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

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

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New post 16 Sep 2019, 21:47
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

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

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

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New post 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

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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.
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Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

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New post 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.

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Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

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New post 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
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Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

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New post 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
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Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

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New post 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).
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Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

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New post 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
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Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

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New post 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.
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Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x  [#permalink]

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New post 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.

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Re: Are negative integers m and n both less than x? (1) m > n (2) m - n >x   [#permalink] 17 Sep 2019, 05:52
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