Given that x = y + z, where the three values are different positive in

Question

Given that x = y + z, where the three values are different positive integers, is x a prime number?

(1) y and z are odd.
(2) z = 3y

chetan2u · Answer

Given that x = y + z, where the three values are  different positive integers , is x a prime number?

(1) y and z are odd.
Since y and z are odd, their SUM, x, has to be od+odd or even..
Only even prime is 2, but x cannot be 2 as that would make both y and z as 1. but  z
eq{y} 
So x is NOT prime.

(2) z = 3y
so x=y+z=y+3y=4y..
As x is a multiple of 4, and its least value is 4*1 or 4, x is NOT prime

D

Kinshook · Answer

Given that x = y + z, where the three values are different positive integers, is x a prime number?

(1) y and z are odd.
Since y and z are odd; x = odd + odd = even = 2; Since 2 is the only even prime number
x = 1+ 1 = 2 is the only possibility but y & z are different positive integers; NOT POSSIBLE
x is NOT a prime number
SUFFICIENT

(2) z = 3y
x = y + 3y = 4y 
x is divisible by 2 and is NOT 2; x is NOT a prime number
SUFFICIENT

IMO D

Given that x = y + z, where the three values are different positive in

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