8 years from now, the bottle of wine labeled "Aged" will be

[rgaddam]

Question: 8 years from now, the bottle of wine labeled "Aged" will be 7 times as old as the bottle of wine labeled "Table". 1 year ago, the bottle of wine labeled "Table" was one-fourth as old as the bottle of wine labeled "Vintage." If the "Aged" bottle was 20 times as old as the "Vintage" bottle 2 years ago, then how old is each bottle now?

Guide: Word Translations 4 ed. Chapter # 1 - In Action problem # 15

The explanation says "Let t be the current age of the Table wine. We fill in the rest of the row by adding and subtracting time."

This works good as one can come up with straight forward equations for "Aged" and "Vintage" wines at a point of time.

When I solved this problem before looking at the solution, I said " Let a be the current age of Aged wine" and solved the rest of the problem to arrive at the answers. The difference I noticed between picking t vs a as the current age is that with "a as current age of aged wine" the equations become little complex.

The reasons I picked "a as the current age of aged wine" are the question does not ask the age of 1 particular wine - it asks the age of each of them and when I read the question, out of the 3 equations(a=7t, t=v/4 and a=20v) 2 of them had "a" in them.

My question is how to pick a variable to represent the current age so that the equations to solve do not become needlessly complex.

Thanks

[jnelson0612]

Hi rgaddam,
Thank you for asking about this question. It is one of my favorite problems in the strategy guides.

I think the key to solving this problem efficiently is appropriately choosing which of the variables to use as the "common" variable.

In this case, we have three wines: aged, table, and vintage. The problem tells us that in 8 years aged will be seven times as old as table, and that 1 year ago table was one-fourth as old as vintage.

In choosing my common variable, I should select the one that is used as the basis for comparison to the others. Thus, I should choose table, because table is compared to both vintage and aged.

From there it is easy to fill in the values for table. I can then calculate aged in eight years as seven times as old as table in eight years (t+8). So aged is 7(t+8) or 7t + 56. I can then fill in the rest of the values for aged.

I use a similar process with vintage; I know that one year ago, table was one-fourth as old as vintage. Thus, (t-1)=1/4V, of vintage is 4t-4. I can then fill in all of my values from vintage.

Finally, by interpreting the last sentence, I have an equation to solve for table.

I hope this information was helpful. The real trick is to choose table as the variable to use throughout the chart because table is the common basis for comparison with the other two wines.

[rgaddam]

Jamie,

Thank you for the quick response. Please see my comment below. I appreciate all your help.

Thus, I should choose table, because table is compared to both vintage and aged.

[From the question we can form the following equations - a=7t, t=v/4 and a=20v - "aged" is also used as the basis for comparison with "table" and "vintage". I chose "aged" as a common variable originally and the equations were slightly more complex than the equations when I chose "table" as common variable. Choosing "table" as a common variable makes it easy to solve for the answer. Is there a quick way to know that choosing "table" over "aged" makes it easy to solve?]

Thanks

[jnelson0612]

Jamie,

Thank you for the quick response. Please see my comment below. I appreciate all your help.

Thus, I should choose table, because table is compared to both vintage and aged.

[From the question we can form the following equations - a=7t, t=v/4 and a=20v - "aged" is also used as the basis for comparison with "table" and "vintage". I chose "aged" as a common variable originally and the equations were slightly more complex than the equations when I chose "table" as common variable. Choosing "table" as a common variable makes it easy to solve for the answer. Is there a quick way to know that choosing "table" over "aged" makes it easy to solve?]

Thanks

Yes--there is a quick way to know that choosing "table" over "aged" will make solving the problem easier. Again, since table is compared to both of the other wines, choosing table as our common variable should make the setup easier.

There is a good takeaway from this problem--if you have three or more variables, use the variable that is given as the common basis for comparison as your base variable.

[rgaddam]

Again, Jamie thanks for your response. Unfortunately, my original question still exists. Sorry for coming back to the same question. I will try to phrase it in a better way. Please see my comments.

Yes--there is a quick way to know that choosing "table" over "aged" will make solving the problem easier. Again, since table is compared to both of the other wines, choosing table as our common variable should make the setup easier. [I agree that "table" is compared to both of the other wines, but so is "aged". Unless I am missing something, "table" is compared with "aged" & "vintage" and "aged" is compared with "table" & "vintage". Till now both "table" and "aged" are equally attractive to be a common variable. So now, we have 2 options (table or aged) for common variable. In this case, how do I choose "table" over "aged"? ]

There is a good takeaway from this problem--if you have three or more variables, use the variable that is given as the common basis for comparison as your base variable.

Thanks for your help.

[tim]

hi rgaddam,
the beauty of this type of question is that you can choose any of the types of wine as your variable. when practicing a question such as this, you should try it with different variables to see which work out most efficiently. this is the only way you'll be able to begin making appropriate decisions about which variable to assign in this sort of problem. let me be clear: no answer we could give you will help you as much in your understanding of this sort of problem as will working out various options on your own..

[Awesome]

Hello,

I hope someone can help me with this question. I got stuck and I can't seem to understand why we get 7t+56 for aged wine. I get the 7t part but I have no idea where the 56 came from.

Any help will be much appreaciated!

[jnelson0612]

Hello,

I hope someone can help me with this question. I got stuck and I can't seem to understand why we get 7t+56 for aged wine. I get the 7t part but I have no idea where the 56 came from.

Any help will be much appreaciated!

Hi Urska,
We are told:
8 years from now, the bottle of wine labeled "Aged" will be 7 times as old as the bottle of wine labeled "Table".

So we can say:
Table(now)=T
Table(8 years from now)=T+8

8 years from now, Aged will be 7 times as old as Table. Thus:
Aged = 7(T+8)
*note that T+8 is how old Table will be 8 years from now*

Thus, Aged=7T+56.

[ray_kang]

To the original poster, this may help to explain why using Table as the common variable is the right choice. I too had trouble with this until I thought about the consequences of using whole numbers vs. fractions.

There are basically three different pieces of information given to us:

1. In 8 years, Aged will be 7 times as old as Table
2. 1 year ago, Table was one fourth the age of Vintage
3. 2 years ago, Aged was 20 times as old as Vintage

1. Given this bit of information, in 8 years, its easier to think of Aged as 7T+56, and Table as T+8, as opposed to Aged as A+8, and Table as 1/7(A +8). Doing it the first way gives us easy whole numbers to deal with, and doing it the second way gives us messy fractions.

2. Given this info, like above, it is easier to think of Vintage 1 year ago as 4T-4, and Table as T-1, as opposed to looking at Table as 1/4(V-1), and Vintage as V-1. Again, just like above, we make life easier by going with whole numbers as opposed to fractions.

3. When taking the 3rd piece of information, we can easily set 7T+46 equal to 20*(4T-5).

Again, the key to picking the right common variable is to find out which one lets us avoid fractions like 1/4th and 1/7th.

[tim]

Thanks, Ray..

[chuperman601]

Hello,

I too also chose to solve in terms of Aged "A" before I quickly discovered that it would result in messy fractions. I eventually solved it in terms of T; however, out of curiosity, I decided to try and solve it in terms of "A".

Unfortunately, I cannot come to the correct solution and am unsure of where I went wrong. I would appreciate any assistance or guidance.

Here is a pdf of my chart and equation setup:
http://tinyurl.com/3mhsywx


For T in 8 years from now:
I arrived at (A+8)/7 since in 8 years "A" will be 7 times as old as T. Then T must be 1/7 of A+8

For T in 1 year ago:
I simply took (A+8)/7 and subtracted 9 years from it. This was done to bring the future back 9 years. This resulted in:
(A-55)/7

Also, since "1 year ago, the bottle of wine labeled "Table" was one-fourth as old as the bottle of wine labeled "Vintage", then
(A+8)/7 is the result of (1/4) of V.

Therefore, 1 year ago, V must be 4*((A+8)/7)

As such, 2 years ago, V must have been (4*((A+8)/7)) - 1
(Just subtract 1)

For V in 2 years ago:
Since "A" is "20 times as old as the "V" bottle 2 years ago", then 2 years ago, "V" must have been:

((4*((A+8)/7)) - 1)/20

in other words, 1/20 of A

At this point, I tried to solve for "A" but I either get negative values or decimal values.

Thank you for your guidance and advice

[StaceyKoprince]

I can't, unfortunately, open your file (we're not allowed to download anything or follow masked links for security purposes).

8 years from now, the bottle of wine labeled "Aged" will be 7 times as old as the bottle of wine labeled "Table". 1 year ago, the bottle of wine labeled "Table" was one-fourth as old as the bottle of wine labeled "Vintage." If the "Aged" bottle was 20 times as old as the "Vintage" bottle 2 years ago, then how old is each bottle now?

If A = aged today
then
A + 8 = aged in 8 years
(A+8)/7 = table in 8 years
next step, for 1 year ago for table, you subtracted 9 years:
(A+8)/7 - 9 = (A+8)/7 - 63/7 = (A-55)/7 = table 1 year ago

table 1 year ago was also 1/4 vintage, so we can do something with this... but you used the label for AGED, not for TABLE in your next step.

table 1 year ago = (A-55)/7. multiply that by 4 to get vintage:
4(A-55)/7

Keep going from there and see what you get. Although know that you never want to do a real GMAT Q this way - too convoluted. I'm not even finishing it myself right now - too much! :)