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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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16 Sep 2019, 21:47
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Competition Mode Question 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
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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
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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
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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 mn>x mn>x implies m>x+n If m=2 and n=5, and x= 3, mn=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 mn=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
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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
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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
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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
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17 Sep 2019, 02:02
#1 m>n relation b/w m&n know but not with x insufficient #2 mn>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 mn>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
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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) mn>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
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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 —>( mn) is greater than zero, and x is less than (mn)—> 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
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