NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 09:19 It is currently 25 Apr 2024, 09:19
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 and y are positive integers such that x < y and z=x/y, which of

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618961 [3]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
If x and y are positive integers such that x < y and z=x/y, which of [#permalink] New post   05 Apr 2016, 07:46
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

68% (01:58) correct 32% (01:58) wrong based on 195 sessions
Hide Show timer Statistics
If x and y are positive integers such that x < y and z=x/y, which of the following must be true?

I. z>(x − 1)/(y − 1)
II. z<(x − 1)/(y − 1)
III. z>(x + 1)/(y + 1)

A. I only
B. I and II
C. II and III
D. II only
E. I and III
ShowHide Answer
Official Answer
A
User avatar
D
Kurtosis
Current Student
Joined: 13 Apr 2015
Posts: 1436
Own Kudos [?]: 4548 [1]
Given Kudos: 1228
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Re: If x and y are positive integers such that x < y and z=x/y, which of [#permalink] New post   06 Apr 2016, 01:38
1
Kudos
x < y --> Let x = 2 and y = 3 --> z = 2/3

I. z>(x − 1)/(y − 1) --> 2/3 > 1/2 --> True

II. z<(x − 1)/(y − 1) --> 2/3 < 1/2 --> False

III. z>(x + 1)/(y + 1) --> 2/3 > 3/4 --> False

Answer: A
avatar
B
toby001
Intern
Intern
Joined: 19 May 2016
Posts: 17
Own Kudos [?]: 7 [0]
Given Kudos: 86
Location: United States
Concentration: Strategy, Human Resources
Schools: Cnsrtm-Tuck '20 (D) Cnsrtm-Goizueta '20 (A) Cnsrtm-Darden '20 (A$) Cnsrtm-Ross '20 (A$) Kellogg '20 (A$) Duke '20 (A$) Cnsrtm-McCombs '20 (I)
GMAT 1: 680 Q46 V37
GMAT 2: 710 Q46 V41
GMAT 3: 730 Q49 V41
WE:Operations (Manufacturing)
Send PM
Reviews Badge
If x and y are positive integers such that x < y and z=x/y, which of [#permalink] New post   Updated on: 26 Sep 2016, 07:26
Bunuel wrote:
If x and y are positive integers such that x < y and z=x/y, which of the following must be true?

I. z>(x − 1)/(y − 1)
II. z<(x − 1)/(y − 1)
III. z>(x + 1)/(y + 1)

A. I only
B. I and II
C. II and III
D. II only
E. I and III



Hi Banuel,

Is the answer given above the most efficient way to approach this problem?

Thanks.

Originally posted by toby001 on 30 Jun 2016, 12:07.
Last edited by toby001 on 26 Sep 2016, 07:26, edited 1 time in total.
User avatar
P
mvictor
Board of Directors
Joined: 17 Jul 2014
Posts: 2163
Own Kudos [?]: 1180 [2]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Send PM
GMAT ToolKit User Reviews Badge
If x and y are positive integers such that x < y and z=x/y, which of [#permalink] New post   26 Sep 2016, 07:05
2
Kudos
Bunuel wrote:
If x and y are positive integers such that x < y and z=x/y, which of the following must be true?

I. z>(x − 1)/(y − 1)
II. z<(x − 1)/(y − 1)
III. z>(x + 1)/(y + 1)

A. I only
B. I and II
C. II and III
D. II only
E. I and III


fastest way is to know the basics...

if x/y <1, then x+1/y+1 will get closer to 1, which means that z must be smaller in this case than x/y
C and E are out.


the same with x-1/y-1, it should move further away from 1, aka decrease, and in this case Z is bigger.
II is false - B and D are out.
A is correct.

update:

Bunuel wrote:
If x and y are positive integers such that x < y and z=x/y, which of the following must be true?

I. z>(x − 1)/(y − 1)
II. z<(x − 1)/(y − 1)
III. z>(x + 1)/(y + 1)

A. I only
B. I and II
C. II and III
D. II only
E. I and III


if x<y - then (x+1)/(y+1) will get the fraction closer to 1.
if the opposite, it will move the fraction farther from 1.

1. it is true.
2. can't be, as A is true.
3. it should be <.

therefore, A is the answer.

damn - i didn't look that i already commented here :D
User avatar
B
deepak.brijendra
Intern
Intern
Joined: 02 May 2023
Posts: 30
Own Kudos [?]: 0 [0]
Given Kudos: 35
Location: India
GMAT 1: 540 Q57 V19
Send PM
Re: If x and y are positive integers such that x < y and z=x/y, which of [#permalink] New post   04 Sep 2023, 02:57
What if X=1 and Y=2. Then the condition in (i) doesnt suffice.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618961 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: If x and y are positive integers such that x < y and z=x/y, which of [#permalink] New post   04 Sep 2023, 06:32
Expert Reply
deepak.brijendra wrote:
What if X=1 and Y=2. Then the condition in (i) doesnt suffice.


If x = 1 and y = 2, then we'd get:

1/2 > (1 − 1)/(2 − 1)
1/2 > 0

Which is correct.
GMAT Club Bot
gmatclubot
Re: If x and y are positive integers such that x < y and z=x/y, which of [#permalink]
04 Sep 2023, 06:32
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 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