GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 04 Apr 2020, 14:25

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

Which of the following must be true if x/y and x/z > y/z?

  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: 62499
Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 06 Nov 2019, 23:28
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:14) correct 21% (01:26) wrong based on 98 sessions

HideShow timer Statistics

SVP
SVP
avatar
V
Joined: 20 Jul 2017
Posts: 1519
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post Updated on: 06 Nov 2019, 23:54
2
\(\frac{x}{z} > \frac{y}{z}\)
--> \(\frac{(x - y)}{z} > 0\)
Since, \(x < y\),
--> \(x - y < 0\)
--> \(z\) < 0 ALWAYS (Since for \(\frac{(x - y)}{z} > 0\), ONLY negative/negative > 0)

IMO Option A

Originally posted by Dillesh4096 on 06 Nov 2019, 23:51.
Last edited by Dillesh4096 on 06 Nov 2019, 23:54, edited 1 time in total.
Manager
Manager
avatar
S
Joined: 30 Nov 2017
Posts: 66
GMAT 1: 690 Q49 V35
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 06 Nov 2019, 23:52
Which of the following must be true if x<y and x/z >y/z?

The eqs. x<y and x/z >y/z will only be valid when z<0.
Senior Manager
Senior Manager
avatar
P
Joined: 01 Mar 2019
Posts: 491
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GMAT 1: 580 Q48 V21
GPA: 4
Reviews Badge
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 07 Nov 2019, 00:10
2
x<y
and x/z > y/z

i.e x/z - y/z > 0
x-y/z > 0
Since x-y <0, so z has to be < 0 to make the equation > 0
So z must be < 0

OA:A
Senior Manager
Senior Manager
avatar
G
Joined: 23 Nov 2018
Posts: 254
GMAT 1: 650 Q49 V28
GPA: 4
Reviews Badge
Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post Updated on: 08 Nov 2019, 01:14
z(x-y)>0

given x-y<0 therefore Z<0

option A
_________________
.

Originally posted by sampriya on 07 Nov 2019, 00:31.
Last edited by sampriya on 08 Nov 2019, 01:14, edited 1 time in total.
Director
Director
User avatar
D
Joined: 07 Mar 2019
Posts: 911
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 07 Nov 2019, 01:48
1
Which of the following must be true if x < y and \(\frac{x}{z} > \frac{y}{z}\) ?

A. z < 0

B. z > 0

C. \(\frac{x}{y}\) > 0

D. x > 0

E. y > 0

Since x < y and inequality \(\frac{x}{z} > \frac{y}{z}\) is with opposite sign, z must be an entity that must be causing the change of sign.

Among the choices D and E are straightforward out since both can have both + and - signs.
C is also ruled out since x and y can have opposite signs.

Only possibility left is A because z > 0 would not lead to change in sign from < to >.

Answer A.
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1349
Location: United States
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 07 Nov 2019, 06:42
1
Quote:
Which of the following must be true if x<y and x/z >y/z?

A. z<0
B. z>0
C. xy>0
D. x>0
E. y>0


x<y…x-y<0
x/z>y/z…x/z-y/z>0…x-y/z>0
x-y<0 so z<0

Ans. (A)
CR Forum Moderator
avatar
P
Joined: 18 May 2019
Posts: 788
GMAT ToolKit User Premium Member
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 07 Nov 2019, 07:39
1
Given x<y, and x/z > y/z,
this can only be true if x>0 and y>0 and z<0
or x<0 and y<0 and z<0.
In both cases, z<0 must be true.

To illustrate, lets consider the case where x>0 and y>0 and z<0
Let x=2 and y=3, we know x=2 < y=3. if z=-1, then x/z=-2 and y/z=-3. Since -2(x/z) > -3(y/z), then the given condition is satisfied.

In the other case where x<0 and y<0, let x=-3 and y=-2. -3(x) < -2(y). x/z can only be greater than y/z if z<0, so let z=-1. Then x/z=3 and y/z=2. Since 3(x/z) > 2(y/z), then the given condition is satisfied.

In both instances, z<0.

Hence the answer is option A
Intern
Intern
avatar
B
Joined: 15 Aug 2017
Posts: 24
CAT Tests
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 07 Nov 2019, 07:44
1
I cross multiplied, to get zx > zy which would indicate that a sign change has occurred so z < 0

A IMO
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 6038
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 07 Nov 2019, 07:47
1
the given condition x<y and x/z >y/z can be true if x & z are -ve and y is +ve
so IMO A ; z<0 should be correct

Which of the following must be true if x<y and x/z >y/z?

A. z<0

B. z>0

C. xy>0

D. x>0

E. y>0
Manager
Manager
avatar
G
Joined: 31 Oct 2015
Posts: 95
GMAT ToolKit User
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 07 Nov 2019, 13:55
1
Given x<y but \frac{x}{z}>\frac{y}{z}. Note that the sign is changed when divided by Z.

Theory : Multiplication/division with a negative number can change the inequality sign. Thefore Z has to be negative for this to hold true.

Answer is A.
Director
Director
avatar
P
Joined: 25 Jul 2018
Posts: 628
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 07 Nov 2019, 14:21
1
Which of the following must be true if x < y and \((\frac{x}{z}) > (\frac{y}{z})\)?

\(\frac{(x —y)}{z} > 0\)
x—y < 0.

—> in order \(\frac{(x —y)}{z}\) to be positive, z must be less than zero. (z < 0)

The answer is A

Posted from my mobile device
Intern
Intern
User avatar
B
Joined: 09 Sep 2018
Posts: 2
Location: Iran (Islamic Republic of)
Concentration: Finance, Accounting
GMAT 1: 620 Q45 V30
GPA: 3.85
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 07 Nov 2019, 14:43
Z should be negative. For example:
x=2 and y=3 and z=-3 then we have 2<3 so x<y and also -2/3 > -3/3 so x/z > y/z.
Current Student
User avatar
G
Joined: 11 Feb 2013
Posts: 266
Location: United States (TX)
Schools: Neeley '21 (A$)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
GMAT ToolKit User Premium Member Reviews Badge
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 07 Nov 2019, 20:34
1
A is my answer

Given,
(X/z)>(y/z)
Here, z can not be zero.
So, z must be positive or negative.
If z is positive, x>y.
If z is negative, x<y

it is also given that x<y. So, Z must be negative.
Director
Director
avatar
D
Joined: 22 Feb 2018
Posts: 598
GMAT ToolKit User CAT Tests
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 07 Nov 2019, 21:22
1
Imo. A

Which of the following must be true if x<y and x/z >y/z?

Let's try from options.

A. z<0, Z is negative, x/z >y/z, If z = -1, -x>-y, y>x and the same condition x<y is mentioned. Hence, Z must be true to suffice the condition.

B. z>0, Z is positive, x/z >y/z, If z = 1, x>y, which contradicts the give condition x<y. incorrect

C. x/y>0, We don't know the signs of any variables, so there can be multiple options, which could be true, are available.

D. x>0, If x is positive, Y is also positive. But no more information about Z. So multiple values for inequality can be obtained

E. y>0. It implies that y = +ve and x can be +ve/-ve. So, again multiple values for inequality can be obtained
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9960
Location: United States (CA)
Re: Which of the following must be true if x/y and x/z > y/z?  [#permalink]

Show Tags

New post 12 Nov 2019, 19:37
1
Bunuel wrote:

Competition Mode Question



Which of the following must be true if \(x < y\) and \(\frac{x}{z}\) >\(\frac{y}{z}\)?

A. \(z < 0\)

B. \(z > 0\)

C. \(\frac{x}{y} > 0\)

D. \(x > 0\)

E. \(y > 0\)


We see that the inequality sign flips when both x and y are divided by z. This happens when z is negative, i.e., z < 0.

Alternate Solution:

Using the second inequality, we have:

x/z - y/z > 0

(x - y)/z > 0

Since (x - y)/z is positive, (x - y) and z are either both positive or both negative. On the other hand, from the first inequality, we have:

x - y < 0

Since (x - y) is negative, it follows that z must also be negative; i.e. z < 0.

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: Which of the following must be true if x/y and x/z > y/z?   [#permalink] 12 Nov 2019, 19:37
Display posts from previous: Sort by

Which of the following must be true if x/y and x/z > y/z?

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





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