GMATPrep Question - need expert help

[voodoo_child]

The price of a radio decreased m percent between 2010 and 2011 and then increased n percent between 2011 and 2012. Was the price of the automobile lower in 2010 than in 2012?

1) m<n
2) mn<100(n-m)


Here's what I did:

2010 :X = price of the radio
2011 :(1-m)X
2012 : (1-m) (1+n) X


Question : Is X< X(1-m)(1+n)?

Solving above equation, we get Is n-m>mn?


now, if m=0.2; n-0.2>0.2n => 0.8n>0.2 => n>0.25 (required)

1) m<n => if m=0.2; n>0.2 Not sufficient
2) mn <100(n-m) => 0.2n<100 (n-0.2) => 0.2n < 100n - 20 => 20<99.8n => n>0.2004

I ended up finding the same equation for 'n'. However, OA is B.

Can someone please tell me what's wrong with my method?

[aneesh.kg]

Taking m and n as percentages,

the questions is:
Is 100(n - m) > mn?

The eyes roll to Statement (2), because it says exactly that.
SUFFICIENT.

Statement(1):
If n = 0.5, m = 0.2
n - m = 0.3, nm = 0.1
n - m > nm YES!
BUT
If n = 0.5, m = 0.49 (when n and m are very close values)
n - m = 0.01
nm = 0.245
n - m < nm PROBLEM!
INSUFFICIENT

[spoiler](B)[/spoiler] is correct

[voodoo_child]

Taking m and n as percentages,

the questions is:
Is 100(n - m) > mn?

Aah ok. But how does it matter ? If I say that X reduced by 5 percent, it means that X(1-0.05) Correct?

A percent could also be expressed as decimal.....?

[aneesh.kg]

Right.
But, to notice that the Statement (2) says exactly what has to be found, you've to either take n and m as percentages initially (as given in the question) OR convert the Statement(2) so that n and m are fraction values (in your method).

If you want to take n and m as fractions, go ahead, but then:
Statement (2) is
(100m)*(100n) < 100*(100n - 100m)
mn < n - m
(where n and m are fractions, NOT percentages)

Now, the Statement(2) resembles the form that you had got.

[voodoo_child]

Exactly. The point is not about "decimals" or "percentages" but something else. Let's ignore the discussion about decimals and percentages.

If we substitute m=0.2; we get n>0.2 (1); However, the funny part is that I got n>0.2 from (2)!! However, the original equation requires n>0.25. (Please see my working). Unfortunately, I am not able to understand what's missing. Something is wrong....

Any thoughts?

[aneesh.kg]

Unfortunately, we cannot ignore the discussion on fractions and percentages. You will not realise your mistake without it.

In, Statement(2), you CANNOT move ahead with taking n and m as fractions and substituting into a Statement that is taking them as percentage values.
If you have to substitute m = 0.2, do it in
mn < n - m
which is the converted form of Statement (2)

[GMATGuruNY]

The price of a radio decreased m percent between 2010 and 2011 and then increased n percent between 2011 and 2012. Was the price of the automobile lower in 2010 than in 2012?

1) m<n
2) mn<100(n-m)

Let the original price = 100.
Percent decrease between 2010 and 2011 = (m/100)100 = m.
New price = 100-m.
Percent increase between 2011 and 2012 = (n/100)(100-m) = n - mn/100
Thus, the total percentage change = -m + n - mn/100 = n - m - mn/100.

For the price in 2012 to be lower than the price in 2010, the total percent change must be less than 0.
Question rephrased: Is n - m - mn/100 < 0?

Statement 1: m<n
If m=10 and n=20, then n - m - mn/100 = 20 - 10 - 200/100 = 8.
If m=90 and n=100, the n - m - mn/100 = 100 - 90 - 9000/100 = -80.
Since in the first case the total percent change is positive, and in the second case the total percent change is negative, INSUFFICIENT.

Statement 2: mn<100(n-m)
mn/100 < n-m
n - m - mn/100 > 0.
SUFFICIENT.

The correct answer is B.

[voodoo_child]

I think that my question is different. It's a conceptual one.

Let me try to explain it to you.

To begin with, let's say that m=0.2; Now, the original inequality requires us to find out whether .. "n-m>mn" holds good. Correct. OR,................(I)

if m= 0.2; Is n>0.25. . I think that you agree with the solution above.

1) n>m is insufficient because n>m => n>0.2. Therefore, the equation (I) doesnt hold good for n=0.21, 0.22..0.25. The eqation (I) holds good only for n>0.25.

2) this is where the problem is. We know that this equation is just a restatement of (I). However, if you substitute m=0.2; you will get n>0.2 which is same as (#1){AND NOT EQUATION (I)}. I am not able to understand - why is it that if I substitute m=0.2 in (I); I get n > 0.25. However, if I substitute m=0.2 in 2), I get n>0.2 (approx) and NOT n>0.25.

Do you see the problem? I am a bit lost.

[voodoo_child]

Unfortunately, we cannot ignore the discussion on fractions and percentages. You will not realise your mistake without it.

In, Statement(2), you CANNOT move ahead with taking n and m as fractions and substituting into a Statement that is taking them as percentage values.
If you have to substitute m = 0.2, do it in
mn < n - m
which is the converted form of Statement (2)

I think that my question is different. It's a conceptual one.

Let me try to explain it to you.

To begin with, let's say that m=0.2; Now, the original inequality requires us to find out whether .. "n-m>mn" holds good. Correct. OR,................(I)

if m= 0.2; Is n>0.25. . I think that you agree with the solution above.

1) n>m is insufficient because n>m => n>0.2. Therefore, the equation (I) doesnt hold good for n=0.21, 0.22..0.25. The eqation (I) holds good only for n>0.25.

2) this is where the problem is. We know that this equation is just a restatement of (I). However, if you substitute m=0.2; you will get n>0.2 which is same as (#1){AND NOT EQUATION (I)}. I am not able to understand - why is it that if I substitute m=0.2 in (I); I get n > 0.25. However, if I substitute m=0.2 in 2), I get n>0.2 (approx) and NOT n>0.25.

Do you see the problem? I am a bit lost.