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

Question

8 years from now, the bottle of wine labeled 'Aged' will be 7 times older than the bottle of wine labe1ed 'Table.' I 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 older than the 'Vintage' bottle 2 years ago, then how old is each bottle now?

this question from manhattan word prep
in solution the equations are given as:
a+8 = 7( t+8)
t-1 = ( v-1)/4
& a-2 =20( v-2)
 
i am just curious to know if first and third equations are translated as given in problem.
what i perceived is it should be 
a+8 = (a+8) + 7( t+8)
t-1 = ( v-1)/4
& a-2 =(v-2)+20( v-2)
 as question stem says 7 times older than.. and 20times older than..

please, any one can clarify this.
Thanks

vannbj · Answer

That can't logically make any sense unless t=-8. It has to be translated as you had it above. Here’s what I got.

Wines 2 yrs ago 1 yr ago Now 8 yrs future
aged a-2 a-1 a a+8
table t-2 t-1 t t+8
vintage v-2 v-1 v v+8
 
What the question tells us 
(a-2)=20(v-2) 
4(t-1)=v-1 
(a+8)=7(t+8)

a=20v-40+2 
a=20v-38 
 so 20v-38+8=7t+56 
 20v-30=7t+56 
 20v=7t+86 
 v=7t/20 + 4+ 3/10 
 so 
 
 4(t-1) = 7t/20 + 3.3 
 4t-4 = 7t/20 + 3.3 
 4t-7.3 = 7t/20 
 4t-7t/20=7.3 
 80t/20 - 7t/20=7.3 
 73t/20=7.3 
 73t=146 
 t=2 so 
 4(2-1)=v-1 
 v=3 
 so 
 (a+8)=7(2+8)
 a+8=70 
 a=62

jeeteshsingh · Answer

Let the current age of each wine be A - Aged, V - Vintage & T - Table.

You get three eq from the wordings:
A+8 = 7(t+8)
A-2 = 20(V-2)
T-1 = 0.25(V-1)

Solving them you get T = 2, V = 5, A = 62

einstein10 · Answer

thank you for the reply.
my doubt is whether the wording of question stem is correct. first equation is equivalent to saying "x is 7 times as old as y", not as mentioned in question stem. similarly 3rd equation..

mads · Answer

8 years from now, the bottle of wine labeled 'Aged' will be 7 times older than the bottle of wine labe1ed 'Table.'
==> when you say 8 years from now, we should add 8 to the current value. So it will be Aged+8 and Table+8.
At this time first one is 7 times older than second. Times is always a multiplication.
So Equation is Aged+8 = 7 (Table+8)

If the'Aged' bottle was 20 times older than the 'Vintage' bottle 2 years ago
==> With the same logic, 2 years ago means subtract 2 from those values. So it will be Aged-2 and Vintage-2.
20 times older again will be a multiplication.
So Equation is Aged-2 = 20 (Vintage-2)

Hope it helps to clarify your question.

sidhu4u · Answer

No the first equation is not equivalent to saying "x is 7 times as old as y", 
take for example, x is 10 yrs old now and y is 118 yrs old, so right now x:y is 10:118 which is 5:59
but after 8 years x will be 18 and y will 126 and now the ratio x:y is 18:126 and if u simplify it is 1:7
Age always increase linearly with years so you cannot say that the multiplicative ratio holds good as the years pass by.

summer101 · Answer

This question took me 4+ minutes!!! Do we expect this kind of problems? Is there a faster way ?

jlgdr · Answer

I honestly think this problem takes way too long and there isn't really any shortcut to it. Would take an educated guess on real GMAT and move on with it Cheers J

LeenaSai · Answer

Hi all ,

Is there any short cut for solving the three equations ?

I am ending up taking more than 2 mins to solve this question

Posted from my mobile device

IanStewart · Answer

There's a shortcut to solve this problem, which avoids equations altogether. We know from the last piece of information, if we subtract 2 from the 'Aged' bottle's age, we must get a multiple of 20, and therefore of 10. Notice that means if we add 8 to the 'Aged' bottle's age, we must also get a multiple of 10, since multiples of ten are ten apart (if a-2 is a multiple of 10, a+8 will always also be a multiple of 10). But from the first piece of information, we also know that if we add 8 to the 'Aged' bottle's age, we must get a multiple of 7. So when we add 8 to the 'Aged' bottle's age, we must get a multiple of both 7 and 10, and thus of 70, and unless, from the answer choices, we need to consider the possibility that this bottle is centuries old, we can conclude the bottle will be 70 years old in 8 years, and is 62 years old now. Then it's easy to work out (if we even need to -- again there should be answer choices) the other bottles' ages.

With answer choices you could also just use the fact that adding 8 to the 'Aged' age must produce a multiple of 7, subtracting 2 from the 'Aged' age must produce a multiple of 20, and subtracting 1 from the 'Vintage' age must produce a multiple of 4; those observations alone would almost always let you pick the right answer without doing algebra. That would work even if you couldn't find a relationship similar to the one I explain in the paragraph above (which relied on a detail specific to the numbers in the question).

LeenaSai · Answer

Yes sir , you are absolutely right ! We can stick to the ground rules of multiples and factors , thereby solve these kind of question easily .. Scanning the answer choice and sticking to the basics are the ultimate approaches

Thankuuu so much Sir Posted from my mobile device

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