Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 18 Jul 2019, 02:03

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.

Close

Request Expert Reply

Confirm Cancel

Is the positive integer x prime?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56261
Is the positive integer x prime?  [#permalink]

Show Tags

New post 31 Jul 2018, 22:03
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:16) correct 38% (00:54) wrong based on 98 sessions

HideShow timer Statistics


Senior Manager
Senior Manager
User avatar
G
Joined: 17 Jan 2017
Posts: 300
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Premium Member
Re: Is the positive integer x prime?  [#permalink]

Show Tags

New post 31 Jul 2018, 22:11
1
Bunuel wrote:
Is the positive integer x prime?

(1) The Greatest Common Factor of x and y is 1.

(2) The Least Common Multiple of x and y is xy.


Statement 1:
Suppose x=9 ,y=2 GCF = 1 . X is not prime
If x=2, y=9 GCF = 1 . X is prime
Insufficient

Statement2:
Suppose x=9 ,y=2 LCM = xy = 18 . X is not prime
If x=2, y=9 LCM = xy = 18 . X is prime
Insufficient

1&2: Give same data

Hence E
_________________
Only those who risk going too far, can possibly find out how far one can go
Director
Director
User avatar
S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 541
Location: India
Re: Is the positive integer x prime?  [#permalink]

Show Tags

New post 01 Aug 2018, 00:41
Hi,

Again this question, if we know the below simple properties then it’s just a 20-sec problem.

Product of two numbers = Products of their HCF and LCM

• If two numbers are m and n, then HCF of m and n cannot be larger than the difference between m and n

• Two consecutive numbers (x and x+1) can share no factors other than 1, HCF will be 1 and LCM will be x(x + 1).

Two numbers are called co-prime(relatively prime) if HCF of two numbers is 1 and LCM is product of two numbers.

For two numbers to be co-prime not necessary that numbers has to be prime.

If you don’t know the below above rule, then don’t hesitate plug in numbers.

Question is “x” prime ?

That’s is, whether x = 2,3,5,7,11, ….

Statement I is insufficient:

The Greatest Common Factor of x and y is 1.

If x = 2 and y =3 , then G.C.F is 1 and answer to the question is YES(x is prime).

But if x = 4 and y = 3, then G.C.F is 1 and answer to the question is NO(x is not prime).

Statement II is insufficient:

The Least Common Multiple of x and y is xy.

We can take the same examples,

If x = 2 and y =3 , then L.C.M is 6 and answer to the question is YES(x is prime).

But if x = 4 and y = 3, then L.C.M is 12 and answer to the question is NO(x is not prime).

Together also we can use the same numbers,

So not sufficient.

Answer is E.
_________________
GMAT Mentors
Image
Director
Director
User avatar
P
Joined: 20 Sep 2016
Posts: 636
Location: India
Concentration: Strategy, Operations
GPA: 3.95
WE: Operations (Real Estate)
GMAT ToolKit User
Re: Is the positive integer x prime?  [#permalink]

Show Tags

New post 18 Aug 2018, 21:30
E

We can use the property of Co-primes .
Q: is X prime?
Does X have only 2 factors Viz 1 and itself?
Does X^2 have only 3 factors?

St1. NOT SUFFICIENT
X and Y are consecutive integers-
Property- Consecutive integers have only 1 as a common factor. Hence a pair of consecutive integers is co-prime.
X=2 Y=3 >> X is prime
x=4 y=5 >> X is not a prime

st.2 - NOT SUFFICIENT
LCM OF X anf y =xy

Same property of co primes- use x any y as consecutive integers. You'll get 2 cases. So insufficient

Posted from my mobile device
GMAT Club Bot
Re: Is the positive integer x prime?   [#permalink] 18 Aug 2018, 21:30
Display posts from previous: Sort by

Is the positive integer x prime?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne