NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 07:31 It is currently 27 Apr 2024, 07:31
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 xy = z , where x ,y and z are positive integers and x and y are pri

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92952
Own Kudos [?]: 619391 [0]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
If xy = z , where x ,y and z are positive integers and x and y are pri [#permalink] New post   31 Jul 2019, 01:25
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

79% (01:03) correct 21% (00:58) wrong based on 66 sessions
Hide Show timer Statistics
If xy = z, where x, y and z are positive integers and x and y are prime numbers, what is the value of y?

(1) z is even
(2) x is odd
ShowHide Answer
Official Answer
C
User avatar
D
lacktutor
Director
Director
Joined: 25 Jul 2018
Posts: 668
Own Kudos [?]: 1119 [0]
Given Kudos: 69
Send PM
Re: If xy = z , where x ,y and z are positive integers and x and y are pri [#permalink] New post   31 Jul 2019, 02:58
x , y , and z — positive integers
x and y — prime numbers
xy=z
—> y=?

Statement1:
z is even
(Even=even*odd)
—> if z is even, one of the x and y should be 2.

But no info about whether y is 2
Insufficient

Statement2:
x is odd.
x could any odd prime numbers:3,5,7...
But no info about y.

Insufficient

Taken together 1 and 2,
y*ODD= EVEN
y should be EVEN—> only one even prime number satisfies the equation —2.
Sufficient

The answer choice is C

Posted from my mobile device
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8021
Own Kudos [?]: 4099 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
If xy = z , where x ,y and z are positive integers and x and y are pri [#permalink] New post   31 Jul 2019, 05:12
Bunuel wrote:
If xy = z, where x, y and z are positive integers and x and y are prime numbers, what is the value of y?

(1) z is even
(2) x is odd


given x&y are prime
#1
z is even so x or y has to be even insufficient
#2
x is odd so y has to be 2 or any other no
insufficient
from 1 &2
y = 2
IMO C
User avatar
L
CrackverbalGMAT
GMAT Club Legend
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4946
Own Kudos [?]: 7629 [0]
Given Kudos: 215
Location: India
Send PM
Re: If xy = z , where x ,y and z are positive integers and x and y are pri [#permalink] New post   31 Jul 2019, 09:37
The fundamentals of the multiplication of positive integers is the concept being tested in this question here.

Remember,
Odd * Odd = Odd

Odd * Even = Even

Even * Even = Even

The product of any two positive integers will be even, if at least one of them is even. On the other hand, the product of any two positive integers will be odd only when both of them are odd.

From the question statement, we know that all three of x, y and z are positive integers. We also know that x and y are prime numbers. A couple of points to be noted from this data:

    It is not given that x and y are distinct. So, we can take a case where x and y are same.
    2 is an even prime number, so x and y CAN be even.

With this, let us look at the statements now.

From statement I, we know that z is even. This means that at least one among x and y is an even prime number. But, this is not sufficient for us to find a unique value of y. Statement I alone is insufficient.

Answer options A and D can be eliminated. Possible answer options at this stage are B, C or E.

From statement II, we know that x is odd. There is no data whatsoever about either z or y to help us find out a unique value for y. Statement II is insufficient.
Answer option B can be ruled out.

Combining statements I and II, we know that z is even and x is odd. Since the product of x and y is yielding an even integer z, it follows that y HAS to be an even integer. But, y is also a prime number.
Therefore, the value of y HAS to be 2. The combination of statements is sufficient to find a unique value of y.

The correct answer option is C.

Hope this helps!
User avatar
L
freedom128
Director
Director
Joined: 30 Sep 2017
Posts: 956
Own Kudos [?]: 1256 [1]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Send PM
Reviews Badge
Re: If xy = z , where x ,y and z are positive integers and x and y are pri [#permalink] New post   31 Jul 2019, 09:43
1
Bookmarks
x and y are prime positive integers. z is positive integer.

xy=z

#1
z is even, then either x or y can be even. y can be odd or even, depending on x.
NOT SUFFICIENT

#2
No information about x and z
NOT SUFFICIENT

Combining #1 and #2
If z is even and x is odd, then y must be even. Y is given to be a prime positive integer , then y=2.

Answer is C

Posted from my mobile device
GMAT Club Bot
gmatclubot
Re: If xy = z , where x ,y and z are positive integers and x and y are pri [#permalink]
31 Jul 2019, 09:43
Moderator:
Bunuel
Math Expert
92952 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