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GMAT Diagnostic Test Question 33 Field: word problems (mixture) Difficulty: 650

Rating:

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 B. $2.50 C. $5.00 D. $7.50 E. $10.00
_________________

Weight of chestnut = x% of 1 kg Price of chestnut = A Weight of walnut = y% of 1 kg = (1-x)% of 1 kg Price of chestnut = B

XA + (1-X) B = 7 ……………………….i (1.5X) A + (1 - 1.5X) B = …………….ii

From 1 and 2: 0.5XA – 0.5XB = 1 XA – XB = 2 XA = 2 + XB…………………………… iii

Substitute the value of XA on Equation i: XA + (1-X) B = 7 XA + B - XB = 7 2 + XB + B - XB = 7 B = 7 - 2 B = 5.00

Where this 1,5 x comes from? Does not it increased by %20? How can the price of wallnut be less than 7? We increased the rate of wallnut and price of it increased but price of 1kg of wallnut is less than the mixture price.

The Question says '...Ratio of Walnuts is increased by 50%...'. Therefore, the multiplication by '1.5' has to be for Walnuts (Y). Since, this is done to 'X' (Corresponding to Chestnuts), I guess people are confused. However, the answer remains the same. I have solved it, and verified.

Thanks for the wonderful effort guys. I really appreciate it.

The question above is updated. I will update the PDF in a minute too. +1.

charimaalu wrote:

The Question says '...Ratio of Walnuts is increased by 50%...'. Therefore, the multiplication by '1.5' has to be for Walnuts (Y). Since, this is done to 'X' (Corresponding to Chestnuts), I guess people are confused. However, the answer remains the same. I have solved it, and verified.

Thanks for the wonderful effort guys. I really appreciate it.

Could you explain where do you get 20% of walnuts?

Thanks

From the question:

33. A kilogram of nut mixture contains X% chestnuts and Y% walnuts and sells for $7.00/kg. If the ratio of walnuts is increased by 20% so that the new mixture is sold for $8.00/kg, what is the price of 1 kg of walnuts?
_________________

Could you explain where do you get 20% of walnuts?

Thanks

From the question:

33. A kilogram of nut mixture contains X% chestnuts and Y% walnuts and sells for $7.00/kg. If the ratio of walnuts is increased by 20% so that the new mixture is sold for $8.00/kg, what is the price of 1 kg of walnuts?

This question has gone through several revisions (originally 20%) and currently modified to 50%. (The idea behind the test is to revise questions as we find issues with them or cleaner solutions). That's what happened - please download the latest PDF.

I think there is issue with problem. Last part of the question asks for the price of 1 KG of Walnut, not the price of the walnut in the mixture...

I tried in this way

.4 kg of X .6 kg of Y

total 1 kg.

Now increase X by 50%...now it becomes .6 , which means .2 increase costs $1 more. Hence, .4 Kg cost of X will be $2. Remaining $ 5 is for .6 Kg of Y. So for 1 kg of Y will be $8.34 (5/ 0.6)

GMAT Diagnostic Test Question 33 Field: word problems (mixture) Difficulty: 650

Rating:

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 B. $2.50 C. $5.00 D. $7.50 E. $10.00

I am afraid this question has more than one correct answer unless you provide in the statement one of the percentages of the mixture either the chestnuts content or the walnuts content.

I did not see any confusion here. TIGER's solution is absolutely rite.

For those guys who were confused, I believe it is helpful to always keep in mind that: 1) the sum of weights of 2 nuts is always 1 kilo no matter how the mixture changes, which implies: 2) when chestnut in the mixture is increased by 50%, do remember that the weight of walnut should be decreased by a certain percetage (generally NOT by 50% unless the original mixture is 50% vs. 50%) to keep the sum of 1 kilo (implication 1)