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GMAT Diagnostic Test Question 33

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GMAT Diagnostic Test Question 33 [#permalink] New post 06 Jun 2009, 22:16
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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
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 10 Jun 2009, 19:04
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Explanation
Rating:

Official Answer: C

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 walnut = B

XA + (1-X) B = 7 ……………………….i
(1.5X) A + (1 - 1.5X) B = 8 …………….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
2 + XB + B - XB = 7
B = 7 - 2
B = 5.00

Therefore, it is C.
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 18 Jul 2009, 14:53
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I didn't solve this one, so I don't know if it's correct, but all the numbers are different in the PDF.
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 23 Jul 2009, 04:39
GMAT TIGER wrote:
Explanation
Rating:

Official Answer: C

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.
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 24 Jul 2009, 05:23
I have not got an answer yet ;) What is 1,5x?
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 24 Jul 2009, 05:31
Hold a second something is missing in the OE :oops:
Will post by tonight.

maliyeci wrote:
I have not got an answer yet ;) What is 1,5x?



Done. Guys, please check it.

Also let me know if the question has still an issue(s).
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 28 Jul 2009, 14:11
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GMAT TIGER wrote:
Hold a second something is missing in the OE :oops:
Will post by tonight.

maliyeci wrote:
I have not got an answer yet ;) What is 1,5x?



Done. Guys, please check it.

Also let me kn oe if the question has issues.


Hi

where can i find the new question and solution to this problem
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 28 Jul 2009, 15:43
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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.

Harry
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 30 Jul 2009, 03:05
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.

Harry

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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 03 Aug 2009, 11:35
20% of walnuts is sold for 1 $ more, so:

0,2Y=1 --> Y=5 $

Quicker.

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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 22 Aug 2009, 22:54
Noboru,

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

Thanks
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Last edited by powerka on 23 Aug 2009, 08:03, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 23 Aug 2009, 03:30
powerka wrote:
Nobory,

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?
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Expert Post
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 23 Aug 2009, 07:10
Expert's post
noboru wrote:
powerka wrote:
Nobory,

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.


Thanks!
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 23 Aug 2009, 09:52
So I guess there's no valid shortcut. Ideas anybody?
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 31 Aug 2009, 11:47
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is it safe to assume....

a 50% increase in x (chestnuts) yields a dollar increase in the total amount (from $7 to $8);

so a 50% increase in chestnuts equal $1 and 100% of the chestnuts will equal $2.

there for 7 - 2 = 5 total amount for walnuts.

do you think this solution is feasible for any problem like this? or would this simply be coincidence?
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 21 Sep 2009, 18:19
Hi,

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)

Do you think I am in a right direction ?
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 22 Sep 2009, 09:50
adssaini wrote:
Hi,

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...


adssaini:

I think you are right.

Question does ask for the price of 1 KG of Walnut, not the price of the walnut in the mixture.

A0 = C + W = 7
A1 = 1.5C + W = 8
=> C=2 => W=5

$5 is the price of walnuts in the mixture, not the price of 1 KG of walnuts.

We don't have the value of Y => can't know how many KG of walnuts the mixture has => can't calculate the price of 1 KG of walnuts.
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 19 Oct 2009, 02:57
bb wrote:
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.
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 19 Oct 2009, 21:39
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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)

Did I make it clear?
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Re: GMAT Diagnostic Test Question 33 [#permalink] New post 13 Nov 2009, 10:23
I don't think this isn't a 650 level question...
Re: GMAT Diagnostic Test Question 33   [#permalink] 13 Nov 2009, 10:23
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