inequalities

Question

Is m not equal to n? 1) m + n < 0 2) mn < 0

raju232007 · Answer

statement 1:

m+n<0

Here both m and n can be negative and satisfy the above condition..
For example let m=-1 and n=-1
-2<0

Consider a case wherein m and are different but satisfy the above statement

Let m=-2 and n=1
-1<0

Insufficient

statement 2

mn<0

for the above statement to be true any one of the numbers ((either m or n) must be negative.

So this statement clearly indicates that m is not equal to n

Sufficient

The ans is B..Hope this helps

beater · Answer

Here is how I approached stat 1:

Stat 1:
m+n<0

m < -n
Values for m and n:

-2 < -1

-4 < -2

-5 < -4

As you can see none of the above values would allow m to equal n. Hence sufficient. However, there is definitely somethign wrong with my analysis becuase the answer is B. Could you please reivew my working and let me know what I'm doing wrong for statement 1. Thanks!

Gmatss · Answer

beater wrote:Here is how I approached stat 1:

Stat 1:
m+n<0

m < -n
Values for m and n:

-2 < -1

-4 < -2

-5 < -4

As you can see none of the above values would allow m to equal n. Hence sufficient. However, there is definitely somethign wrong with my analysis becuase the answer is B. Could you please reivew my working and let me know what I'm doing wrong for statement 1. Thanks!

Think about 0.
0<0 does not always satisfy the condition

bekkilyn · Answer

Here's what I'm getting. I also went ahead and changed m + n < 0 to m < -n.

For this first statement, m could equal n if m = -2 and n = - 2:

-2 + -2 < 0 or -2 < -(-2)

Or m could not equal n if m = -7 and n = 3:

-7 + 3 < 0 or -7 < -3.

Since m and n could either be equal or not equal, we don't have enough information to answer the question, so insufficient.

beater · Answer

Perfect. I know exactly where I went wrong. Thanks for all your input guys!

lunarpower · Answer

hmm.

in general, you will probably find that "m + n < 0" is a much more useful phrasing than is "m < -n".

if you don't see why, then consider a test case, such as m = -5, n = 6.
with the former version, it's easy to see that the statement is false; because the size (i.e., absolute value) of n is larger, it's easy to see that adding m + n will create a positive result.

with the latter version, it's much more difficult to verify the falsity of the given inequality, because not only do you have to flip the sign of the '6' but you also have to evaluate an inequality involving two negative numbers, which is not an easy thing to do.

in general, though, you should go with whichever rephrase is most convenient for you. if you are one of the select few who prefer "m < -n" to "m + n is negative", then go for it.

Ron has been teaching various standardized tests for 20 years.

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yezz · Answer

beater wrote:Is m not equal to n? 1) m + n < 0 2) mn < 0 FROM 1 could be = (-5,-5) could be not = ( -5,-3)....insuff from 2 they have different signs thus they are not = ............b

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