og ds 143

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simba12123: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Tue Oct 14, 2008 1:05 pm

og ds 143

by simba12123 » Sun Nov 02, 2008 7:04 pm

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

Advancing to be reckoned with!

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Source: Beat The GMAT — Data Sufficiency | Sun Nov 02, 2008 7:04 pm

stubbornp: Master | Next Rank: 500 Posts; Posts: 496; Joined: Sun May 04, 2008 11:01 pm; Location: mumbai; Thanked: 7 times; GMAT Score:640

Re: og ds 143

by stubbornp » Sun Nov 02, 2008 8:43 pm

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

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pm; Thanked: 237 times; Followed by:25 members; GMAT Score:730

by logitech » Sun Nov 02, 2008 11:33 pm

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...

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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anniev2: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Tue Sep 09, 2008 11:39 am

by anniev2 » Tue Mar 17, 2009 4:57 pm

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.

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

by cramya » Tue Mar 17, 2009 5:10 pm

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!

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

by cramya » Tue Mar 17, 2009 5:18 pm

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

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anniev2: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Tue Sep 09, 2008 11:39 am

by anniev2 » Tue Mar 17, 2009 5:24 pm

Thanks crayma...that explanation helps.

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hijazim: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Sun Feb 22, 2009 11:27 pm; GMAT Score:600

by hijazim » Wed Mar 18, 2009 6:12 am

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??

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Wed Mar 18, 2009 6:50 am

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.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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