If M

Question

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

(1) M <= 0
(2) N < 0

GMATBeast · Answer

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

(1) S
(2) S

Answer is...

bhatiamanu05 · Answer

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.

Bunuel · Answer

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.

GMATBeast · Answer

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?

Paris75 · Answer

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

Bunuel · Answer

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.

supermann · Answer

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.

Bunuel · Answer

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.

JusTLucK04 · Answer

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

Bunuel · Answer

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.

JusTLucK04 · Answer

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

Bunuel · Answer

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

yankeegooner · Answer

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?

Bunuel · Answer

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.

yankeegooner · Answer

Thanks Bunuel. I think I get it now.

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

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