Is m ≠ n ? (1) m + n < 0 (2) mn < 0 : Data Sufficiency (DS)

Spidy001

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

28 Jun 2011, 17:46

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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.

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

05 Jun 2013, 22:00

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.

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

11 May 2014, 11:01

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!

L

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

30 Sep 2019, 21:42

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.

B

babloorudra

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

20 Apr 2020, 03:05

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

L

Bunuel

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

20 Apr 2020, 03:10

Expert Reply

babloorudra wrote:

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

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.

B

babloorudra

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

20 Apr 2020, 07:19

Bunuel wrote:

babloorudra wrote:

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

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.

Thanks a lot.

S

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

14 May 2020, 12:48

Bunuel wrote:

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.

Can we slove it algebraically?

B

Chetan1286

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

15 May 2020, 04:07

Bunuel wrote:

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.

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

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

15 May 2020, 04:23

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

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

20 Aug 2020, 03:06

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"?

L

Bunuel

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

20 Aug 2020, 03:17

Expert Reply

TakingtheEA wrote:

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"?

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.

B

revamoghe

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

03 Sep 2020, 20:54

Bunuel wrote:

babloorudra wrote:

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

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.

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.

L

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

29 Sep 2020, 00:41

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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

G

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

01 Nov 2020, 13:37

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.

B

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Re: Is m ≠ n ? (1) m + n < 0 (2) mn < 0 [#permalink]

21 Jan 2022, 17:10

Bunuel wrote:

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.

Yes its clear! Thanks for the explanation!

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Re: Is m n ? (1) m + n < 0 (2) mn < 0 [#permalink]

13 Mar 2024, 05:04

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Re: Is m n ? (1) m + n < 0 (2) mn < 0 [#permalink]

13 Mar 2024, 05:04

GMAT Data Sufficiency (DS) Questions

Is m ≠ n ? (1) m + n < 0 (2) mn < 0