Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

From stmt 1:
factors of 57 are 1,3,19,57
For x and y to be prome numbers and their sum to be any of these
x has to be 2 and y has to 17.
We don't know anything about z.
INSUFF

From stmt 2:
Z is 1 or 3 or 19 or 57.
INSUFF

Combining:
Z can not be 1 or 3.(x and y are prime and they are less than z)
2 is not a factor of 19 or 57.

So C.

One question though,
It is time consuming to find whether 57 is the sum of any prime numbers.
I had to pick the primes below 57 and find out whether 2 primes can sum up to 57.
Is there any easy way?

Question gives: x < y < z, each is +int
z is odd +int

Question asks: is X factor of Z ? [ does X*K = Z, K:+int ]

Statement 1: X & Y are prime and X+Y factor of 57
-----------------------------------------------------------
57 is a prime number --> x+y =1 or 57
since x and y are each +tive int., then neither x nor y can be zero
Therefore, x+y = 57

this leads us to nothing as I know nothing about z
Note: you don't really need to find what X and Y are

Statement 2: Z is a factor of 57
--------------------------------------
57 is prime, Z can not be 1 because z>y>z and non of x and y can be zero or negative
So Z = 57
Yet, this tells us nothing about x and y

Statements 1 and 2
-----------------------
from 2, z = 57 and the only factors of 57 are 1 and 57
from question, neither x nor y can be zero or 1
from statement 1, neither x nor y can be 57
So, X is NOT a factor of Z

Thus, the answer is C

Is it helpful, the way I expain ? or is too much details and too confusing ?

there is an easy way to verify that 57 is not the sum of primes...
for a sum of two numbers to be odd - one must be even and one odd. if these are primes then the even number must be 2 and the odd must be 55 which is not a prime ... hence no solution to that. no need to pick numbers.

exactly , no way sum of two primes can equate 57. if x + y = 57, then one of them has to be even, and the only even prime is 2.
==> y has to be 55 which is not prime.

Re: DS_If x, y, and z are positive integers... [#permalink]

Show Tags

27 May 2012, 00:55

6

This post received KUDOS

Swagatalakshmi wrote:

mm007 wrote:

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

57 has following factors 1,3, 19, 57

From (1) :

x+y =3 if x =1 then x is not prime x+y =19 Therefore x=2, y=17 x+y =57 can't be expressed as sum of two prime numbers.

Answer is A. Since x has to be 2, and it is given in the question that z is an odd integer. Thus we know that 2 cannot be the factor of an odd integer.

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

Notice that we are told that z is an odd number.

(1) x and y are prime numbers, whose sum is a factor of 57 --> factors of 57 are 1, 3, 19 and 57. Since we are told that x and y are prime numbers then x can only be 2 and y can only be 17 (x+y=19). x=2=even cannot be a factor of the odd integer z. Sufficient.

(2) z is a factor of 57. Clearly insufficient as we have no info about x.

Re: If x, y, and z are positive integers such that x < y < z [#permalink]

Show Tags

09 Feb 2014, 04:53

2

This post received KUDOS

1

This post was BOOKMARKED

A is the answer.

Z is odd from question stem.

statement 1 says x & y are primes whose sum is a factor of 57. First lets deduce factors of 57.

57 = 1 * 57 = 3 * 19

so x+y must be equal to one of these factors. x+y cannot be equal to 1 or 3 since x & y are positive prime integers.

we have x+y=57 or x+y = 19. Lets take x+y=57 for this to happen one of the x & y must be even and remember both must be prime so only even prime is 2. if x=2 then y will be 55 and not prime so x+y = 57 is ruled out.

taking what is left. x+y=19 and using same logic as above x has to be 2. and y=17 hence both are prime and sum is factor of 57. Going back to the question, is x a factor of odd integer z? NO x=2 it cannot be. Sufficient!

Statement 2 is clearly insufficient. no information about x.
_________________

Re: If x, y, and z are positive integers such that x < y < z, is x a facto [#permalink]

Show Tags

11 Nov 2014, 23:55

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

Statement 1: Factors of 57 = 3 * 19 Therefore X, Y, Z could be: 1, 2, 3 >> Yes 2, 17, 19 >> No INSUFFICIENT

Statement 2: z is a factor of 57, meaning z is either 3 or 19 However, we don't know anything about x INSUFFICIENT

Statements 1+2: If x+y is 3 or 19 and z is 3 or 19 The numbers could be: 1, 18, 19 >> Yes (because 1 is a factor of 19) 1, 2, 3 >> Yes (because 1 is a factor of 3) 8, 11, 19 >> No INSUFFICIENT

Re: If x, y, and z are positive integers such that x < y < z, is x a facto [#permalink]

Show Tags

12 Nov 2014, 00:05

kthxbye wrote:

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

Statement 1: Factors of 57 = 3 * 19 Therefore X, Y, Z could be: 1, 2, 3 >> Yes 2, 17, 19 >> No INSUFFICIENT

Statement 1 also says that x and y are prime numbers. 1 is not a prime. It's always a No with statement 1 and hence is sufficient. Will post detailed solution tonight.

Please press Kudos if you find the question helpful!

Re: If x, y, and z are positive integers such that x < y < z [#permalink]

Show Tags

12 Nov 2014, 03:18

Hi,

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

57= 1 x 57 & 57= 3 x 19 Factors are 1, 3, 19, 57 1, 3 and 57 cannot be the sum!! ( 3 = 2+1 but 1 is not a prime number; try any combination for 57, it will always be the sum of an even integer and odd integer and 2 is the only even prime number. So you cannot have 57 as the sum of two prime numbers!!!)

So the sum should be 19 and 19 = 2 + 17 is the only way you can write it as a sum of two prime numbers.

So the numbers are x,y, z which is 2,17, an odd integer!! Now ask the question : Is x a factor of odd integer z? The answer is No for sure. Hence Statement 1 alone is sufficient!!

Statement 2 alone doesn't tell you anything about x, so you cannot say that x is a factor of 57!!

Correct answer would be A
_________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Kindly press Kudos if the explanation is clear. Thank you Ambarish

Re: If x, y, and z are positive integers such that x < y < z [#permalink]

Show Tags

22 May 2015, 23:29

1

This post was BOOKMARKED

Nayan wrote:

One question though, It is time consuming to find whether 57 is the sum of any prime numbers. I had to pick the primes below 57 and find out whether 2 primes can sum up to 57. Is there any easy way?

57 is an odd number.. All prime numbers are odd except 2 ..therefore ODD+ODD=ODD is not possible only possibility to check is 57=2+prime numb (which in this case is not possible)

This is the fastest way to do it.. Hope this Helps!

Re: If x, y, and z are positive integers such that x < y < z [#permalink]

Show Tags

01 Jan 2018, 20:55

x,y,z are +ve integers.. need to find whether x is a factor of z (an odd integer)

stmt1: x,y => prime nos. whos sum is a factor of 57 (3 x 19) . Sum(x,y) cannot be 3 as it would mean one of x or y needs to be 1 (not prime) Sum =19 & since x<y , the only possible pair of (x,y) = (2,17)

And since z is an odd integer x cannot divide z => Stmt 1 sufficient

Stmt2 : z is a factor of 57, but gives no information on x, y => not sufficient