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

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Manager
Joined: 02 Dec 2012
Posts: 178
The price per share of Stock X increased by 10 percent over [#permalink]

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18 Dec 2012, 06:47
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78% (01:31) correct 22% (01:41) wrong based on 777 sessions

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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.
Math Expert
Joined: 02 Sep 2009
Posts: 47109
Re: The price per share of Stock X increased by 10 percent over [#permalink]

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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

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Manager
Joined: 02 Jan 2017
Posts: 81
Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34
GPA: 3.41
Re: The price per share of Stock X increased by 10 percent over [#permalink]

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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

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
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Math Expert
Joined: 02 Sep 2009
Posts: 47109
Re: The price per share of Stock X increased by 10 percent over [#permalink]

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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

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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Manager
Joined: 02 Jan 2017
Posts: 81
Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34
GPA: 3.41
Re: The price per share of Stock X increased by 10 percent over [#permalink]

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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

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
Math Expert
Joined: 02 Sep 2009
Posts: 47109
Re: The price per share of Stock X increased by 10 percent over [#permalink]

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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.
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Re: The price per share of Stock X increased by 10 percent over   [#permalink] 13 Dec 2017, 08:19
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