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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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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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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

Source: GMAT Prep
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Source: — Data Sufficiency |

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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 Brent@GMATPrepNow » Sat Feb 12, 2022 6:30 am

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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) \(x < y < z\)

Answer: A

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.

Answer: A
Brent Hanneson - Creator of GMATPrepNow.com
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