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
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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