## If $$x, y,$$ and $$z$$ are three positive consecutive odd integers, what is the value of $$x + y + z?$$

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### If $$x, y,$$ and $$z$$ are three positive consecutive odd integers, what is the value of $$x + y + z?$$

by Gmat_mission » Fri Feb 11, 2022 8:31 am

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## Global Stats

If $$x, y,$$ and $$z$$ are three positive consecutive odd integers, what is the value of $$x + y + z?$$

(1) $$x, y,$$ and $$z$$ are prime numbers.
(2) $$x < y < z$$

Source: GMAT Prep

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### Re: If $$x, y,$$ and $$z$$ are three positive consecutive odd integers, what is the value of $$x + y + z?$$

by [email protected] » Sat Feb 12, 2022 6:30 am

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## Global Stats

Gmat_mission wrote:
Fri Feb 11, 2022 8:31 am
If $$x, y,$$ and $$z$$ are three positive consecutive odd integers, what is the value of $$x + y + z?$$

(1) $$x, y,$$ and $$z$$ are prime numbers.
(2) $$x < y < z$$

Source: GMAT Prep
Given: x, y, and z are three positive consecutive odd integers

Target question: What is the value of x + y + z ?

Statement 1: x, y, and z are prime numbers.
Useful property: Every third odd integer is divisible by 3.
For example: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,...

Since 3 is both prime and divisible by 3, we know that 3, 5 and 7 are the ONLY set of three consecutive odd integers that are all prime
So, the answer to the target question is x + y + z = 3 + 5 + 7 = 15
Statement 1 is SUFFICIENT

Statement 2: x < y < z
Statement 2 is clearly NOT SUFFICIENT, since x, y, and z can be ANY set of three consecutive odd integers.