If X is the sum of the integers from 21 to 70 and Y is the sum from 121 to 170, what is Y -X ?

Question

 I cant solve this question...

Answer 1

X=21+22+23+24+...+69+70  (there are 50 numbers)

Y=121+122+123+...+168+169+170  (there are also 50 numbers)

notice that each number from 121 to 170 are all of the numbers from 21 to 70 with 100 added to each one

Y-X=121-21+122-22+123-23+...+168-68+169-69+170-70

Y-X=100+100+100+...+100+100

there are 50 numbers in each of X and Y, so there are 50 100's

50*100=5000

Y-X=5000