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) \(x < y < z\)
Answer: A
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If \(x, y,\) and \(z\) are three positive consecutive odd integers, what is the value of \(x + y + z?\)
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Given: x, y, and z are three positive consecutive odd integersGmat_mission wrote: ↑Fri Feb 11, 2022 8:31 amIf \(x, y,\) 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) \(x < y < z\)
Answer: A
Source: GMAT Prep
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.
Answer: A