Last visit was: 24 Apr 2026, 16:16 It is currently 24 Apr 2026, 16:16
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
User avatar
bettatantalo
User avatar
Joined: 26 Apr 2018
Last visit: 20 Nov 2018
Posts: 33
Own Kudos:
162
 [3]
Given Kudos: 36
Posts: 33
Kudos: 162
 [3]
If |x|y < 0, which of the following must be positive? 22 Sep 2018, 06:48
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

74% (01:10) correct 26% (01:23) wrong based on 418 sessions

History

Date
Time
Result
Not Attempted Yet
If |x|y < 0, which of the following must be positive?

a) |x| - y
b) |y| - x
c) -|x-y|
d) x|y|
e) xy

source gmat tutor
ShowHide Answer
Official Answer
A
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,459
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,459
If |x|y < 0, which of the following must be positive? 22 Sep 2018, 09:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
bettatantalo
If |x|y < 0, which of the following must be positive?

a) |x| - y
b) |y| - x
c) -|x-y|
d) x|y|
e) xy

source gmat tutor
Show more

GIVEN: |x|y < 0

|x| ≥ 0 so, in order for |x|y < 0, it must be the case that y is NEGATIVE

Now check the answer choices...

a) |x| - y
We know that |x| is greater than or equal to 0.
Also, y is negative, so when we SUBTRACT y from |x|, we are actually adding a positive value to |x|. For example, subtracting -3 is the same as adding 3
So, |x| - y = some number greater than or equal to 0 + some positive value = positive

Answer: A

Cheers,
Brent
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,459
 [1]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,459
 [1]
If |x|y < 0, which of the following must be positive? 22 Sep 2018, 09:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
bettatantalo
If |x|y < 0, which of the following must be positive?

a) |x| - y
b) |y| - x
c) -|x-y|
d) x|y|
e) xy

Show more

The key here is MUST BE TRUE
If we can find an example in which an answer choice is NOT true, then we can eliminate it.

GIVEN: |x|y < 0
One possible pair of value for x and y is: x = 1 and y = -1
Notice that |x|y < 0 becomes |1|(-1) < 0. WORKS

Now plug x = 1 and y = -1 into the answer choices...

a) |1| - (-1) = 2. This IS positive. So, keep A
b) |-1| - (1) = 0. This is NOT positive. ELIMINATE B
c) -|1 - (-1)| = -2. This is NOT positive. ELIMINATE C
d) 1|(-1)| = 1. This IS positive. So, keep D
e) (1)(-1) = -1. This is NOT positive. ELIMINATE E

We're left with 2 remaining answer choices.
Let's test another pair of value for x and y

How about: x = -1 and y = -1
Notice that |x|y < 0 becomes |-1|(-1) < 0. WORKS

Now plug x = -1 and y = -1 into the 2 remaining answer choices...

a) |-1| - (-1) = 2. This IS positive. So, keep A
d) -1|(-1)| = -1. This is NOT positive. ELIMINATE D

Answer: D

Cheers,
Brent
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 03 Apr 2026
Posts: 2,286
Own Kudos:
2,680
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,286
Kudos: 2,680
If |x|y < 0, which of the following must be positive? 01 Dec 2024, 20:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
|x|y < 0
=> Both x and y are non-zero
Since |x| is non negative and |x| * y < 0
=> y < 0

We need to find which of the following must be positive

a) |x| - y
|x| > 0 (as x is non-zero)
y is negative
=> -y > 0
=> |x| - y > 0
=> ALWAYS POSITIVE

b) |y| - x
x can be positive or negative and depending on the value
|y| - x can be positive or negative
Ex 1: y = 2, x = 3 , |y| - x = |2| - 3 = 2 - 3 = -1
Ex 2: y = 2, x = -1, |y| - x = |2| - (-1) = 2 + 1 = 3
=> NEED NOT BE POSITIVE ALWAYS

c) -|x-y|
This can be negative or zero, but cannot be positive
If x = y then -|x - y| = -|y-y| = 0
In any other case it will be negative as it is negative of modulus of a number
=> ALWAYS NEGATIVE

d) x|y|
This can be negative or positive depending on the value of x
If x is negative then x|y| will be negative
If x is positive then x|y| will be positive
=> NEED NOT BE POSITIVE ALWAYS

e) xy
This can be negative or positive depending on the value of x
If x is negative then xy will be positive as y is negative
If x is positive then xy will be negative as y is negative
=> NEED NOT BE POSITIVE ALWAYS

So, Answer will be A
Hope it helps!

Watch the following video to MASTER Absolute Values

Moderators:
Bunuel
Math Expert
109818 posts
Krunaal
Tuck School Moderator
853 posts