A casino pays players with chips that are either turquoise

Expert replies

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2585; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Wed Nov 28, 2018 2:45 pm

Timer

00:00

Answers

Stats

Difficulty—

Source: Manhattan Prep

A casino pays players with chips that are either turquoise- or violet- colored. If each turquoise- colored chip is worth t dollars, and each violet- colored chip is worth v dollars, where t and v are integers, what is the combined value of four turquoise- colored chips and two violet- colored chips?

1) The combined value of six turquoise- colored chips and three violet- colored chips is 42 dollars.
2) The combined value of five turquoise- colored chips and seven violet- colored chips is 53 dollars.

The OA is D.

Like this post

Source: Beat The GMAT — Data Sufficiency | Wed Nov 28, 2018 2:45 pm

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Nov 28, 2018 4:20 pm

Hi All,

We're told that a casino pays players with chips that are either turquoise- or violet- colored; each turquoise- colored chip is worth T dollars, and each violet- colored chip is worth V dollars, where T and V are INTEGERS. We're asked for the combined value of four turquoise- colored chips and two violet- colored chips. This question is based on a number of different math skills - as well as your ability to 'play around' with a question and look for Number Properties.

To start, we're asked to find the value of 4T + 2V. This can be rewritten as "what is the value of 2(2T + V)?"

1) The combined value of six turquoise- colored chips and three violet- colored chips is 42 dollars.

The information in Fact 1 gives us the equation 6T + 3V = 42.
The entire equation can be 'divided by 3' to give us 2T + V = 14.
With this equation, we CAN answer the question --> 2(2T+V) = 2(14) = 28
Fact 1 is SUFFICIENT

2) The combined value of five turquoise- colored chips and seven violet- colored chips is 53 dollars.

The information in Fact 2 gives us the equation 5T + 7V = 53.

At first glance, this might appear insufficient, since we have 2 variables, but only one equation. However, the total (53) is relatively small for a sum that is based off of TWELVE coins. Since both T and V are INTEGERS, it's possible that there's only one solution to this equation (and if that's the case, then Fact 2 is also sufficient).

We're essentially adding a multiple of 5 to a multiple of 7 and ending up with 53. You can look for the options rather easily by listing out all of the multiples:
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Multiples of 7: 7, 14, 21, 28, 35, 42, 49

Looking at these two lists, can you pull a number from each and get a sum of 53...? You would probably find it easiest to start with a multiple of 7, since the 'rest' of the total would have to be from the multiple of 5 (meaning that that 'piece' would end in a 5 or a 0).

With 28 and 25 (re: 4x7 and 5x5), you get a total of 53. There is no other option though. There's just one solution.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Wed Nov 28, 2018 5:50 pm

BTGmoderatorLU wrote:Source: Manhattan Prep

A casino pays players with chips that are either turquoise- or violet- colored. If each turquoise- colored chip is worth t dollars, and each violet- colored chip is worth v dollars, where t and v are integers, what is the combined value of four turquoise- colored chips and two violet- colored chips?

1) The combined value of six turquoise- colored chips and three violet- colored chips is 42 dollars.
2) The combined value of five turquoise- colored chips and seven violet- colored chips is 53 dollars.

\[{\text{chips}}\,\left\{ \begin{gathered}
\,{\text{turqu}}:\$ \,t\,\,{\text{each}} \hfill \\
\,{\text{violet}}:\$ \,v\,\,{\text{each}} \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\left( {t,v \geqslant 1\,\,\,{\text{ints}}\,\,\left( * \right)} \right)\]
\[? = 4t + 2v\,\,\,\left[ \$ \right]\]

\[\left( 1 \right)\,\,6t + 3v = 42\,\,\,\left[ \$ \right]\,\,\,\,\,\mathop \Rightarrow \limits^{:\,3} \,\,2t + v = 14\,\,\,\left[ \$ \right]\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,2} \,\,\,\,\,? = 28\,\,\,\left[ \$ \right]\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\]

\[\left( 2 \right)\,\,5t + 7v = 53\,\,\,\left[ \$ \right]\,\,\,\,\, \Rightarrow \,\,53 - 7v = 5t\,\,,\,\,t\mathop \geqslant \limits^{\left( * \right)} 1\,\,\operatorname{int} \,\,\,\, \Rightarrow \,\,1\mathop \leqslant \limits^{\left( * \right)} v\,\,\left( {\operatorname{int} } \right) \leqslant 7\,\,\,\left( {**} \right)\]
\[\frac{{\left( {3 + 50} \right) - \left( {5v + 2v} \right)}}{5} = \operatorname{int} \,\,\,\, \Leftrightarrow \,\,\,\,\frac{{3 - 2v}}{5} = \operatorname{int} \,\,\,\,\mathop \Leftrightarrow \limits^{\left( {**} \right)} \,\,\,\,v = 4\,\,\,\,\mathop \Rightarrow \limits^{\left( 2 \right)} \,\,\,\,t = 5\]
\[\left( {t,v} \right)\,\,{\text{unique}}\,\,\,\, \Rightarrow \,\,\,{\text{?}}\,\,\,{\text{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}{\text{.}}\]

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

Like this post

swerve: Legendary Member; Posts: 2564; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Thu Nov 29, 2018 9:34 am

Given
t = Value of one turquoise chip.
v = Value of one violet chip.

we have to find :
4t + 2v = ?

Statement (1) The combined value of six turquoise- colored chips and three violet- colored chips is 42 dollars.

6t + 3v = 42
simplify

3(2t + v ) = 42
2t + v = 14

So if we multiply the above equation by 2 we get
4t + 2v = 28

so, Statement 1 is sufficient.

Statement(2) The combined value of five turquoise- colored chips and seven violet- colored chips is 53 dollars.
5t + 7v = 53

Now if we analyse we see the value v can take are:

v = 1 so 7v = 7
v = 2 so 7v = 14
v = 3 so 7v = 21
v = 4 so 7v = 28
v = 5 so 7v = 35
v = 6 so 7v = 42
v = 7 so 7v = 49

Now if we put the value of 7v in the equation 5t + 7v =53 we get:

for v = 1 so 7v = 7 ----------> 5t = 46
for v = 2 so 7v = 14 ----------> 5t = 39
for v = 3 so 7v = 21 ----------> 5t = 32
for v = 4 so 7v = 28 ----------> 5t = 25 ---> only possible vaule since t and v are both integer
for v = 5 so 7v = 35 ----------> 5t = 18
for v = 6 so 7v = 42 ----------> 5t = 9
for v = 7 so 7v = 49 ----------> 5t = 4

So from statement 2 we get value of t =5, v = 4 so ve can get the value of 4t + 2v = 28.

So, the OA is D

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review