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akhileshgupta05
Joined: 01 May 2011
Last visit: 26 Mar 2012
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GMAT 1: 670 Q48 V35
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GMAT 1: 670 Q48 V35
Posts: 348
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
69% (01:04) correct
31%
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wrong
based on 2597
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Is m ≠ n ?
(1) m + n < 0
(2) mn < 0
(1) m + n < 0
(2) mn < 0
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
akhileshgupta05
St1: m+n <0
m = -1 n = -1 m+n<0 and m =n
m =-4 n =-1 m+n < 0 but m not equal to n .............. insufficient
st2: mn<0 if the product of 2 numbers is <0 then either of the numbers is <0 and in this case they can be be equal to each other .
hence B
1. Not sufficient
m+n <0 => m<-n
we dont know the sign of n
n........-n ( considering n <0) => as m<-n , by looking at the graph , we can say m may or may not be equal to n
-n........n (considering n>0) as m<-n , by looking at the graph we can say that m is not equal to n
2. Sufficient
mn<0
when m =n
n^2<0 which cannot be true . square of number will always be positive. So we can conclude that m is
not equal to n.
Answer is B.
m+n <0 => m<-n
we dont know the sign of n
n........-n ( considering n <0) => as m<-n , by looking at the graph , we can say m may or may not be equal to n
-n........n (considering n>0) as m<-n , by looking at the graph we can say that m is not equal to n
2. Sufficient
mn<0
when m =n
n^2<0 which cannot be true . square of number will always be positive. So we can conclude that m is
not equal to n.
Answer is B.
monirjewel
Joined: 06 Feb 2010
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Schools: University of Dhaka - Class of 2010
Posts: 122
Stm1: m+n <0
m = -1 n = -1 m+n<0 and m =n
m =-4 n =-1 m+n < 0 but m not equal to n .............. insufficient
stm2 when mn<0, m or n must be negative & postive....So m not equal to n.
m = -1 n = -1 m+n<0 and m =n
m =-4 n =-1 m+n < 0 but m not equal to n .............. insufficient
stm2 when mn<0, m or n must be negative & postive....So m not equal to n.
Is m not equal to n ?
(1) m + n < 0. If m=n=-1, then the answer is YES but if m=-1 and n=-2, then the answer is NO. Not sufficient.
(2) mn < 0. This implies that m and n have opposite signs, thus \(m\neq{n}\). Sufficient.
Answer: B.
Hope it's clear.
_________________
(1) m + n < 0. If m=n=-1, then the answer is YES but if m=-1 and n=-2, then the answer is NO. Not sufficient.
(2) mn < 0. This implies that m and n have opposite signs, thus \(m\neq{n}\). Sufficient.
Answer: B.
Hope it's clear.
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Is m ≠ n ?
(1) m + n < 0
(2) mn < 0
(1) m + n < 0
Let's use numbers:
Take m=-1 and n=-1, then the condition m + n < 0 holds true and m=n
Take m=-2 and n=-1, then the condition m + n < 0 holds true but m≠n
Since we don't get a clear 100% answer, Insufficient!
(2) mn < 0
If mn < 0, either m or n must be negative, and the other variable must be positive. Therefore, m ≠ n
Sufficient!
(1) m + n < 0
(2) mn < 0
(1) m + n < 0
Let's use numbers:
Take m=-1 and n=-1, then the condition m + n < 0 holds true and m=n
Take m=-2 and n=-1, then the condition m + n < 0 holds true but m≠n
Since we don't get a clear 100% answer, Insufficient!
(2) mn < 0
If mn < 0, either m or n must be negative, and the other variable must be positive. Therefore, m ≠ n
Sufficient!
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GMAT 1: 560 Q41 V26
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Schools: INSEAD Sept'21 Intake (WA$$$) Melbourne (A$$$$) AGSM (A$$$$) Kellogg '23 (WL) Said '22 (A$$$$) CBS '23 (D) Booth '23 (WA) Anderson '23 (WA) Cambridge '22 (WL) LBS '23 (D) Stern '24 (WA)
GMAT 6: 710 Q47 V41
Posts: 1,017
statement 1
Test m=-1 n=-1
-2<0
-->No
Test m=-2 n=-1
--> yes
statement 2
The only ways statement 2 works are:
(+)(-) < 0
or
(-)(+)<0
In either case m is different from n
Sufficient.
Test m=-1 n=-1
-2<0
-->No
Test m=-2 n=-1
--> yes
statement 2
The only ways statement 2 works are:
(+)(-) < 0
or
(-)(+)<0
In either case m is different from n
Sufficient.
Posts: 13
For stmnt 1-
m+n<0 therefore, m<-n and so m!=n. What is wrong with this approach?
m+n<0 therefore, m<-n and so m!=n. What is wrong with this approach?
babloorudra
m < -n does not necessarily mean the m ≠ n. For example, consider m = n = -2. Basically m < -n and m ≠ can both be true if both m and n are negative.
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Posts: 13
Bunuel
Thanks a lot.
Bunuel
Can we slove it algebraically?
Posts: 13
Bunuel
where is it written that m and n are integers 0.4*0.4=0.16 and are less than 0
and m= n
Posts: 5
0.16 is not negative.
mn < 0 given in statement (2).
So your consideration of m = n = 0.4 is wrong.
Posted from my mobile device
mn < 0 given in statement (2).
So your consideration of m = n = 0.4 is wrong.
Posted from my mobile device
Posts: 1
For statement B ... what if M was 0? then wouldn't any value of N multiplied by 0 not be < 0 but = to 0 and therefore the question is insufficient because you could get a "yes" and "no"?
TakingtheEA
mn < 0 implies that neither m nor m could be 0. mn < 0 implies that m and n have opposite signs (one must be positive and another must be negative), thus m ≠ n.
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Bunuel
Shouldn't it always mean that m < -n irrespective of the values?
So, if m = n = 5, m and n will always have opposite signs. It means they can never be equal to each other.
We are asked to determine whether the two variables 'm' and 'n' are different from each other.
(1) m + n < 0
Assume a contrary position to the question. That is, assume that m and n are equal to each other: m = n
Then, this statement gives us m + m < 0
or, m < 0.
Since we are not given the sign of m, this statement is INSUFFICIENT to tell us whether m and n are different from each other.
(2) mn < 0
This statement simply means that m and n are of opposite signs to each other. This information is SUFFICIENT for us to state that m and n are different from each other.
ANSWER: B
(1) m + n < 0
Assume a contrary position to the question. That is, assume that m and n are equal to each other: m = n
Then, this statement gives us m + m < 0
or, m < 0.
Since we are not given the sign of m, this statement is INSUFFICIENT to tell us whether m and n are different from each other.
(2) mn < 0
This statement simply means that m and n are of opposite signs to each other. This information is SUFFICIENT for us to state that m and n are different from each other.
ANSWER: B
Is m ≠ n ?
(1) m + n < 0
if m = n = -2
-2 + -2 < 0; no
if m = 0 n = -1
0 + -1 < 0; yes
INSUFFICIENT.
(2) mn < 0
m and n must have opposite signs. SUFFICIENT.
Answer is B.
(1) m + n < 0
if m = n = -2
-2 + -2 < 0; no
if m = 0 n = -1
0 + -1 < 0; yes
INSUFFICIENT.
(2) mn < 0
m and n must have opposite signs. SUFFICIENT.
Answer is B.
Bunuel
Yes its clear! Thanks for the explanation!
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