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Denote the 4 numbers with a, b, c, d, a<b<c<d.

we know d=a+42.
The mean is [a+b+c+(a+42)]/4.

The question is: Is mean – a =const. ?

<=> -a + [a+b+c+(a+42)]/4 = const?

<=> 10,5 – a/2 + b/4 + c/4 = const?

It is pretty intuitive that since this term depends on the choice of a, b and c, it is not const [and there are infinity many a | a/3 is an int.].

Hence: (E)
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E.

Let the numbers be S M1 M2 and L
L-S = 42
So Av = (S+M1+M2+L)/4

4A -(L+S) = M1 + M2

From 1)

Median = (M1+M2)/2
(M1+M2)/2 - A > 5

[4A-(L+S)]/2 - A >5
2A -(L+S)/2 -A >5
A - (42+2S)/2 > 5
A - 21 -S > 5
A-S > 26 Not Suff


From 2)
Then numbers are multiple of 3. Not suff many possibilities.

E



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