For each customer, a bakery charges p dollars for the first

This topic has expert replies
Moderator
Posts: 2205
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Source: GMAT Prep

For each customer, a bakery charges p dollars for the first loaf of bread bought by the customer and charges q dollars for each additional loaf bought by the customer. What is the value of q?

(1) A customer who buys 2 loaves is charged 10 percent less per loaf than a customer who buys a single loaf.
(2) A customer who buys 6 loaves of bread is charged 10 dollars.

The OA is C.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Sun Sep 09, 2018 11:11 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGmoderatorLU wrote:Source: GMAT Prep

For each customer, a bakery charges p dollars for the first loaf of bread bought by the customer and charges q dollars for each additional loaf bought by the customer. What is the value of q?

(1) A customer who buys 2 loaves is charged 10 percent less per loaf than a customer who buys a single loaf.
(2) A customer who buys 6 loaves of bread is charged 10 dollars.

The OA is C.
Let's take each statement one by one.

(1) A customer who buys 2 loaves is charged 10 percent less per loaf than a customer who buys a single loaf.

=> (p + q)/2 = 90% of p
(p + q)/2 = 0.9p
p + q = 1.8p
q = 0.8p

Can't get the value of q since we do not have the value of p. Insufficient.

(2) A customer who buys 6 loaves of bread is charged 10 dollars.

=> p + 5q = 10

Can't get the value of q since we do not have the value of p. Insufficient.

(1) and (2) together

From q = 0.8p and p + 5q = 10, we get q = $1.60. Sufficient.

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GRE Prep

Locations: GMAT Classes San Diego | GRE Prep Course Boston | GRE Prep Chicago | TOEFL Prep Classes NYC | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

by fskilnik@GMATH » Sun Sep 16, 2018 11:40 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGmoderatorLU wrote:Source: GMAT Prep

For each customer, a bakery charges p dollars for the first loaf of bread bought by the customer and charges q dollars for each additional loaf bought by the customer. What is the value of q?

(1) A customer who buys 2 loaves is charged 10 percent less per loaf than a customer who buys a single loaf.
(2) A customer who buys 6 loaves of bread is charged 10 dollars.
\[\$ \,p\,\,\,:\,\,{\text{first}}\,\,{\text{loaf}}\]
\[{\text{\$ }}q\,\,\,{\text{:}}\,\,\,{\text{any}}\,\,{\text{additional}}\,\,{\text{loaf}}\]
\[? = q\]

\[\left( 1 \right)\,\,{\left( {\frac{{\,{\text{charge}}\,}}{{{\text{loaf}}}}} \right)_{\,2\,\,{\text{loaves}}}} = \frac{{p + q}}{2}\,\,\,\,\mathop = \limits^{{\text{given}}} \,\,\frac{9}{{10}}p\,\,\,\,\, \Rightarrow \,\,\,\, \ldots \,\,\,\,\, \Rightarrow \,\,\,\frac{q}{p} = \frac{4}{5}\]
\[\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {p,q} \right) = \left( {0.5,0.4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 0.4 \hfill \\
\,{\text{Take}}\,\,\left( {p,q} \right) = \left( {1,0.8} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 0.8 \hfill \\
\end{gathered} \right.\]

\[\left( 2 \right)\,\,6\,\,{\text{loaves}}\,\,{\text{for}}\,\,\$ 10\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {p\,;q} \right) = \left( {2\,;\frac{8}{5}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{8}{5} \hfill \\
\,{\text{Take}}\,\,\left( {p\,;q} \right) = \left( {3\,;\frac{7}{5}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{7}{5} \hfill \\
\end{gathered} \right.\]
\[\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered}
p + 5q = 10 \hfill \\
\frac{q}{p} = \frac{4}{5} \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{k}}\,\,{\text{technique}}} \,\,\,\,\left( {5k} \right) + 5\left( {4k} \right) = 10\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 4k\,\,{\text{unique}}\,\]

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