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Need help with this MGMAT Problem! (book explanation so-so)

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Need help with this MGMAT Problem! (book explanation so-so)

by thp510 » Wed Oct 13, 2010 6:25 am
Book 4 on MGMAT. Page 24, Q14. I couldn't understand the book's explanation and I don't think it's solvable in 2min.


8 years from now, the bottle of win labeled "Aged" will be 7 times as old the bottle of wine labeled "Table." 1 year ago, the bottle of wine labeled "Table" was one-forth 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?


Thanks!
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by kmittal82 » Wed Oct 13, 2010 6:31 am
Let current age of "Aged" = x
Current age of "Table" = y
Current age of "vintage" = z

>8 years from now, the bottle of win labeled "Aged" will be 7 times as old the bottle of wine labeled "Table."

x + 8 = 7(y+8)

=> x = 7y + 48

>1 year ago, the bottle of wine labeled "Table" was one-forth as old as the bottle of wine labeled "Vintage
y - 1 = (z-1)/4

=> 4y = z + 3

>If the "Aged" bottle was 20 times as old as the "Vintage" bottle 2 years ago
x - 2 = 20(z-2)

=> x = 20z -38


Once you have these equations, you should plug in answer values to see which ones hold true.
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by kmittal82 » Wed Oct 13, 2010 6:38 am
Just for the sake of completeness:

y (Table) = 2, x (aged) = 62 and z (vintage)= 5

Took me longer to type my posts than to solve it :)
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by GMATGuruNY » Wed Oct 13, 2010 6:48 am
thp510 wrote:Book 4 on MGMAT. Page 24, Q14. I couldn't understand the book's explanation and I don't think it's solvable in 2min.


8 years from now, the bottle of wine labeled "Aged" will be 7 times as old 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?

Thanks!
If this question were on the GMAT, I would plug in the answer choices, one of which would say that t=2, v=5, and a=62. Let's plug these values into the problem:

8 years from now, the bottle of wine labeled "Aged" will be 7 times as old the bottle of wine labeled "Table.'' 8 years from now, t=2+8=10 and a=62+8=70. This works because 70 = 7*10.

1 year ago, the bottle of wine labeled "Table" was one-fourth as old as the bottle of wine labeled "Vintage." 1 year ago, t=2-1=1 and v=5-1=4. This works because 1 = 1/4 * 4.

If the "Aged" bottle was 20 times as old as the "Vintage" bottle 2 years ago...
2 years ago, a=62-2=60 and v=5-2=3. This works because 60 = 20*3.

Having satisfied all the conditions in the problem, we would have found the correct answer.
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by goyalsau » Wed Oct 13, 2010 6:58 am
thp510 wrote:Book 4 on MGMAT. Page 24, Q14. I couldn't understand the book's explanation and I don't think it's solvable in 2min.


8 years from now, the bottle of win labeled "Aged" will be 7 times as old the bottle of wine labeled "Table." 1 year ago, the bottle of wine labeled "Table" was one-forth 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?


Thanks!
Aged = 62
Table = 2
Vintage = 5

I think it must be a pleasure to have wine like Aged for the evening... :wink:
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by Geva@EconomistGMAT » Wed Oct 13, 2010 7:09 am
goyalsau wrote:
thp510 wrote:
I think it must be a pleasure to have wine like Aged for the evening... :wink:
Nah - would've oxygenated completely by now, and turned into very expensive vinegar.

Scotch, however....
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by thp510 » Wed Oct 13, 2010 11:34 am
Thanks for the help! I hate these questions.
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by thp510 » Tue Nov 16, 2010 7:57 pm
kmittal82 wrote:Let current age of "Aged" = x
Current age of "Table" = y
Current age of "vintage" = z

>8 years from now, the bottle of win labeled "Aged" will be 7 times as old the bottle of wine labeled "Table."

x + 8 = 7(y+8)

=> x = 7y + 48

>1 year ago, the bottle of wine labeled "Table" was one-forth as old as the bottle of wine labeled "Vintage
y - 1 = (z-1)/4

=> 4y = z + 3

>If the "Aged" bottle was 20 times as old as the "Vintage" bottle 2 years ago
x - 2 = 20(z-2)

=> x = 20z -38


Once you have these equations, you should plug in answer values to see which ones hold true.

Kimittal82 & others...

Revisiting the question. Why would I set up the problem the way you did? For example, when the problem says...

"8 years from now, the bottle of win labeled "Aged" will be 7 times as old the bottle of wine labeled "Table."
x + 8 = 7(y+8)

I understand where the +8 came from in the parenthesis, but why would I do that? I originally put x+8 = 7y. What is it in the wording that should trigger my mind into thinking that I'm also compensating for "table" wine in the future by adding +8 to it? What would the sentence be if I didn't add +8? I'm thinking: "8 years from now, the bottle of wine labeled "Aged" IS 7 times as old as the bottle of wine labeled "Table". No?
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by Geva@EconomistGMAT » Wed Nov 17, 2010 12:49 am
thp510 wrote:
kmittal82 wrote:Let current age of "Aged" = x
Current age of "Table" = y
Current age of "vintage" = z

>8 years from now, the bottle of win labeled "Aged" will be 7 times as old the bottle of wine labeled "Table."

x + 8 = 7(y+8)

=> x = 7y + 48

>1 year ago, the bottle of wine labeled "Table" was one-forth as old as the bottle of wine labeled "Vintage
y - 1 = (z-1)/4

=> 4y = z + 3

>If the "Aged" bottle was 20 times as old as the "Vintage" bottle 2 years ago
x - 2 = 20(z-2)

=> x = 20z -38


Once you have these equations, you should plug in answer values to see which ones hold true.

Kimittal82 & others...

Revisiting the question. Why would I set up the problem the way you did? For example, when the problem says...

"8 years from now, the bottle of win labeled "Aged" will be 7 times as old the bottle of wine labeled "Table."
x + 8 = 7(y+8)

I understand where the +8 came from in the parenthesis, but why would I do that? I originally put x+8 = 7y. What is it in the wording that should trigger my mind into thinking that I'm also compensating for "table" wine in the future by adding +8 to it? What would the sentence be if I didn't add +8? I'm thinking: "8 years from now, the bottle of wine labeled "Aged" IS 7 times as old as the bottle of wine labeled "Table". No?
There's no immediate trigger except for common sense and staying alert: It's a common mistake people make, and a thus a concept tested by the GMAT. Time passes for all, and no one is exempt. The instant the problem talks about "now", and "8 years from now", you need to add 8 years to everyone involved - it simply doesn't make sense for time to pass for one bottle of wine but not for other, currently existing ones.
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