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?

Answer 1

$a,b,c,d,e$ are consecutive even

integers

$\Rightarrow b=a+2;c=a+4;d=a+6$

& $e=a+8$

$v,w,x,y,z$ are consecutive

odd integers

$\Rightarrow w=v+2;x=v+u;y=v+6$

$z=v+8$

& $v=a+1$

$\Rightarrow (a+b+c+d+e)(v+w+x+y+z)IN$

$\Rightarrow (5a+20)(5v+20)=N$

$\Rightarrow (5a+20)(5a+25)=N$

$\Rightarrow 25(a+4)(a+5)=N$