GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 14:02

### 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

# Are negative integers m and n both less than x? (1) m > n (2) m - n >x

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58396
Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

### Show Tags

16 Sep 2019, 21:47
00:00

Difficulty:

55% (hard)

Question Stats:

71% (01:21) correct 29% (01:56) wrong based on 31 sessions

### HideShow timer Statistics

Competition Mode Question

Are negative integers m and n both less than x?

(1) $$m > n$$
(2) $$m - n > x$$

_________________
Senior Manager
Status: Whatever it takes!
Joined: 10 Oct 2018
Posts: 383
GPA: 4
Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

### Show Tags

Updated on: 17 Sep 2019, 21:56
Are negative integers m and n both less than x?

(1) m>n
-1>-2 or -5>-10....anything. But we don't know about x.
INSUFFICIENT!

(2) m−n>x
-4+5>x => x<1 => -4<x? Yes and -5<x yes

If -3+1>x => x<-2 => -3<x? No and -1<x No

INSUFFICIENT!

(1) + (2)
m>n and m−n>x

-4+5>x => x<1 => x>-4? Yes(not always) and x>-5 yes(not always)

-1+10>x => x<9 => x>-1? Yes(not always) and x>-10 yes(not always)

INSUFFICIENT!

imo answer is option E

Posted from my mobile device
_________________
Kudos OK Please!!

ALL ABOUT GMAT- $$https://exampal.com/gmat/blog/gmat-score-explained$$

Originally posted by EncounterGMAT on 16 Sep 2019, 22:15.
Last edited by EncounterGMAT on 17 Sep 2019, 21:56, edited 1 time in total.
Senior Manager
Joined: 18 May 2019
Posts: 369
Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

### Show Tags

16 Sep 2019, 22:30
We are to determine if the integers m and n are both less than x.

We can answer this question when we can prove that either m or n is greater than x.

1. m>n
This is clearly insufficient since we don’t have any information on the possible value of x.

2 m-n>x
m-n>x implies m>x+n
If m=2 and n=-5, and x= 3,
m-n=7>x(3) and both m and n are less than x so we can answer yes to the question.

Now when m=4 and n=-5 and x=3
m-n=9>x(3) but m>x so No, both m and n are not greater than x.
Statement is also insufficient.

1+2 Is still insufficient because no new information is provided by combining both options.

The answer is E in my opinion.

Posted from my mobile device
Manager
Joined: 01 Mar 2019
Posts: 172
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

### Show Tags

16 Sep 2019, 22:36
(1) m>n.....clearly insufficient
(2) m−n>x
i) m=-3,n=-4 =>x<1......so it can be greater than or less than m,n
ii) m=-4,n=-3 =>x<-1......so it can be greater than or less than m,n

Even after combining both....same situation: x can be greater than or less than m,n

OA :E
_________________
Appreciate any KUDOS given
Manager
Joined: 05 Aug 2018
Posts: 68
Location: Thailand
Concentration: Finance, Entrepreneurship
GPA: 3.68
WE: Business Development (Energy and Utilities)
Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

### Show Tags

16 Sep 2019, 22:50
negative integer m and n both less than x?

1. m>n. definitely not sufficient because we do not know anything about x
2. m - n > x
if m = -2, n = -1 ; x< -1 so x can be -2, -3, -4. In case that x = -2 the answer is No
if m = -1, n = -2; x>1 so x can be 2, 3 ,4. In this case the answer is Yes

1 + 2 together we get m = -1, n = -2 so the answer always is yes.

Therefore C. statement 1 and 2 together is sufficient
Senior Manager
Joined: 07 Mar 2019
Posts: 329
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

### Show Tags

16 Sep 2019, 23:38
Are negative integers m and n both less than x?

m < 0 and n < 0 if m < x and n < x?

(1) m > n
Let m = - 2 and n = - 3
x can be positive or negative.
INSUFFICIENT.

(2) m – n > x
If m > n, Let m = - 2 and n = - 4
 - 2 – (- 4) > x
 2 > x

i.e. x can take any value less than 2. (YES and NO both cases)
INSUFFICIENT.

If m < n, Let m = - 4 and n = - 2
 - 4 – (- 2) > x
 - 2 > x

i.e. only m < x but n > x.
INSUFFICIENT.

Together 1) and 2)
If m > n, Let m = - 2 and n = - 4
 - 2 – (- 4) > x
 2 > x

i.e. x can take any value less than 2. (YES and NO both cases)
INSUFFICIENT.

Answer (E).
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5027
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

### Show Tags

17 Sep 2019, 02:02
#1
m>n
relation b/w m&n know but not with x insufficient
#2
m-n>x
if m=-2 n=-1 then -1>x
x can be -2,-3 ...
if m=-2 and n=-5 then 3>x ; x can be + or -ve insufficient

from 1 &2
m>n and m-n>x
and m,n are -ve integers
m=-5 and n=-10
-5+10>x
5>x ; x can be +ve or -ve insufficient
IMO E

Are negative integers m and n both less than x?

(1) m>n
(2) m−n>x
Director
Joined: 24 Nov 2016
Posts: 624
Location: United States
Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

### Show Tags

17 Sep 2019, 04:37
Quote:
Are negative integers m and n both less than x?

(1) m>n
(2) m−n>x

[#] m…n…x…answer
[1] -1…-2…-2…no
[2] -1…-2…-3…yes

(1) m>n: case [1] and [2] are valid, insufic.
(2) m-n>x: insufic.
rearrange, m>x+n; [1] -1>(-2)+(-2)…-1>-4 valid, answer is no; [2] -1>(-2)+(-3)…-1>-5 valid, answer is yes

(1&2) m>n and m>x+n, cases [1] and [2] are valid, insufic.
Senior Manager
Joined: 25 Jul 2018
Posts: 276
Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

### Show Tags

17 Sep 2019, 05:52
If m<0 and n<0, then are m <x and
n <x ???

Stat(1): m> n
—> still no info about what x is.
Insufficient

Stat(2): m—n> x
If m=—2, n=—5 and x=—1, then
—> —2–(—5)>—1
3> —1 (ok)
m <x and n <x (yes)

If m=—1, n=—5 and x=—2, then
—> —1–(-5)> —2
4>—2 (ok)
m >x and n <x (NO)
Insufficient

Taken together 1 &2,
m—n >0
m—n>x
—>( m-n) is greater than zero, and x is less than (m-n)—> x could be positive and negative. We can’t conclude whether negative m and n are both less than x.
Insufficient

The answer is E.

Posted from my mobile device
Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x   [#permalink] 17 Sep 2019, 05:52
Display posts from previous: Sort by

# Are negative integers m and n both less than x? (1) m > n (2) m - n >x

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

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