A casino pays players with chips that are either turquoise- or violet-

Question

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.

lovenish · Answer

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?

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 OA is D

EMPOWERgmatRichC · Answer

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

fskilnik · Answer

{	ext{chips}}\,\left\{ \begin{gathered}
 \,{	ext{turqu}}:\$ \,t\,\,{	ext{each}} \hfill \
 \,{	ext{violet}}:\$ \,v\,\,{	ext{each}} \hfill \ 
\end{gathered} ight.\,\,\,\,\,\,\left( {t,v \geqslant 1\,\,\,{	ext{ints}}\,\,\left( * ight)} ight)

? = 4t + 2v\,\,\,\left

\left( 1 ight)\,\,6t + 3v = 42\,\,\,\left \,\,\,\,\,\mathop \Rightarrow \limits^{:\,3} \,\,2t + v = 14\,\,\,\left \,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,2} \,\,\,\,\,? = 28\,\,\,\left \,\,\,\,\, \Rightarrow \,\,\,\,\,{	ext{SUFF}}.

\left( 2 ight)\,\,5t + 7v = 53\,\,\,\left \,\,\,\,\, \Rightarrow \,\,53 - 7v = 5t\,\,,\,\,t\mathop \geqslant \limits^{\left( * ight)} 1\,\,\operatorname{int} \,\,\,\, \Rightarrow \,\,1\mathop \leqslant \limits^{\left( * ight)} v\,\,\left( {\operatorname{int} } ight) \leqslant 7\,\,\,\left( {**} ight)

\frac{{\left( {3 + 50} ight) - \left( {5v + 2v} ight)}}{5} = \operatorname{int} \,\,\,\, \Leftrightarrow \,\,\,\,\frac{{3 - 2v}}{5} = \operatorname{int} \,\,\,\,\mathop \Leftrightarrow \limits^{\left( {**} ight)} \,\,\,\,v = 4\,\,\,\,\mathop \Rightarrow \limits^{\left( 2 ight)} \,\,\,\,t = 5

\left( {t,v} ight)\,\,{	ext{unique}}\,\,\,\, \Rightarrow \,\,\,{	ext{?}}\,\,\,{	ext{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{	ext{SUFF}}{	ext{.}}

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

jabhatta2 · Answer

chetan2u ,  VeritasKarishma ,  Bunuel , nick1816,  GMATBusters

Hi Experts -

While i did get this accurate -- i took 3.10 seconds to get it accurate

I was able get S1 easily but S2 took a little time because i drew out the table

My strategy is to draw out the table for questions like S2

Question : On the test, Is it worth my time (extra 1 minute) to do this problem and get it right (but spending 1 minute extra) or rather skipping this problem entirely and spending the extra 1 minute on perhaps easier questions

I am able to get it right eventually but in 3 minutes (above the 2 min mark)

Please let me know your thoughts !

GMATBusters · Answer

This is a 700 level question (95%). whether you should put 3 min on one question or not depends on many factors:
  how much time u take in easy questions, if you can do easier questions under 1 min and moderate level under 1.5 min, then you can afford to min 3 min on 95% hard level question. 
 but if you are taking 2 min even in easier level, you cant afford to so. 
 how much time generally remains at the end in ur GMAT exam, or you struggle in completing the questions itself. 
 whats your mock score? 
 whats your target Score?

jabhatta2 · Answer

Hi  GMATBusters

Can I respond in perhaps 3 weeks with these details and thus followup on this thread with you ?

I haven't taken an exam for a while so I don't have this information on my fingertips

Would it be okay if I give this in 3 weeks and take it from there ?

Posted from my mobile device

GMATinsight · Answer

Hi jabhatta@umail.iu.edu When we say the Quant questions give you an average time per question = 2 mins Please mind the fact that it's the AVERAGE time per question There are questions that may be solved in 45 seconds too so it's imperative that a few question might demand more than 2 mins because they deserve it. In any situation, if you are aptly prepared for the exam then skipping a question does NOT qualify to be an effective test taking strategy. However if the situation is completely uncontrollable then you have to use your managerial aptitude (which the test intends to keep in check) and take a calculated decision. In such unwanted scenarios, you might want to skip time-consuming question from unpleasant topics which have shown a pattern to hurt your accuracy. I hope it help!

GMATBusters · Answer

Yes, remember to revert with the mock score, so that I can access the condition better.

Happy Learning!!!

KarishmaB · Answer

Depends on where you are in the test time-wise. If you have enough time and few questions left, you can spend extra time on one question. If you are already short, skip as soon as you figure that it is a time consuming question and utilise that time in other questions.

Note that 2 mins is just the average. Your actual question solving time will be all over the place - from 30 secs to 4 mins. You need to take intelligent calls throughout the test. Try to focus on holistic (faster) methods of solving while practicing.

milkyway · Answer

Interest Ask. Perhaps the color is somehow related to the value of the chips?

bumpbot · Answer

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A casino pays players with chips that are either turquoise- or violet-

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