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

Question

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!

kmittal82 · Answer

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.

kmittal82 · Answer

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

GMATGuruNY · Answer

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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goyalsau · Answer

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...

Saurabh Goyal
[email protected]
-------------------------

EveryBody Wants to Win But Nobody wants to prepare for Win.

Geva@EconomistGMAT · Answer

goyalsau wrote:thp510 wrote: I think it must be a pleasure to have wine like Aged for the evening... Nah - would've oxygenated completely by now, and turned into very expensive vinegar. Scotch, however....

thp510 · Answer

Thanks for the help! I hate these questions.

thp510 · Answer

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?

Geva@EconomistGMAT · Answer

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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