Deducing an incorrect statement when the mean and median are given

49 Views Asked by At

$~a,~b,~c,~d$ are positive integers such that $a~<~b~<~c~<~d$ If mean and median of $~a, ~b, ~c,~d$ are $35$ and $39$ respectively, then which one of the following statements cannot be true?

  • a = 21
  • a+c =71
  • a+c=60
  • d = 61

I after some attempts made it up to $b+c = 78$ and $a+d = 62$ but can't proceed further.

Moreover, please suggest a good title for this post.

1

There are 1 best solutions below

0
On

With great help of @John Omielan's and @Gabriel Romon's comment, here is what I figured out: Since $c < d \implies a+c < a+d$

and since $a+d = 62 \implies a+c<62 \implies a+c \neq 72$