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

Question

If x, y, and z are positive integers such that x < y < z, is x a factor of the even integer z?

(1) x and y are prime numbers whose sum is a factor of 57.
(2) y is not a factor of z

Harley1980 · Answer

1) 57 = (x+y)*c
57 has two factors 19 and 3 so x+y = 3 or 19
3 can be received by 1 + 2 but this is not primes so x + y = 19 
and x and y equal to 17 and 2
and as x < y we can infer that x = 2 and x is a factor of even integer z
Sufficient

2) y not factor of z 
Insufficient because we know nothing about x

Answer is A

GMATinsight · Answer

Given: z is an even Integer

Question: is x a factor of the even integer z?

Statement 1: x and y are prime numbers whose sum is a factor of 57.

Factors of 57 are {1, 3, 19, 57}

But x+y can't be 1 or 3 or 57 because x and y are prime and sum of two primes can't be 1 or 3 or 57

i.e. x+y = 19 i.e x = 2 and y = 17

i.e. x=2 will always be a factor of EVEN integer z

Hence,   SUFFICIENT

Statement 2: y is not a factor of z

It doesn't give us any information about x

Hence,   NOT SUFFICIENT

Answer: Option  A

EMPOWERgmatRichC · Answer

Hi All,

This DS question is built around a significant number of 'restrictions' - if you can recognize all of the restrictions, then there isn't much "math" to be done (although TESTing VALUES and knowing Number Properties would help)....

We're told that X, Y and Z are POSITIVE INTEGERS, that Z is EVEN and X < Y < Z. We're asked if X is a factor of Z. This is a YES/NO question.

Fact 1: X and Y are PRIME numbers whose sum is a factor of 57.

Let's break this down into pieces....
First, the factors of 57: 1, 3, 19 and 57

So X<Y and they are both PRIMES and the (X+Y) is limited to one of those four values.

At the minimum, X+Y would be 2+3 = 5, so the sum cannot be 1 or 3
Since 57 is an odd number, X and Y CANNOT BOTH be odd (since Odd+Odd = Even). So we're restricted to 1 even and 1 odd, which would make X = 2 (since that's the only even prime). If X = 2, then Y would = 55, but that's NOT possible since 55 is NOT prime. Thus 57 is also NOT a possible sum....

That just leaves 19....
X+Y = 19.....AND they're both primes AND X<Y....

The ONLY option is...
X = 2, Y = 17

Since we already know that Z is EVEN, X is ALWAYS a factor of Z and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

Fact 2: Y is not a factor of z

While it might be easy to 'dismiss' this Fact, since it tells us nothing about X, here's the proof about Fact 2....

IF....
X = 2, Y = 3, Z = 4
the answer to the question is YES.

IF....
X = 3, Y = 4, Z = 5
the answer to the question is NO.
Fact 2 is INSUFFICIENT

Final Answer:  A

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

bluesquare · Answer

Important: z is even integer.

1: The factors of 57 are: 1, 3, 19, 57; all odd. odd+odd = even; therefore, x and y must be 2 and 17. Sufficient, since y > x so y = 17, x = 2, and since z is an even integer, the answer is yes.
2: not sufficient.

The answer is A.

Vaibhav21 · Answer

ST(1) x and y are prime numbers whose sum is a factor of 57.
Factor of 57? 57=19x3 where 19 is a prime number. We cannot sum two primes to get 3 ;for 19 we have 17(prime) and 2(prime) ->17+2 = 19 perfect! also x < y < z,so 2<17<z and since z is even is x a factor of the even integer z.
Suff
(2) y is not a factor of z
Insuff

AnsweA

EMPOWERgmatRichC · Answer

Hi Ted21,

Your answer is correct, but you have to be careful about the thoroughness of your work. There are 4 factors of 57 (1, 3, 19 and 57) - not just 2. DS questions almost always test the thoroughness of your thinking (among other things), so you have to make sure that you've considered more than just the obvious possibilities.

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

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

If x = 2, then x is a factor of any even integer. Thus, this question can be rephrased “Is x = 2 or any other factor of z?”

(1) SUFFICIENT: We know that x and y are primes and that x < y. The factors of 57 are 1, 3, 19, and 57, all odd numbers. Thus x + y = odd, which eliminates the possibility that x and y are both odd, implying that x = 2 and y = an odd prime (i.e. 17).

If x = 2, then x must be a factor of the even integer z.

(2) INSUFFICIENT: If y is not a factor of z, then y ≠ 2. y cannot be 1 either, as x must be positive and x < y. Thus, y ≥ 3, but we still cannot determine the shared factors (if any) of x and z.

For example, it is possible that x = 2, y = 4, and z = 6. In this case, x is a factor of z, and the answer is Yes.

It is also possible that x = 3, y = 5, and z = 8. In this case, x is not a factor of z, and the answer is No.

The correct answer is A.

vishwaprakash · Answer

Given
X < Y < Z , x, Y, Z are positive integer

Statement 1 : 
x and y are prime numbers whose sum is a factor of 57.

57 can be broken into 19 * 3.
X and Y are prime numbers and X + y is factor of either 19 or 3.

X + Y cannot be factor of 3, since lowest prime is 2. If we consider X = 2, Y has to be equal to 1 and 1 is not prime.
Hence X + Y is factor of 19. Only combination which satisfies this condition is 2 and 17
Consider X = 2 and Y =17 since X <y

If X = 2 (Even) then it will be factor of any even integer. Z is even integer. Hence X is factor of Z,

Sufficient.

X is not factor of Z, Not sufficient to answer the question in stem.

Hence Option A

GMATBusters · Answer

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

Factors of 57 : 57, 19, 3, 1

If the sum of two prime numbers is odd, then exactly one of them is 2.

57: 2, 55 NOT possible
   19: 2, 17   possible 
3: 2, 1 NOT possible
1: NOT possible

Hence, x is 2. so it is a factor of even integer Z.

Suff

(2) y is not a factor of z

No further info about x. NOT suff

Answer A

If x, y, and z are positive integers such that x < y < z, is x a facto

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