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The price of an automobile decreased m percent between 2010

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The price of an automobile decreased m percent between 2010 [#permalink]

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New post 14 Dec 2012, 09:19
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The price of an automobile 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 < 100n – 100m
[Reveal] Spoiler: OA

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Re: The price of an automobile decreased m percent between 2010 [#permalink]

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New post 14 Dec 2012, 09:51
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The price of an automobile 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?

The price in 2010 - \(p\);
The price in 2011 - \(p*(1-\frac{m}{100})\);
The price in 2012 - \(p*(1-\frac{m}{100})*(1+\frac{n}{100})\);

Question: is \(p<p*(1-\frac{m}{100})*(1+\frac{n}{100})\)? --> is \(1<(1-\frac{m}{100})*(1+\frac{n}{100})\)? --> is \(100n-100m>mn\)?

(1) m < n. Not sufficient.
(2) mn < 100n – 100m. Directly answers the question. Sufficient.

Answer: B.

Identical question from OG to practice: the-annual-rent-collected-by-a-corporation-from-a-certain-89184.html
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Re: The price of an automobile decreased m percent between 2010 [#permalink]

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New post 14 Dec 2012, 12:14
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1 ) is clearly insufficient

2) \(MN\) \(<\) \(100 N - 100 M\)

here a faster approach is simply pickying a %. for instance: first we have a decrease so we could have 0.8 % (decrease by 20%) the an increse %, for instance 1.2 % (increase by 20 %).

Always the LHS is not smaller than the RHS

\(0.96 < 0.4\) The answer, even with other numbers will be always NO. So is sufficient

B is the answer
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Re: The price of an automobile decreased m percent between 2010 [#permalink]

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New post 13 Sep 2013, 01:07
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Bunuel wrote:
The price of an automobile 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?

The price in 2010 - \(p\);
The price in 2011 - \(p*(1-\frac{m}{100})\);
The price in 2012 - \(p*(1-\frac{m}{100})*(1+\frac{n}{100})\);

Question: is \(p<p*(1-\frac{m}{100})*(1+\frac{n}{100})\)? --> is \(1<(1-\frac{m}{100})*(1+\frac{n}{100})\)? --> is \(100n-100m>mn\)?

(1) m < n. Not sufficient.
(2) mn < 100n – 100m. Directly answers the question. Sufficient.

Answer: B.

Identical question from OG to practice: the-annual-rent-collected-by-a-corporation-from-a-certain-89184.html


Hi Bunuel,
How we can say that Stat.1 is NOT sufficient even without plugging in values? I'm getting it clear by plugging values but what I'd like to know is there any faster way to determine the sufficiency of Stat.1 from the inequality?

Would you please explain?
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Re: The price of an automobile decreased m percent between 2010   [#permalink] 13 Sep 2013, 01:07
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