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

It is currently 16 Feb 2020, 10:51

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

If b < x < 0 and w < x < y

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

Hide Tags

Find Similar Topics 
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4318
Location: Canada
If b < x < 0 and w < x < y  [#permalink]

Show Tags

New post 20 Mar 2017, 06:40
1
Top Contributor
21
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

28% (02:34) correct 72% (02:39) wrong based on 229 sessions

HideShow timer Statistics

If b < x < 0 and w < x < y, then which of the following MUST be true?

I. \(\frac{w + b}{y} < 0\)

II. \(\frac{y – b}{b} < 0\)

III. \((b + w) – (x + y) < 0\)

(A) II only
(B) III only
(C) I and II only
(D) I and III only
(E) II and III only

*Kudos for all correct solutions

_________________
Test confidently with gmatprepnow.com
Image
Most Helpful Expert Reply
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4318
Location: Canada
Re: If b < x < 0 and w < x < y  [#permalink]

Show Tags

New post 20 Mar 2017, 08:43
5
Top Contributor
2
GMATPrepNow wrote:
If b < x < 0 and w < x < y, then which of the following MUST be true?

I. \(\frac{w + b}{y} < 0\)

II. \(\frac{y – b}{b} < 0\)

III. \((b + w) – (x + y) < 0\)

(A) II only
(B) III only
(C) I and II only
(D) I and III only
(E) II and III only


Here's a different approach:

I. (w + b)/y < 0
We know that w and b are NEGATIVE, so (w + b) = NEGATIVE
However, we don't know whether y is NEGATIVE or POSITIVE
As such, (w + b)/y can be either POSITIVE or NEGATIVE
So, statement 1 need not be true.

II. (y – b)/b < 0
From the given information, we know that b < y. So, if we subtract b from both sides, we get y - b > 0
In other words, y-b is POSITIVE
Since we also know that b is NEGATIVE, we can see that (y – b)/b = POSITIVE/NEGATIVE = NEGATIVE
So, statement II must be true

III. (b + w) – (x + y) < 0
First rewrite the inequality as: b + w - x - y < 0
The rewrite as: (b - x) + (w - y) < 0
So, statement III can be rewritten as: (b - x) + (w - y) < 0

From the given information, we know that b < x.
If we subtract x from both sides, we get: b - x < 0
In other words, b-x is NEGATIVE

Also, from the given information, we know that w < y.
If we subtract y from both sides, we get: w - y < 0
In other words, w-y is NEGATIVE

This means that (b - x) + (w - y) = NEGATIVE + NEGATIVE = NEGATIVE
So, it must be true that (b - x) + (w - y) < 0

Answer: E

RELATED VIDEOS



_________________
Test confidently with gmatprepnow.com
Image
General Discussion
Marshall & McDonough Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1675
Location: India
GMAT ToolKit User
Re: If b < x < 0 and w < x < y  [#permalink]

Show Tags

New post 20 Mar 2017, 07:34
1
b < x < 0 --> b and x are negative. b is greater in magnitude than x.

w < x < y --> w and x are negative. w is greater in magnitude than x. We do not know anything about y.

I. (w + b)/y < 0 --> -ve/(Don't know whether y is positive or negative). Not a must be true statement.

II. (y – b)/b < 0 --> If y is negative then b is greater in magnitude than y and y - b will be positive.
If y is positive then y - b will always be positive.
In both the cases (y - b)/b = +ve/-ve = -ve.
Hence its a must be true statement.

III. (b + w) – (x + y) < 0 --> Magnitude wise b + w > x --> b + w - x = -ve
We have to find the sign of -ve - y
If y is negative the b + w - x is greater in magnitude than y --> The expression is negative.
If y is positive then the overall expression is negative.
Hence its a must be true statement.

Answer: E
Director
Director
User avatar
V
Joined: 05 Mar 2015
Posts: 959
Reviews Badge
If b < x < 0 and w < x < y  [#permalink]

Show Tags

New post 20 Mar 2017, 07:59
2
GMATPrepNow wrote:
If b < x < 0 and w < x < y, then which of the following MUST be true?

I. \(\frac{w + b}{y} < 0\)

II. \(\frac{y – b}{b} < 0\)

III. \((b + w) – (x + y) < 0\)

(A) II only
(B) III only
(C) I and II only
(D) I and III only
(E) II and III only

*Kudos for all correct solutions



(1) w+b<0 but y can be >0 or <0
not must be true.

(2) y-b = if y>0 then y-b>0 or if y<0 then y-b>0
and b<0 thus y-b/b<0
must be true

(3)b +w has more magnitude than x+y if y<0
Also if y>0 and more magnitude than b+w then entire equation is more negative value..
thus it must be true for every case
suff

Ans E
Manager
Manager
avatar
S
Joined: 03 Jan 2016
Posts: 57
Location: India
WE: Engineering (Energy and Utilities)
GMAT ToolKit User
Re: If b < x < 0 and w < x < y  [#permalink]

Show Tags

New post 20 Mar 2017, 09:06
1
b < x < 0 and w < x < y
With the above info, we are pretty sure that b,x,w <0 .
We dont know about y , whether it is >0, 0, or <0.
1. (w+b)/y <0
we know that w+b is <0 , but given equation varies with y. So it must not be true
2. (y-b)/b <0,
we know y>b & b<0.= > y-b >0 & b<0 .
So the given equation always holds & must be true.
3. (b+w) - (x+y)<0
the given equation can be written as (b-x) - (w-y)<0
we know, from given data in the question, that b-x<0 & w-y<0
therefore, subtraction of two negative numbers always be negative.
So, Given equation must be true.

Ans :- E


Regards
Narayana raju
Manager
Manager
avatar
S
Joined: 18 Oct 2016
Posts: 128
Location: India
WE: Engineering (Energy and Utilities)
Re: If b < x < 0 and w < x < y  [#permalink]

Show Tags

New post 17 Apr 2017, 03:28
1
Option E

b<x<0 & w<x<y.

i.e., x, b & w are <0. And, y<0 or >0.

I. \(\frac{{(w+b)}}{y}\)<0 : Not true can be +ve or -ve. Y is unknown.

II. \(\frac{{(y–b)}}{b}\)<0 : -ve. If y is -ve, |b| > |y| & y - b is +ve. If y is +ve, y-b is +ve. True

III. \((b+w)–(x+y)\)<0 : -ve. True
Intern
Intern
avatar
B
Joined: 28 Dec 2010
Posts: 21
If b < x < 0 and w < x < y  [#permalink]

Show Tags

New post 19 Jul 2017, 20:31
Another approach:

b < x < 0
w < x < y

y can be +ve or -ve

We can pick number here:

b = -4
w = -3
x = -2

Values of y when -ve can be -1
Value of y when +ve can be 10

Statement 1:

1) w+b/y <0

case 1: y is +ve

(-3)+(-4)/10 < 0 - "True"

case 2: y is -ve

(-3)+(-4)/-1 < 0 - "False"

Thus, statement 1 is - "Not always true"

Statement 2:

2) y-b/b <0

simpilfying:

y/b - 1 < 0
y/b < 1

Case 1: y is -ve

(-1)/(-4) < 1 - "True"

Case 2: y is +ve

(10)/(-4) < 1 - "True"

Thus, statement 2 is - "True"

3) (b+w)-(x+y)<0

Case 1: y is +ve

(-4)+(-3)-(-2)-(10)< 0
(-17)+(2)< 0
-15< 0 ------------> "True"

Case 2: y is -ve

(-4)+(-3)-(-2)-(-1)< 0
(-7)+(3)< 0
-4< 0 ------------> "True"

Thus, statement 3 is "True"

Hence, the solution is E.
SVP
SVP
User avatar
D
Joined: 03 Jun 2019
Posts: 2001
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Premium Member Reviews Badge
Re: If b < x < 0 and w < x < y  [#permalink]

Show Tags

New post 22 Aug 2019, 00:52
1
GMATPrepNow wrote:
If b < x < 0 and w < x < y, then which of the following MUST be true?

I. \(\frac{w + b}{y} < 0\)

II. \(\frac{y – b}{b} < 0\)

III. \((b + w) – (x + y) < 0\)

(A) II only
(B) III only
(C) I and II only
(D) I and III only
(E) II and III only

*Kudos for all correct solutions


Given:
1. b < x < 0
2. w < x < y

{b,w}<x<{0,y}

Asked: Which of the following MUST be true?

I. \(\frac{w + b}{y} < 0\)
w+b<0 since w<0 & b<0
y may or may not be >0
NOT NECESSARILY TRUE

II. \(\frac{y – b}{b} < 0\)
y-b>0 & b<0
\(\frac{y-b}{b}<0\)
MUST BE TRUE

III. \((b + w) – (x + y) < 0\)
b+w < x+y
MUST BE TRUE

IMO E
GMAT Club Bot
Re: If b < x < 0 and w < x < y   [#permalink] 22 Aug 2019, 00:52
Display posts from previous: Sort by

If b < x < 0 and w < x < y

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





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