NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 22:48 It is currently 25 Apr 2024, 22:48
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If x, y, and z are different positive integers, is x prime?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619064 [7]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
If x, y, and z are different positive integers, is x prime? [#permalink] New post   27 Jan 2015, 07:43
1
Kudos
5
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

70% (01:35) correct 30% (01:16) wrong based on 235 sessions
Hide Show timer Statistics
If x, y, and z are different positive integers, is x prime?

(1) xyz = 30
(2) z < x < y

Kudos for a correct solution.
ShowHide Answer
Official Answer
C
avatar
eddyki
Intern
Intern
Joined: 17 Dec 2013
Posts: 49
Own Kudos [?]: 38 [3]
Given Kudos: 35
GMAT Date: 01-08-2015
Send PM
GMAT ToolKit User
Re: If x, y, and z are different positive integers, is x prime? [#permalink] New post   27 Jan 2015, 08:52
2
Kudos
1
Bookmarks
Quote:
If x, y, and z are different positive integers, is x prime?

(1) xyz = 30
(2) z < x < y


y=/=x=/=z but all >0 and int.
(1) -> x could be 15 (z=1 and y=2) or 3 (z=5 and y=2) , its insuff.
(2) -> 100<200<300 (no prime) or 1<2<3 (prime!) -> insuff.

(1/2) -> we need 3 distinct factors of 30 -> 1/2/15 or 1/5/6 or 2/3/5 or 1/3/10 . every middle number is a prime, and since z is the smallest pos. int. and y the biggest pos. int., x is a prime number.

C
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11178
Own Kudos [?]: 31934 [1]
Given Kudos: 290
Send PM
Reviews Badge
If x, y, and z are different positive integers, is x prime? [#permalink] New post   27 Jan 2015, 09:07
1
Kudos
Expert Reply
ans C..
1) it tells us that x is a divisor of 30..... x,y,z can be 1,2,3,5,6,10,15
2) insufficient..tells us x is middle value
combined it tells us that x can be only 2,3,5 or 1,3,10, or 1,2,15 or 1,5,6 or .. so sufficient
User avatar
gmat6nplus1
Manager
Manager
Joined: 04 Oct 2013
Posts: 141
Own Kudos [?]: 584 [1]
Given Kudos: 29
Concentration: Finance, Leadership
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE:Project Management (Entertainment and Sports)
Send PM
Re: If x, y, and z are different positive integers, is x prime? [#permalink] New post   27 Jan 2015, 14:03
1
Kudos
Bunuel wrote:
If x, y, and z are different positive integers, is x prime?

(1) xyz = 30
(2) z < x < y

Kudos for a correct solution.


1) case_1 xyz=3*2*5 answer=yes; case_2 xyz=1*2*15 answer no.

Not sufficient

2) Not sufficient

1+2) x is every time going to be a prime number. Sufficient

Answer C.
avatar
DesiGmat
Manager
Manager
Joined: 27 Oct 2013
Posts: 176
Own Kudos [?]: 225 [1]
Given Kudos: 79
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Send PM
Re: If x, y, and z are different positive integers, is x prime? [#permalink] New post   28 Jan 2015, 01:33
1
Kudos
Here we go:

x, y, and z are different positive integers

St1: xyz = 30

30 = 2*3*5

x = 2, y = 3 and z = 5 (Is X prime? -> true)
x = 1, y = 6 and z = 5 (Is X prime? -> false)

Not sufficient

St2: z < x < y

Clearly not sufficient

Combining both

z = 2, x = 3, y = 5 (Is X prime? -> true)
z = 1, x = 2, y = 15 (Is X prime? -> true)
z = 1, x = 5, y = 6 (Is X prime? -> true)
z = 1, x = 3, y = 10 (Is X prime? -> true)

So C is the answer
User avatar
P
santorasantu
Senior Manager
Senior Manager
Joined: 27 Aug 2014
Posts: 253
Own Kudos [?]: 424 [1]
Given Kudos: 76
Location: Netherlands
Concentration: Finance, Strategy
Schools: ISB '21 LBS '22
GPA: 3.9
WE:Analyst (Energy and Utilities)
Send PM
Re: If x, y, and z are different positive integers, is x prime? [#permalink] New post   28 Jan 2015, 07:19
1
Kudos
Bunuel wrote:
If x, y, and z are different positive integers, is x prime?

(1) xyz = 30
(2) z < x < y

Kudos for a correct solution.


Answer c:

from stem: x,y and z are positive integers

from 1: xyz = 30, prime factors of 30 are 1,2,3 and 5
consider xyz = 2*3*5 = 30 => x is prime, consider xyz = 6*5*1 = 30, x is not prime, 2 answers NSF
from 2: z<x<y, considering only this statement, nohing is known, so NSF

1+2:
z<x<y, the possible multiples are (note that z, x and y are written accordingly below)
1*2*15 = 30
1*5*6 = 30
1*3*10 = 30
2*3*5 = 30
are the only possible solutions and for all the solutions x is prime, so sufficient.
C
avatar
Derkus
Intern
Intern
Joined: 18 Oct 2014
Posts: 7
Own Kudos [?]: 32 [2]
Given Kudos: 2
Schools: CBS '19 Anderson '19 Haas '19
GMAT 1: 750 Q48 V44
Send PM
Re: If x, y, and z are different positive integers, is x prime? [#permalink] New post   30 Jan 2015, 23:30
2
Kudos
Quote:
If x, y, and z are different positive integers, is x prime?

(1) xyz = 30
(2) z < x < y


1) X*Y*Z = 30 so X*Y*Z must be two factors of 30 * 1
X = 5, Y = 6, Z = 1: Yes X is prime
X = 6, Y = 5, Z = 1: No X is not prime

2) Z<X<Y
Z = 1 < X = 2 < Y = 3: Yes X is prime
Z = 5 < X = 6 < Y = 7: No X is not prime

1+2) All possible pairs of factors of 30 are: (1,30) (2,15) (3,10) (5,6) but you can eliminate (1,30) from our choices because all numbers must be different. Thus ordered triples are:
Z = 1 < X = 2 < Y = 15
Z = 1 < X = 3 < Y = 10
Z = 1 < X = 5 < Y = 6
Z = 2 < X = 3 < Y = 5

X = 2, 3, or 5, all of which are Prime. X is Prime, so C.

Final Answer: C
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619064 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: If x, y, and z are different positive integers, is x prime? [#permalink] New post   02 Feb 2015, 02:49
Expert Reply
Bunuel wrote:
If x, y, and z are different positive integers, is x prime?

(1) xyz = 30
(2) z < x < y

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

Solution: C

Let’s take statement (2) first: it gives us no values, so it’s INSUFFICIENT. Move on to statement (1). If three different positive integers have a product of 30, those integers must be one of the following sets:{ 1, 3, 10}; {2, 3, 5}; {1, 2, 15}; {1, 5, 6}. X could be prime or not prime; INSUFFICIENT. Combined, consider the four sets of possible integers. The median value is ALWAYS a prime number, so x must be prime. (C).
User avatar
pacifist85
Senior Manager
Senior Manager
Joined: 07 Apr 2014
Status:Math is psycho-logical
Posts: 340
Own Kudos [?]: 386 [0]
Given Kudos: 169
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
Re: If x, y, and z are different positive integers, is x prime? [#permalink] New post   07 Feb 2015, 05:20
[1] xyz = 30 | NS because:
2*3*5 = 30, x prime
2*1*15 = 30, x prime
15*1*2 = 30, x not prime

[2] z<x<y | NS because:
2<3<6, x prime
3<8<10, x not prime

[1] and [2], S because:
1<1<30, x prime
1<2<15, x prime
1<3<10, x prime
2<3<5, x prime

So, there is no way for x not to be a prime, since, no matter what, y must be the greatest value of the 3 values that multilied together yield 30. Similarly, trying any factor of 30 (it has 8 factors: 1,2,3,5,6,10,15,30) there is no way that the middle one (x) will not be a prime.
avatar
B
shmba
Intern
Intern
Joined: 16 Aug 2018
Posts: 24
Own Kudos [?]: 10 [0]
Given Kudos: 92
Concentration: General Management, Strategy
Schools: Guanghua"21 (A)
GMAT 1: 700 Q49 V36
Send PM
Re: If x, y, and z are different positive integers, is x prime? [#permalink] New post   22 Aug 2018, 20:53
chetan2u wrote:
ans C..
1) it tells us that x is a divisor of 30..... x,y,z can be 1,2,3,5,6,10,15
2) insufficient..tells us x is middle value
combined it tells us that x can be only 2,3,5.. so sufficient


1+2 combined: there should be 4 sets of combinations as stated in other posts. not just 2,3,5.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32680
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If x, y, and z are different positive integers, is x prime? [#permalink] New post   16 Jan 2024, 12:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If x, y, and z are different positive integers, is x prime? [#permalink]
16 Jan 2024, 12:43
Moderator:
Bunuel
Math Expert
92915 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions