 It is currently 15 Jun 2019, 21:34 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

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. If x, y and z are different positive integers,  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: GRE Instructor Joined: 10 Apr 2015
Posts: 1958
Followers: 60

Kudos [?]: 1790  , given: 9

If x, y and z are different positive integers, [#permalink]
1
KUDOS
Expert's post 00:00

Question Stats: 66% (01:00) correct 33% (01:24) wrong based on 18 sessions
If x, y and z are different positive integers, and y is the greatest common divisor of x, y and z, which of the following MUST be true?

i) y < x
ii) the greatest common divisor of x and z is greater than y
iii) the greatest common divisor of x and y is y

A) ii only
B) i and ii only
C) i and iii only
D) ii and iii only
E) I, ii and iii
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com  Director  Joined: 07 Jan 2018
Posts: 644
Followers: 7

Kudos [?]: 601  , given: 88

Re: If x, y and z are different positive integers, [#permalink]
1
KUDOS
This is a must be true question hence the correct ans choice must be true at all times.

Let us pick three +ve numbers 3,6,12
Since y is the greatest common divisor it is safe to take 3 as y

This makes y=3< 6 or 12 hence whatever number is picked for x option i. is correct
If y = 3 x and y can interchangeably be 6 and 12 for which the HCF is 6 option ii. is also correct
Since Y is the least number in the three series and it divides both x and z; The HCF of y,z or y,x is always x option iii. is also correct

However,

Instead of taking three number set of a multiple of a number such as the one we have taken earlier which is a multiple of 3. If we take numbers such as 1,2,3
option ii. will not be correct.

Only i. and iii. are correct all the time
option C
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

GRE Instructor Joined: 10 Apr 2015
Posts: 1958
Followers: 60

Kudos [?]: 1790 , given: 9

Re: If x, y and z are different positive integers, [#permalink]
Expert's post
GreenlightTestPrep wrote:
If x, y and z are different positive integers, and y is the greatest common divisor of x, y and z, which of the following MUST be true?

i) y < x
ii) the greatest common divisor of x and z is greater than y
iii) the greatest common divisor of x and y is y

A) ii only
B) i and ii only
C) i and iii only
D) ii and iii only
E) I, ii and iii

Let's examine each statement separately...

i) y < x
If y is the greatest common divisor of x, y and z, we can also say that y is a divisor of x
IMPORTANT CONCEPT: The divisors of a number are always less than or equal to that number. For example, the divisors of 10 are {1, 2, 5, 10).
So, the divisors of x must be less than or equal to x
If y is a divisor of x, then y must be less than or equal to x
Since we're told that x, y and z are different positive integers, we can be certain that y is less than x
So, statement i is TRUE
Check the answer choices....ELIMINATE A and D

ii) the greatest common divisor of x and z is greater than y
Let's test some values of x, y and z that satisfy the given information ( x, y and z are different positive integers, and y is the greatest common divisor of x, y and z)
x = 4, y = 2 and z = 6. Notice that y (2) is the greatest common divisor of 4, 2 and 6
Here, the greatest common divisor of x (4) and z (6) is 2.
So, the greatest common divisor of x and z is NOT greater than y
So, statement ii is FALSE
Check the answer choices....ELIMINATE B and E

By the process of elimination (and without having to even look at statement iii), the correct answer must be C

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Re: If x, y and z are different positive integers,   [#permalink] 26 May 2018, 05:16
Display posts from previous: Sort by

If x, y and z are different positive integers,  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.