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## If x, y, and z are positive integers such that x < y <

tagged by: M7MBA

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### Top Member

M7MBA Moderator
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#### If x, y, and z are positive integers such that x < y <

Sat Dec 02, 2017 5:14 am
If x, y, and z are positive integers such that x < y < z, is x a factor of the odd integer z?

(1) x and y are prime numbers, whose sum is a factor of 57

(2) z is a factor of 57

The OA is A.

I don't know how to solve this DS question. Experts, may you give me some help? Thanks.

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Mon Dec 04, 2017 12:02 pm
Hi M7MBA,

We're told that X, Y and Z are positive integers, X < Y < Z and that Z is an ODD. We're asked if X is a factor of Z. This is a YES/NO question and is based on a couple of Number Property rules.

1) X and Y are prime numbers and the sum is a factor of 57.

The factors of 57 are 1, 3, 19 and 57 (which are all odd numbers). Since X and Y are PRIMES - and Fact 1 tells us that the sum of those numbers must be an ODD - there must be one EVEN and one ODD number. This means that X MUST be 2 and Y MUST be an odd prime. Since Z is an ODD number, then X (which is EVEN) will NEVER be a factor of Z. Thus, the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

2) Z is a factor of 57

From Fact 1, we know that the factors of 57 are 1, 3, 19 and 57. Since the 3 variables are all positive integers, then Z must be 3, 9 or 57.
IF....
X=1, then the answer to the question is YES (regardless of the value of Z).
X=2, then the answer to the question is NO (regardless of the value of Z).
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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