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The price per share of Stock X increased by 10 percent over

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The price per share of Stock X increased by 10 percent over  [#permalink]

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New post 18 Dec 2012, 06:47
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The price per share of Stock X increased by 10 percent over the same time period that the price per share of Stock Y decreased by 10 percent. The reduced price per share of Stock Y was what percent of the original price per share of Stock X ?

(1) The increased price per share of Stock X was equal to the original price per share of Stock Y.
(2) The increase in the price per share of Stock X was 10/11 the decrease in the price per share of Stock Y.
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Re: The price per share of Stock X increased by 10 percent over  [#permalink]

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New post 18 Dec 2012, 06:51
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The price per share of Stock X increased by 10 percent over the same time period that the price per share of Stock Y decreased by 10 percent. The reduced price per share of Stock Y was what percent of the original price per share of Stock X ?

Let the initial price per share of stock X be \(x\), so after increase by 10% it would become \(1.1x\);
Let the initial price per share of stock Y be \(y\), so after decrease by 10% it would become \(0.9y\).

Question: \(\frac{0.9y}{x}=\frac{9y}{10x}=?\)

(1) The increased price per share of Stock X was equal to the original price per share of Stock Y --> \(1.1x=y\) --> \(\frac{9y}{10x}=\frac{9*1.1x}{10x}=0.99\) or 99%. Sufficient.

(2) The increase in the price per share of Stock X was 10/11 the decrease in the price per share of Stock Y --> \(1.1x-x=\frac{10}{11}*(y-0.9y)\) --> \(0.1x=\frac{10}{11}*0.1y\) --> \(1.1x=y\) the same info as in (1). Sufficient

Answer: D.
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Re: The price per share of Stock X increased by 10 percent over  [#permalink]

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New post 13 Dec 2017, 07:49
Bunuel wrote:
The price per share of Stock X increased by 10 percent over the same time period that the price per share of Stock Y decreased by 10 percent. The reduced price per share of Stock Y was what percent of the original price per share of Stock X ?

Let the initial price per share of stock X be \(x\), so after increase by 10% it would become \(1.1x\);
Let the initial price per share of stock Y be \(y\), so after decrease by 10% it would become \(0.9y\).

Question: \(\frac{0.9y}{x}=\frac{9y}{10x}=?\)

(1) The increased price per share of Stock X was equal to the original price per share of Stock Y --> \(1.1x=y\) --> \(\frac{9y}{10x}=\frac{9*1.1x}{10x}=0.99\) or 99%. Sufficient.

(2) The increase in the price per share of Stock X was 10/11 the decrease in the price per share of Stock Y --> \(1.1x-x=\frac{10}{11}*(y-0.9y)\) --> \(0.1x=\frac{10}{11}*0.1y\) --> \(1.1x=y\) the same info as in (1). Sufficient

Answer: D.



Shouldn't the highlighted part be [ y- .1y] as its 10/11 of the decease and it is to be decreased by 10 %, correct me if I'm wrong.
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Re: The price per share of Stock X increased by 10 percent over  [#permalink]

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New post 13 Dec 2017, 08:06
mtk10 wrote:
Bunuel wrote:
The price per share of Stock X increased by 10 percent over the same time period that the price per share of Stock Y decreased by 10 percent. The reduced price per share of Stock Y was what percent of the original price per share of Stock X ?

Let the initial price per share of stock X be \(x\), so after increase by 10% it would become \(1.1x\);
Let the initial price per share of stock Y be \(y\), so after decrease by 10% it would become \(0.9y\).

Question: \(\frac{0.9y}{x}=\frac{9y}{10x}=?\)

(1) The increased price per share of Stock X was equal to the original price per share of Stock Y --> \(1.1x=y\) --> \(\frac{9y}{10x}=\frac{9*1.1x}{10x}=0.99\) or 99%. Sufficient.

(2) The increase in the price per share of Stock X was 10/11 the decrease in the price per share of Stock Y --> \(1.1x-x=\frac{10}{11}*(y-0.9y)\) --> \(0.1x=\frac{10}{11}*0.1y\) --> \(1.1x=y\) the same info as in (1). Sufficient

Answer: D.



Shouldn't the highlighted part be [ y- .1y] as its 10/11 of the decease and it is to be decreased by 10 %, correct me if I'm wrong.
Regards


It's should be the way it is written.

The decrease in the price per share of Stock Y is \(y - 0.9y\). 10/11 times that is \(\frac{10}{11}*(y-0.9y)\). I think you misunderstood the statement.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The price per share of Stock X increased by 10 percent over  [#permalink]

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New post 13 Dec 2017, 08:16
Bunuel wrote:
mtk10 wrote:
Bunuel wrote:
The price per share of Stock X increased by 10 percent over the same time period that the price per share of Stock Y decreased by 10 percent. The reduced price per share of Stock Y was what percent of the original price per share of Stock X ?

Let the initial price per share of stock X be \(x\), so after increase by 10% it would become \(1.1x\);
Let the initial price per share of stock Y be \(y\), so after decrease by 10% it would become \(0.9y\).

Question: \(\frac{0.9y}{x}=\frac{9y}{10x}=?\)

(1) The increased price per share of Stock X was equal to the original price per share of Stock Y --> \(1.1x=y\) --> \(\frac{9y}{10x}=\frac{9*1.1x}{10x}=0.99\) or 99%. Sufficient.

(2) The increase in the price per share of Stock X was 10/11 the decrease in the price per share of Stock Y --> \(1.1x-x=\frac{10}{11}*(y-0.9y)\) --> \(0.1x=\frac{10}{11}*0.1y\) --> \(1.1x=y\) the same info as in (1). Sufficient

Answer: D.





Shouldn't the highlighted part be [ y- .1y] as its 10/11 of the decease and it is to be decreased by 10 %, correct me if I'm wrong.
Regards


It's should be the way it is written.

The decrease in the price per share of Stock Y is \(y - 0.9y\). 10/11 times that is \(\frac{10}{11}*(y-0.9y)\). I think you misunderstood the statement.





But the stem states that decrease in y is 10 %, Would we not write this question 1 -.1 =.9 . Sorry, i guess I am overlooking something. I am not understanding why are you subtracting .9y when question states that decrease is 10 % not 90 %.
Kindly explain
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Re: The price per share of Stock X increased by 10 percent over  [#permalink]

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New post 13 Dec 2017, 08:19
mtk10 wrote:
But the stem states that decrease in y is 10 %, Would we not write this question 1 -.1 =.9 . Sorry, i guess I am overlooking something. I am not understanding why are you subtracting .9y when question states that decrease is 10 % not 90 %.
Kindly explain



The price per share of Stock Y decreased by 10 percent:
Let the initial price per share of stock Y be \(y\), so after decrease by 10% it would become \(0.9y\).
Amount by which it decreased is initial price - new price = y-0.9y.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: The price per share of Stock X increased by 10 percent over  [#permalink]

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New post 20 Sep 2018, 12:09
Walkabout wrote:
The price per share of Stock X increased by 10 percent over the same time period that the price per share of Stock Y decreased by 10 percent. The reduced price per share of Stock Y was what percent of the original price per share of Stock X ?

(1) The increased price per share of Stock X was equal to the original price per share of Stock Y.
(2) The increase in the price per share of Stock X was 10/11 the decrease in the price per share of Stock Y.


Important: Bunuel´s explanations (above) ARE FUNDAMENTAL to students who are beginning their "GMAT Quant development".
The solution we present below is for the students who already know "the basics".

(That´s why we postpone Data Sufficiency learning, in our course, till the student´s maturity has changed considerably!)

In our method we make a clear distinction between Problem Solving and Data Sufficiency.

In Data Sufficiency problems, we are FOCUSED in the UNIQUENESS OR NOT of a (numerical) value, not in calculations related to the possible value(s)...

Please read our solution, that starts below, with that in mind!

\(\left( {{\text{DATA}}} \right)\,\,\,\,X\,\,\, \to \,\,\,\frac{{11}}{{10}}X\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,Y\,\,\, \to \,\,\,\frac{9}{{10}}Y\)

\(\left( {{\text{FOCUS}}} \right)\,\,\,\,? = \frac{{\,\frac{9}{{10}}Y\,}}{X}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\boxed{? = \frac{Y}{X}}\,\,\,\,\,\,\,\,\,\,\,\left( {X \ne 0\,\,\,\,{\text{implicitly}}} \right)\)

\(\left( 1 \right)\,\,\,\frac{{11}}{{10}}X = Y\,\,\,\, \Rightarrow \,\,\,\,\,\frac{Y}{X}\,\,\,{\text{unique}}\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\)

\(\left( 2 \right)\,\,\,\frac{1}{{10}}X = \frac{{10}}{{11}}\left( {\frac{1}{{10}}Y} \right)\,\,\,\, \Rightarrow \,\,\,\,\,\frac{Y}{X}\,\,\,{\text{unique}}\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\)

(If you realize this is BRUTAL, SAFE and POWERFUL, you understood correctly. )


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: The price per share of Stock X increased by 10 percent over &nbs [#permalink] 20 Sep 2018, 12:09
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