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A store sells only two types of shirts, branded and

by AAPL » Mon Nov 26, 2018 4:39 am

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A store sells only two types of shirts, branded and non-branded. All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts. What is the number of branded shirts that the store sold on that day?

1. The store sold more than 20 branded shirts on that day.
2. On that day, the total sales from shirts were between $1604 and $1674.

OA B
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Nov 26, 2018 6:41 am

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AAPL wrote:e-GMAT

A store sells only two types of shirts, branded and non-branded. All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts. What is the number of branded shirts that the store sold on that day?

1. The store sold more than 20 branded shirts on that day.
2. On that day, the total sales from shirts were between $1604 and $1674.

OA B
Given: All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts.
Let B = # of branded shirts sold
Let N = # of non-branded shirts sold
If a TOTAL of 30 shirts were sold, we can write: N + B = 30

Target question: What is the value of B?

Statement 1: The store sold more than 20 branded shirts on that day.
All we know so far is that N + B = 30
So, it's possible that B = 21, B = 22, B = 23, etc
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: On that day, the total sales from shirts were between $1604 and $1674.
Branded shirts cost $60 each, and all the non-branded shirts cost $20 each
We can write: 20N + 60B = TOTAL sales
This means: 20N + 60B = some value between $1604 and $1674

Let's see if we can also use the fact that N + B = 30 to help us answer the target question.
We can rewrite 60B as 20B + 40B and see what happens.
We get: 20N + 20B + 40B = some value between $1604 and $1674
Factor first two terms to get: 20(N + B)+ 40B = some value between $1604 and $1674
Replace N + B with 30 to get: 20(30)+ 40B = some value between $1604 and $1674
Evaluate: 600 + 40B = some value between $1604 and $1674
Subtract 600 from both sides to get: 40B = some value between $1004 and $1074

IMPORTANT: B is a POSITIVE INTEGER.
If B = 25, then 40B = 40(25) = 1000, which is NOT between $1004 and $1074
If B = 26, then 40B = 40(26) = 1040, which IS between $1004 and $1074
If B = 27, then 40B = 40(27) = 1080, which is NOT between $1004 and $1074

So, there's only 1 possible value that satisfies statement 2.
The answer to the target question is B = 26
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Brent
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by fskilnik@GMATH » Tue Nov 27, 2018 6:33 pm

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AAPL wrote:e-GMAT

A store sells only two types of shirts, branded and non-branded. All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts. What is the number of branded shirts that the store sold on that day?

1. The store sold more than 20 branded shirts on that day.
2. On that day, the total sales from shirts were between $1604 and $1674.
\[30\,{\text{units}}\,\,\,\left\{ \begin{gathered}
\,B\,\,{\text{branded}}\,{\text{,}}\,\,{\text{\$ 60}}\,\,{\text{each}} \hfill \\
\,N\,\,{\text{non - branded}}\,{\text{,}}\,\,{\text{\$ 20}}\,\,{\text{each}} \hfill \\
\end{gathered} \right.\]
\[? = B\]

\[\left( 1 \right)\,\,B > 20\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {B,N} \right) = \left( {21,9} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 21 \hfill \\
\,{\text{Take}}\,\,\left( {B,N} \right) = \left( {22,8} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 22 \hfill \\
\end{gathered} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{INSUFF}}.\]

\[\left( 2 \right)\,\,1604 < 60B + 20\left( {30 - B} \right) < 1674\,\,\,\,\,\,\left[ \$ \right]\]
\[1604 < 40B + 600 < 1674\]
\[25 \cdot 40 + 4 = 1004 < 40B < 1074 = 26 \cdot 40 + 34\]
\[25 + \frac{4}{{40}} < B < 26 + \frac{{34}}{{40}}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = B = 26\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\]


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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