If x, y, and z are three odd integers such that x

Question

If x, y, and z are three odd integers such that x < y < z and x + y + z = 45, what is the value of z?

(1) z - x = 4
(2) x, y, and z are consecutive odd integers

DavidTutorexamPAL · Answer

Since all we're given is equations, we'll work with them.
This is a Precise approach.

(1) Since x < y < z then z - x = 4 means that z - 4 < y < z. But since all 3 are odd numbers then this means that y must equal z - 2. So, x = z - 4 and y = z - 2 and we can write 45 = x + y + z = z - 4 + z - 2 + z which is an equation with one variable and has one solution.
Sufficient.

(2) This directly gives us the same as (1).
Sufficient.

(D) is our answer.

cardiMoni · Answer

DavidTutorexamPAL

But since all 3 are odd numbers then this means that y must equal z - 2.

Can you please explain this? I am not sure if I understand why this means y must equal z-2

DavidTutorexamPAL · Answer

Hi, sure!

Let's look at an example:
Say x = 1. Since z = x+4 then z = 5.
The only odd number between 1 and 5 is 3, meaning that y = z - 2.

A more general approach is to say that every 2nd number is odd. That is, if x is odd then so is x+2, x+4, x+6 and so on. So if you pick any two odd numbers that are at a distance of 4 from each other, you will find exactly one odd number in between them. That is why y can have only one possible value: z - 2.

Hope that helps

cardiMoni · Answer

DavidTutorexamPAL

thank you! It is actually so easy!

DavidTutorexamPAL · Answer

Happy to help

bumpbot · Answer

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If x, y, and z are three odd integers such that x < y < z and x + y +

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