if (X+17)>(y-19),then which among the following is true?
Answers
If x, y, and z are positive integers such that x < y < z is x a factor : Data Sufficiency (DS)
TAGS
mm007
Dec 20, 2006
00:00 ABCDE
DIFFICULTY: 95% (hard) QUESTION STATS: based on 999 sessions
35% (02:34) correct
65% (02:38) wrong
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
Spoiler: OA
Kudos
8 kudos, 67 bookmarks
Most Helpful Expert Reply
Bunuel
EXPERT'S
POST
May 27, 2012
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.
Answer: A.
Kudos
22 kudos, 12 bookmarks
Most Helpful Community Reply
kunalbh19
May 27, 2012
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.