Question

X, Y and Z are three distinct natural numbers such that X < Y < Z. The only factors of the number (X + Y + Z) are (X – 7), (X – 6), (X + 9), (Y – 10), (Y – 5), (Y + 1), (Z – 12), (Z – 7) and (Z + 20). Which of the following statements is/are true?
I. X is a perfect square
II. Y is a prime number
III. Z is a perfect square​

Answer 1

Answer:

If x, y, and z are positive integers such that x < y < z, is x a factor of the odd integer z?

(1) x and y are prime numbers, whose sum is a factor of 57

(2) z is a factor of 57

57 has following factors 1,3, 19, 57

From (1) :

x+y =3 if x =1 then x is not prime

x+y =19 Therefore x=2, y=17

x+y =57 can't be expressed as sum of two prime numbers.

Step-by-step explanation: