og ds 143

simba12123 wrote:If m>0
N>0

is, (m+x)/(n+x)>m/n?


st. 1 m<n
st. 2 x>0

answer is c

I simplified this down to is n>m? Did I over simplify this statement.
I cross multiplied giving (m+x)(n)>(m)(n+x) then got ----> (mn)(xn)>(mn)(xn) ----> cancel out the mn's on both sides. Left with xn>mx subtract the x's from one side to other and you are left with IS N>M?


IMO answer is A

you cant do this without knowing whether x is positive or negative

let me explain

stmt 1: m<n

m=2 n=3

(2+x)/(3+x)>2/3

if x=-1

(2+(-1))/(3+(-1)) > 2/3

1/2>2/3--wrong

if x=+ve, x=1

(2+1)/(3+1) > 2/3

3/4>2/3--right

Stmt B-x>0--insufficent

by combining both,we come with two eq's

m<n and x>0...sufficient

Simba wants you to know that HE WILL NEVER EVER CROSS MULTIPLY THE INEQS again!!

8)

Simba, please do confirm this statement and explain why...

after reading the explanations on this I still need help.

Why can't the inequalities be cross multiplied? When i do cross multiply the inequalities here is how i simplify:

nm + nx > nm + mx (subtract nm from both sides_
nx > mx

Statement 1 - Sufficient b/c n is greater than m and they are being multiplied by the same number.

The only time we can cross multiplyis if we know signs of the quantities involved on the left hand side and right hand side.

This way if its positive we keep the signs the same and if we are multiplying or dividing by something negative we flip the sign..

Explaining more with Stubbornp's example

(m+x)/(n+x) >m/n

m=2 n=3 x=1

2+1/3+1 > 2/3

3/4>2/3

Cross multiply 9>8

m=2 n=3 x=-2.5



2+ -2.5 / 3+ -2.5 > 1/3

-.5 / .5 > 1/3 (m+x/n+x = -1)

-1 > 1/3

When we cross multiply we get -3> 1 which is not true


Since m+x / n+x is negative when we cross multiply we need to flip the signs

So it should -3 < 1 which is true


In the above problem we dont what the signs of m+x/n+x is going to be no way to know since from stmt I there is no info on x related to m and n

All we know is m < n




Hope this helps!

Rephrase the problem as follows

Is m+x/n+x > m/n can be rephrased as

Is m+x/n+x - m/n > 0

Is (m+x) n - m(n+x) / n(n+x) >0

Is mn+xn -mn -mx / n(n+x) >0

Is x(n-m) / n (n+x) >0


Clearly we can see that we need to know about m,n and x to answer the question and how much each one is one bigger or smaller than the other.


Regards,
CR

Thanks crayma...that explanation helps.

Sorry guys, but the answer should be B. Because we are only concerned with the sign of x as in the both fraction (m+x/n+x) and (m/n) m is always is the numerator and n is the denominator.

stmt B states that x is +ve, so always (m+x)/(n+x) > (m/n)

9/10 > 8/9 > 7/8 > 6/7 > 5/6 > 4/5 > 3/4 > 2/3 > 1/2

IF we are concerned with m and n, we are concerned with the sign of each and not if m>n of m<n.

So, this is either E (if we take into account that we miss the sign of m and n) or B as the explanation above.

Am I missing anything guys??

Yes, you are right Ian. But you know why, because usually our unconscious thinking says that fractions are less than 1, i dont know

Thanks again, it is clear now