Question : x, y, and z are distinct prime numbers where x < y < z. If x + y + z = 70, then what is the value of z?
Option 1: 29
Option 2: 43
Option 3: 31
Option 4: 37
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Correct Answer: 37
Solution : Given: x, y, and z are distinct prime numbers where x < y < z. x + y + z = 70 The sum indicates that at least one integer is even because odd + odd + odd = odd. There is just one even prime number that exists and that is 2. The smallest prime number is 2. This means x = 2. Option first: z = 29 ⇒ y = 68 – 29 = 39 (y is a non-prime number) Option second: z = 43 ⇒ y = 68 – 43 = 25 (y is a non-prime number) Option third: z = 31 ⇒ y = 68 – 31 = 37 (z < y) Option fourth: z = 37 ⇒ y = 68 – 37 = 31 (y < z. Also, it satisfies the conditions.) Hence, the correct answer is 37.
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