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Grade 9Algebra

If the average of 20 different positive integers is 20, then the greatest possible number among these 20 numbers can be:
(a) 210
(b) 200
(c) 190
(d) 180

Profile image of Triangulum Entangulum
7 Years agoGrade 9
Answers icon

2 Answers

Profile image of Aditya Gupta
7 Years ago
obviously the first 19 numbers would have to be the least possible and different from each other in order for the 20th to be maximum.
so let 19 of the nos be 1, 2, 3, …., 19
let the max no be x.
now avg= sum/20= 20
or sum= 400
or x+(1+2+...+19)= 400
but 1+2+...+19= 19*20/2= 190
so x= 400 – 190
x= 210
kindly approve :)
Profile image of Arun
7 Years ago
Dear student
 
greatest number = 400 – ( 19 lowest terms ) = 400 – (1 + 2 + 3 + ….......+19)
 
 = 400 – 19*20/2 = 400 – 210 =190
 
Hope it helps
 
Regards
Arun

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