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If x, y, and z are positive integers such that x < y < z [#permalink]
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20 Dec 2006, 16:05
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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
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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?



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My answer is C
Here is the reason:
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 ?



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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.
amit.



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dr shpak  it doesn't say they are consecutive numbers.
My initial reaction to this was E and I agree with Hobbit.



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Joined: 15 Jan 2007
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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.
so E.



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Re: DS_If x, y, and z are positive integers... [#permalink]
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17 Jan 2007, 00:03
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.
Nothing about z ............ INSUFF
From (2) :
z can be 3,19 or 57 ...... INSUFF
Combining (1) and (2), we get :
when x=2, y=17 and z=19 or 57, x is not a factor of z
(C) is my answer. Please correct me if I'm wrong.
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Re: DS_If x, y, and z are positive integers... [#permalink]
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27 May 2012, 01:55
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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. Thus, correct answer is A.



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Re: If x, y, and z are positive integers such that x < y < z [#permalink]
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27 May 2012, 04:57
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Re: If x, y, and z are positive integers such that x < y < z [#permalink]
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09 Feb 2014, 05:53
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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.
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Re: If x, y, and z are positive integers such that x < y < z, is x a facto [#permalink]
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12 Nov 2014, 00:55
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
Answer is E
Where am I going wrong here? How is the answer A?



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Re: If x, y, and z are positive integers such that x < y < z, is x a facto [#permalink]
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12 Nov 2014, 01:05
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!



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Re: If x, y, and z are positive integers such that x < y < z [#permalink]
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12 Nov 2014, 04:18
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
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Re: If x, y, and z are positive integers such that x < y < z [#permalink]
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23 May 2015, 00:29
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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!



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Re: If x, y, and z are positive integers such that x < y < z [#permalink]
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01 Jan 2018, 21:55
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




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