorrect.$