The sum of 5 consecutive numbers is equal to 170. what is the product of largest and smallest numbers?

Let 5 consecutive even number be A = x, B = x+2, C = x+4, D = x + 6 and E = x + 8.

According to question
x + x +2 + x + 4 + x + 6 + x + 8 = 130
? 5x + 20 = 130
? x = 22
? A = 22, E = 22 + 8 = 30.
? Multiplication of A and E = 22 x 30
= 660

There can be infinite number of rational numbers between 1 and 1000.

Let be the ten's digit be x and unit's digit be y.
So the two digit number = 10x + y ( where x > y )
According to question
x + y = 14 ....(i)
x - y = 2 ....(ii)

Solving Eqs. (i) and (ii), we get
x = 8 and y = 6
? Required product = 8 x 6 = 48

5,15,25,35,40,50,55,65,75,85,95
So there are total 11 such type of numbers.

Let the two consecutive odd numbers be 2x+1 and 2x + 3 .
? Difference = ( 2x + 3 )² - ( 2x + 1 )²
= ( 2x + 3 + 2x + 1 )( 2x + 3 - 2x - 1 )
=( 4x + 4 ) x 2
= 8 (x + 1)
whis is exactly divisible by 8.

9856 x 156 + 9856 x 844 = 9856 x (156 + 844)
= 9856 x 1000
= 9856000

6674 x 625 = 6674 x (5)⁴
= 6674 x (10⁴/2⁴
= 66740000/16 = 4171250

Exp.= 9998 x 999
= 9998 x (1000-1)
= 9998 x 1000 - 9998 x 1
= 9998000 - 9998 = 9988002

Let, 8888 +7777 + 666 + x = 19000
Then, 17331 + x = 19000
? x = 19000 - 17331 = 1669