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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

by BTGmoderatorDC » Mon Sep 17, 2018 6:00 pm

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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

OA D

Source: Official Guide
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Sep 17, 2018 10:15 pm

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BTGmoderatorDC 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

OA D

Source: Official Guide
Say, the original price per share of stock X is x, so after the increase of 10%, it would be 1.1x;
Let the original price per share of stock Y is y, so after the decrease of 10%, it would be 0.9y.

Question: What is the value of (0.9y/x)*100% = 90*(y/x)%?

If we get the value of y/x, we get the answer.

Question rephrased: What's the value of y/x?

(1) The increased price per share of Stock X was equal to the original price per share of Stock Y.

=> 1.1x = y

y/x = 1.1. 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.

=> 0.1x = (10/11)*(0.1y)
y/x = 1.1. Sufficient

The correct answer: D

Hope this helps!

-Jay
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by swerve » Tue Sep 18, 2018 3:53 pm

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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: 0.9y / x = 9y / 10 = ?

(1) The increased price per share of Stock X was equal to the original price per share of Stock Y --> 1.1x=y --> 9y / 10x= 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 = (10/11)*(y-0.9y) --> 0.1x = 10/11 * 0.1y --> 1.1x = y the same info as in (1). Sufficient.

Hence, D is the correct answer.
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by fskilnik@GMATH » Thu Sep 20, 2018 10:59 am

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BTGmoderatorDC 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

Source: Official Guide
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)...

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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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