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29 May 2020, 10:11
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If x, y and z are positive integers such that \(x+y+z=7\), what is the greatest possible value of \(x+y^{z}\)?
(A) 28
(B) 35
(C) 42
(D) 49
(E) 56
(A) 28
(B) 35
(C) 42
(D) 49
(E) 56
29 May 2020, 12:59
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Ravixxx
Values satisfying x,y and z (positive integers) are
1,1,5
1,2,4
1,3,3
2,2,3
We get maximum value when x = 1, y=3 and z =3, i.e \(x+y^{z}\) = 28
Hence, OA is A
30 May 2020, 08:32
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Ravixxx
Exponents will always result bigger values. Each of x, y and z is at least 1. So we have 4 to distribute in two variables. The best case here is to make them equal.
3^3+1=27+1=28
If you go lower you get 2^4 or 4^2 both do not result in more than 27. Hence A.
