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
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you cant do this without knowing whether x is positive or negativesimba12123 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
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
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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...
8)
Simba, please do confirm this statement and explain why...
LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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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.
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.
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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!
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!
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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
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
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??
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??
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hijazim wrote: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??
In your numerical example above, you've only considered examples where m is less than n. Notice that if we use the same numbers, but allow m to be greater than n, we have:
10/9 < 9/8 < 8/7 < ... < 2/1
so it is genuinely important to know that m < n, and Statement 1 is required. The answer is C.
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