Is m ≠ n ? (1) m + n

Question

Is m ≠ n ?

(1) m + n < 0
(2) mn < 0

Bunuel · Accepted Answer

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
eq{n} . Sufficient.

Answer: B.

Hope it's clear.

sudhir18n · Answer

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

Spidy001 · Answer

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.

monirjewel · Answer

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.

dxx · Answer

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!

dcummins · Answer

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.

babloorudra · Answer

For stmnt 1- 
m+n<0 therefore, m<-n and so m!=n. What is wrong with this approach?

Bunuel · Answer

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.

babloorudra · Answer

Thanks a lot.

lakshya14 · Answer

Can we slove it algebraically?

Chetan1286 · Answer

where is it written that m and n are integers 0.4*0.4=0.16 and are less than 0
and m= n

riteshdollar · Answer

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

TakingtheEA · Answer

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"?

Bunuel · Answer

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.

revamoghe · Answer

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.

Hovkial · Answer

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

Basshead · Answer

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.

mba94 · Answer

Yes its clear! Thanks for the explanation!

bumpbot · Answer

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Is m ≠ n ? (1) m + n < 0 (2) mn < 0

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