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Mixtures

by rohu27 » Fri Apr 22, 2011 8:42 am
A kilogram of nut mixture contains X% chestnuts and Y% walnuts and sells for $7.00/kg. If the ratio of chestnuts is increased by 50% so that the new mixture is sold for $8.00/kg, what is the price of a kg of walnuts?

a)1.00 USD
b)2.50 USD
c)5.00 USD
d)7.50 USD
e)10.00 USD

Source: GMATclub
Last edited by rohu27 on Fri Apr 22, 2011 9:14 am, edited 1 time in total.
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by Tani » Fri Apr 22, 2011 9:09 am
The question isn't clear. It says "increase the ratio of chestnuts by 50%". Are we supposed to increase the percent of chestnuts by 50% or increase the ratio of chestnuts to walnuts by 50%. Those would give us very different answers.
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by force5 » Fri Apr 22, 2011 9:41 am
Bro i was thinking if 50% if the chestnuts are causing a $1 change in price then 100% change will cause $2 change...

which means that rate of walnut should be $5.... what say??

also by weighted mean concept. the rate of walnut should be much more than chestnut.
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by rohu27 » Fri Apr 22, 2011 9:50 am
force5 wrote:Bro i was thinking if 50% if the chestnuts are causing a $1 change in price then 100% change will cause $2 change...

which means that rate of walnut should be $5.... what say??

also by weighted mean concept. the rate of walnut should be much more than chestnut.
arrived at the answer (which is C btw)using a similar logic, but then
isnt this 5 $ cost of walnut in the 7$ per kg mixture, whereas we want the the rate of 1kg walnut.

wht im i missing here.

Tani,
the Q is asking to increase ratio of chestnut by 50% so i took the present ratio to be X and new one 1.5X, though im sure original gmat question would be much more clear, i just wanted to knw how to proceed furhter from there.

Cheers,
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by Tani » Fri Apr 22, 2011 9:57 am
You have to have two terms to have a ratio.

For example:
x = 60% and y = 40%
increase x's PERCENT by 50% and you get 60% X and 40% Y.

However, if you increase the RATIO of x to Y by 50%, your original ratio was 60/40 = 3/2.
Increasing that by 50% gives 9/4. so the resulting percentages would be approximately 69% and 31%.
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