If M < N, is M^2-MN < 0? : Data Sufficiency (DS)

bhatiamanu05

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Re: If M < N, is M^2-MN < 0? [#permalink]

25 Dec 2013, 01:20

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GMATBeast wrote:

If M < N, is M^2 - MN < 0?
(1) M <= 0
(2) N < 0

Restated the q to: if M - N < 0, Is M(M-N) < 0?
So basically is M positive?

(1) S
(2) S

Answer is...

Hi GMATBeast,

Using first statement:

if m<=0.

if m = 0 than the expression is =0

if m = -2 and n is -1 .

-2(-2 - (-1) <0

2> 0

so two answer are coming. yes less than zero and equal to zero.

how you can say first statement is sufficient.

using statement 2:

if n<0

n = -2 than m = -3

thn you can answer as no.

so answer should be B not D.

GMATBeast, Can you please tell me where I am wrong.

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Re: If M < N, is M^2-MN < 0? [#permalink]

25 Dec 2013, 04:22

bhatiamanu05 wrote:

GMATBeast wrote:

If M < N, is M^2 - MN < 0?
(1) M <= 0
(2) N < 0

Restated the q to: if M - N < 0, Is M(M-N) < 0?
So basically is M positive?

(1) S
(2) S

Answer is...

Hi GMATBeast,

Using first statement:

if m<=0.

if m = 0 than the expression is =0

if m = -2 and n is -1 .

-2(-2 - (-1) <0

2> 0

so two answer are coming. yes less than zero and equal to zero.

how you can say first statement is sufficient.

using statement 2:

if n<0

n = -2 than m = -3

thn you can answer as no.

so answer should be B not D.

GMATBeast, Can you please tell me where I am wrong.

First statement is sufficient bc m is not positive.

Looking back at your explanation- you answered the question correctly yourself.

0 is not < 0 (m=0) and 2>0, hence s1 is sufficient.

Does that make sense?

B

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Re: If M < N, is M^2-MN < 0? [#permalink]

25 Dec 2013, 11:55

Bunuel wrote:

If M < N, is M^2 - MN < 0?

Is \(M^2 - MN < 0\)? --> is \(M(M-N)<0\)? Since given that \(M-N<0\), then the question basically asks whether M>0.

(1) M <= 0. Sufficient.

(2) N < 0. Sine we also know that \(M < N\), then we have that \(M < N < 0\) --> \(M<0\). Sufficient.

Answer: D.

Hope it's clear.

Hi Bunuel

Can you explain where I got it wrong:

- If M=0 than M(M-N)=0 and thus is not < to zero but equal to 0, making the first statement not sufficient.

Where is my mistake?

Thx

L

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Re: If M < N, is M^2-MN < 0? [#permalink]

26 Dec 2013, 03:11

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Paris75 wrote:

Bunuel wrote:

If M < N, is M^2 - MN < 0?

Is \(M^2 - MN < 0\)? --> is \(M(M-N)<0\)? Since given that \(M-N<0\), then the question basically asks whether M>0.

(1) M <= 0. Sufficient.

(2) N < 0. Sine we also know that \(M < N\), then we have that \(M < N < 0\) --> \(M<0\). Sufficient.

Answer: D.

Hope it's clear.

Hi Bunuel

Can you explain where I got it wrong:

- If M=0 than M(M-N)=0 and thus is not < to zero but equal to 0, making the first statement not sufficient.

Where is my mistake?

Thx

The question asks whether \(M^2 - MN < 0\) or whether \(M>0\).

First statement says that \(M\leq{0}\). For any possible value of M (negative or zero), you get a NO answer to the question.

Hope it's clear.

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Re: If M < N, is M^2-MN < 0? [#permalink]

26 Dec 2013, 14:44

Bunuel wrote:

The question asks whether \(M^2 - MN < 0\) or whether \(M>0\).

First statement says that \(M\leq{0}\). For any possible value of M (negative or zero), you get a NO answer to the question.

Hope it's clear.

So the goal is not really to prove m^2-mn<0, but as long as we have sufficient info to prove it's actually>0, then it's considered sufficient as well? Very weird.

L

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Re: If M < N, is M^2-MN < 0? [#permalink]

27 Dec 2013, 03:35

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supermann wrote:

Bunuel wrote:

The question asks whether \(M^2 - MN < 0\) or whether \(M>0\).

First statement says that \(M\leq{0}\). For any possible value of M (negative or zero), you get a NO answer to the question.

Hope it's clear.

So the goal is not really to prove m^2-mn<0, but as long as we have sufficient info to prove it's actually>0, then it's considered sufficient as well? Very weird.

There are two kinds of data sufficient questions: YES/NO DS questions and DS questions which ask to find a value.

In a Yes/No Data Sufficiency questions, statement is sufficient if the answer is “always yes” or “always no” while a statement is insufficient if the answer is "sometimes yes" and "sometimes no".

When a DS question asks about the value of some variable, then the statement is sufficient ONLY if you can get the single numerical value of this variable.

Our original question is of the first type. Therefore to get whether a statement is sufficient we need “always yes” OR “always no” answer to the question. From both statements we have “always no” answer to the question, thus both statements are sufficient alone.

Hope it's clear.

B

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Re: If M < N, is M^2-MN < 0? [#permalink]

01 Jul 2014, 21:44

Bunuel wrote:

If M < N, is M^2 - MN < 0?

Is \(M^2 - MN < 0\)? --> is \(M(M-N)<0\)? Since given that \(M-N<0\), then the question basically asks whether M>0.

(1) M <= 0. Sufficient.

(2) N < 0. Sine we also know that \(M < N\), then we have that \(M < N < 0\) --> \(M<0\). Sufficient.

Answer: D.

Hope it's clear.

Is it just me or are there more people scratching their head over this explanation.. :stupid

M=0 --> M^2 - MN = 0 --->
M<0 --> M^2 - MN < 0?---> Depends on N

How is A suff? :horror

L

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Re: If M < N, is M^2-MN < 0? [#permalink]

02 Jul 2014, 01:39

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JusTLucK04 wrote:

Bunuel wrote:

If M < N, is M^2 - MN < 0?

Is \(M^2 - MN < 0\)? --> is \(M(M-N)<0\)? Since given that \(M-N<0\), then the question basically asks whether M>0.

(1) M <= 0. Sufficient.

(2) N < 0. Sine we also know that \(M < N\), then we have that \(M < N < 0\) --> \(M<0\). Sufficient.

Answer: D.

Hope it's clear.

Is it just me or are there more people scratching their head over this explanation.. :stupid

M=0 --> M^2 - MN = 0 --->
M<0 --> M^2 - MN < 0?---> Depends on N

How is A suff? :horror

The question asks whether \(M^2 - MN < 0\) or whether \(M>0\).

First statement says that \(M\leq{0}\). For any possible value of M (negative or zero), you get a NO answer to the question.

Hope it's clear.

B

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Re: If M < N, is M^2-MN < 0? [#permalink]

02 Jul 2014, 02:04

Bunuel wrote:

JusTLucK04 wrote:

Bunuel wrote:

If M < N, is M^2 - MN < 0?

Is \(M^2 - MN < 0\)? --> is \(M(M-N)<0\)? Since given that \(M-N<0\), then the question basically asks whether M>0.

(1) M <= 0. Sufficient.

(2) N < 0. Sine we also know that \(M < N\), then we have that \(M < N < 0\) --> \(M<0\). Sufficient.

Answer: D.

Hope it's clear.

Is it just me or are there more people scratching their head over this explanation.. :stupid

M=0 --> M^2 - MN = 0 --->
M<0 --> M^2 - MN < 0?---> Depends on N

How is A suff? :horror

The question asks whether \(M^2 - MN < 0\) or whether \(M>0\).

First statement says that \(M\leq{0}\). For any possible value of M (negative or zero), you get a NO answer to the question.

Hope it's clear.

Hey Bunuel..Agreed..You are reinterpreting the question as M>0 or not..(Which I am not so clear on)

But what is wrong in what I said:
M=0 --> M^2 - MN = 0 --->
M<0 --> M^2 - MN < 0?---> Depends on N

Disprove me...that 2 such cases are not possible

L

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Re: If M < N, is M^2-MN < 0? [#permalink]

02 Jul 2014, 03:57

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JusTLucK04 wrote:

Bunuel wrote:

JusTLucK04 wrote:

Is it just me or are there more people scratching their head over this explanation.. :stupid

M=0 --> M^2 - MN = 0 --->
M<0 --> M^2 - MN < 0?---> Depends on N

How is A suff? :horror

The question asks whether \(M^2 - MN < 0\) or whether \(M>0\).

First statement says that \(M\leq{0}\). For any possible value of M (negative or zero), you get a NO answer to the question.

Hope it's clear.

Hey Bunuel..Agreed..You are reinterpreting the question as M>0 or not..(Which I am not so clear on)

But what is wrong in what I said:
M=0 --> M^2 - MN = 0 --->
M<0 --> M^2 - MN < 0?---> Depends on N

Disprove me...that 2 such cases are not possible

If m<0, then \(m(m-n)=negative*negative=positive\), not negative as you've written.

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Re: If M < N, is M^2-MN < 0? [#permalink]

02 Jul 2014, 22:41

Please help Bunuel,

I definitely see how Statement 2 is sufficient, but I do not see how Statement 1 is.

I get that M(M-N) < 0 only if M>0, but if M = 0 as it is in {m,n}={0,4) then the expression M(M-N)=0

What gives?

L

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Re: If M < N, is M^2-MN < 0? [#permalink]

03 Jul 2014, 06:02

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yankeegooner wrote:

Please help Bunuel,

I definitely see how Statement 2 is sufficient, but I do not see how Statement 1 is.

I get that M(M-N) < 0 only if M>0, but if M = 0 as it is in {m,n}={0,4) then the expression M(M-N)=0

What gives?

I explained this twice above: if-m-n-is-m-2-mn-164993.html#p1310072

If M < 0, then M(M - N) > 0. The question asks: is M(M - N) < 0? What is the answer in this case? The answer to the question is NO.
If M = 0, then M(M - N) = 0. The question asks: is M(M - N) < 0? What is the answer in this case? The answer to the question is STILL NO.

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Re: If M < N, is M^2-MN < 0? [#permalink]

04 Jul 2014, 12:36

Thanks Bunuel. I think I get it now.

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Re: If M < N, is M^2-MN < 0? [#permalink]

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Re: If M < N, is M^2-MN < 0? [#permalink]

06 Oct 2020, 23:27

GMAT Data Sufficiency (DS) Questions

If M < N, is M^2-MN < 0?