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Seed mixture X is 40 percent ryegrass and 60 percent

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Seed mixture X is 40 percent ryegrass and 60 percent [#permalink]

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26 Feb 2008, 19:46
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Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?

A. 10%
B. 33 1/3%
C. 40%
D. 50%
E. 66 2/3%
[Reveal] Spoiler: OA

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Seed mixture X is 40 percent ryegrass and 60 percent [#permalink]

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18 Aug 2009, 00:00
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Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of this mixture is X ?

(A) 10%
(B) 33.33 %
(C) 40%
(D) 50%
(E) 66.66 %

METHOD 1:
Assuming the weight of the mixture to be 100g**, then the weight of ryegrass in the mixture would be 30g.
Also, assume the weight mixture X used in the mixture is Xg, then the weight of mixture Y used in the mixture would be (100-X)g.

So we can now equate the parts of the ryegrass in the mixture as:

0.4X + 0.25(100-X) = 30
0.4X + 25 - 0.25X = 30
0.15X = 5
X = 5/0.15 = 500/15 = 100/3

So the weight of mixture X as a percentage of the weight of the mixture
= (weight of X/weight of mixture) * 100%
= (100/3)/100 * 100%
= 33%

METHOD 2
wt. of 1st mixture = x
therefore concentration of ryegrass in 1st mix = 0.4x

wt. of 2nd mixture = y
therefore concentration of ryegrass in 2nd mix = 0.25y

0.4x+0.25y = 0.3(x+y)

0.4x-0.3x = 0.3y - 0.25y

0.1x=0.05y
or
2x=y

so if weight of x = 50grams
weight of y = 100 grams

total weight of mix = 150 grams

percentage of x in 150 grams of mix is 150*x/100 = 50

x = 50*100/150
x = 100/3
x = 33.3%
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23 Feb 2011, 19:21
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Baten80 wrote:
223. Seed mixture X is 40 percent ryegrass and 60 percent
bluegrass by weight; seed mixture Y is 25 percent
ryegrass and 75 percent fescue. If a mixture of X and
Y contains 30 percent ryegrass, what percent of the
weight of the mixture is X ?
(A) 10%
(B) 33 1/3 (33.33%)
(C) 40%
(D) 50%
(E) 66 2/3 (66.66%)

Just focus on ryegrass. X has 40% ryegrass and Y has 25% ryegrass to give 30% ryegrass in mixture. Therefore, X:Y = 1:2 (because distance of X and Y from average is in the ratio 10:5 i.e. 2:1. If this in unclear, check out http://gmatclub.com/forum/tough-ds-105651.html#p828579)
Hence X is 33.33% in the mixture.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 28 Jan 2010 Posts: 30 Re: Seed mixture X is ryegrass and bluegrass [#permalink] Show Tags 28 Jan 2010, 04:47 14 This post received KUDOS 2 This post was BOOKMARKED Let M = x + y M = New mixture x = Mixture X y = Mixture Y What do we need to find ?? => (x/M)*100 Equating Ryegrass in the mixture - .4x + 0.25y = 0.3M .4x + 0.25(M-x) = 0.3M .4x + 0.25M - 0.25x = 0.3M .15x = .05M x/M = 1/3 Hence ans = 33.33%. Intern Joined: 27 Aug 2010 Posts: 23 Re: Seed mixture X is ryegrass and bluegrass [#permalink] Show Tags 24 Sep 2010, 23:41 9 This post received KUDOS 1 This post was BOOKMARKED IMHO this task is better to solve with absolute numbers. Say, there are 100 liters of X (40+60) and Y (25+75) that add to 200 liters in total. The weight of reygrass in the united mixture is 0,3*200=60. The weight of reygrass in X is 40. 40/60=2/3=33,33% SVP Joined: 29 Aug 2007 Posts: 2473 Re: 240. PS.Mixture [#permalink] Show Tags 27 Feb 2008, 01:41 8 This post received KUDOS 3 This post was BOOKMARKED sondenso wrote: 240. Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X? A.10% B.33 1/3% C.40% D.50% E.66 2/3% B. x = weight of x 40 x + 25 (1-x) = 30 solve for x, x = 33.33% _________________ Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html GT Manager Joined: 13 Aug 2009 Posts: 148 WE 1: 4 years in IT Re: Seed mixture X is ryegrass and bluegrass [#permalink] Show Tags 28 Jan 2010, 22:57 3 This post received KUDOS Hi Tejal777 we can make the method 2 more simpler METHOD 2 wt. of 1st mixture = x therefore concentration of ryegrass in 1st mix = 0.4x wt. of 2nd mixture = y therefore concentration of ryegrass in 2nd mix = 0.25y 0.4x+0.25y = 0.3(x+y) 0.4x-0.3x = 0.3y - 0.25y 0.1x=0.05y or 2x=y [b]so if weight of x = 50grams weight of y = 100 grams total weight of mix = 150 grams percentage of x in 150 grams of mix is 150*x/100 = 50 x = 50*100/150 x = 100/3 x = 33.3%[/b]. what we need is x/x+y *100 we know x and y so solving it we get 33.33% Senior Manager Joined: 22 Nov 2010 Posts: 284 Location: India GMAT 1: 670 Q49 V33 WE: Consulting (Telecommunications) Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink] Show Tags 09 Mar 2013, 00:05 3 This post received KUDOS 4 This post was BOOKMARKED RG detail table: X----------------------------------Y 40%------------------------------25% -----------------30%-------------- 30-25 = 5------------------40-30 = 10 RG ratio 5:10 = 1:2 Therefore, % of X in new mixture = 1/3 = 33.3% _________________ YOU CAN, IF YOU THINK YOU CAN Math Forum Moderator Joined: 20 Dec 2010 Posts: 2010 Re: Seed mixture X is ryegrass and bluegrass [#permalink] Show Tags 05 Feb 2011, 05:27 2 This post received KUDOS take X=100 In it: Ryegrass=40 Others = 60 take Y=y Ryegrass=0.25y Others = 0.75y Mix both; Total weight: X+Y=100+y In it; Weight of Ryegrass = 40+0.25y Given: 40+0.25y=0.3(100+y) 40+0.25y=30+0.3y 0.05y=10 y=200 So; total X+Y = 100+200=300 Percentage of X in it: (X/X+Y)*100 = (100/300)*100=100/3=33.33% Ans: B _________________ Intern Joined: 26 Feb 2008 Posts: 8 Re: 240. PS.Mixture [#permalink] Show Tags 27 Feb 2008, 19:06 1 This post received KUDOS the answer is E.66 2/3% solve for 25x + 40 [1-x] = 30 so, x = 2/3 = 66 2/3% Intern Joined: 15 Mar 2012 Posts: 3 Location: India GPA: 3.2 WE: Information Technology (Computer Software) Re: Seed mixture X is ryegrass and bluegrass [#permalink] Show Tags 10 May 2012, 08:10 1 This post received KUDOS 1 This post was BOOKMARKED Final Requirement is to calculate "X/(X+Y) * 100" We have the information about the quantity by weight of ryegrass in X,Y and also the quantity by weight of ryegrass after mixing i.e in X+Y. So the equation satisfying the above mentioned criteria would be : (40/100)*X+(25/100)*Y=(30/100)*(X+Y) Solving this will lead us to the result... 2X=Y So, the weight percent of X : (X/X+Y)*100 = (X/X+2X)*100 = 33.33% Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7440 Location: Pune, India Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink] Show Tags 09 Mar 2013, 00:25 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED Sachin9 wrote: Is this Question correct? It is asking. what percent of the weight of this mixture is X ? And we are answering percent of the ryegrass in X /ryegrass in mixture.. Yes it is. The question tells us that mixture X and mixture Y (both of which are themselves mixtures of ryegrass and bluegrass) are mixed together to give a super mixture. We need to find the weight of mixture X in this super mixture. We know the % of ryegrass in X and in Y and we also know the % of ryegrass in the super mixture (i.e. the average % of ryegrass when you mix X and Y). This tells us the ratio of X and Y in the super mixture i.e. in what ratio were X and Y mixed together (using our standard weighted averages method). When you have the ratio of X and Y, you can say what the % of mixture X is in the super mixture. For more on such questions, check out the second example in my post: http://www.veritasprep.com/blog/2011/04 ... -mixtures/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink]

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21 Jul 2013, 14:21
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........,,,,,,...X...,.. Y
Ryegrass:.... 40.... 0,25X
Bluegrass:... 60....
fescue:. ............. 0,75X
----------------------------------------------
Total:........ 100..... X--...---100+X

40 + 0,25X = 0,3(100+X)
0,05X = 10
X = 200

---> X/Y = 100/200 ; X+Y = 300 ---> X/(X+G) = 100/300 = 33,3% (B)

I've solved it this way, I hope it will be useful for some of you......
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Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink]

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21 Jul 2013, 18:43
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Expert's post
1. x and y should have been mixed in the ratio, 30-25 / 40-30 = 1/2 to get the resulting mixture
2. So the weight of x in the resulting mixture is 1/3 * 100 % = 33.33 %
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Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink]

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11 Nov 2013, 21:01
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sondenso wrote:
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?

A. 10%
B. 33 1/3%
C. 40%
D. 50%
E. 66 2/3%

Its very simple ..

30/100(x+y)= 40/100(x) + 25/100(y)
after solving we'll get, y=2x ... and we know x + y = 100(Total mixture)

x = 33.33
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Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink]

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Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink]

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29 Apr 2016, 09:38
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sondenso wrote:
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?

A. 10%
B. 33 1/3%
C. 40%
D. 50%
E. 66 2/3%

This is a great problem because we can solve it using equations and substitution, or we can employ some estimation because the equation we create is a weighted average. Let’s first do the equation-substitution method.

Equation-Substitution Method

We are given information about ryegrass, bluegrass, and fescue. However, we are told the mixture of X and Y is 30 percent ryegrass. Thus, we only care about the ryegrass, so we can ignore fescue or bluegrass.

We are given that seed mixture X is 40% ryegrass and that seed mixture Y is 25% ryegrass. We are also given that the weight of the combined mixture is 30% ryegrass. With x representing the total weight of mixture X, and y representing the total weight of mixture Y, we can create the following equation:

0.4x + 0.25y = 0.3(x + y)

We can multiply the entire equation by 100, and we have:

40x + 25y = 30x + 30y

10x = 5y

2x = y

The question asks what percent of the weight of the mixture is x.

We can create an expression for this:

x/(x+y) * 100 = ?

Since we know that 2x = y, we can substitute in 2x for y in our expression. So we have:

x/(x+2x) * 100 = x/(3x) * 100 = 1/3 * 100 = 33.33%

Estimation Method

This is a method I would suggest using only if you are short on time.

We are given that seed mixture X is 40% ryegrass and that seed mixture Y is 25% ryegrass. We are also given that the overall weight of the mixture is 30% ryegrass.

Since 30% is closer to 25% than it is to 40%, we know that there is more of mixture Y than there is of mixture X, but not by a large amount. So let’s analyze our answer choices.

A) 10%

This tells us that the mixture is made up of 10% x and 90% y. That discrepancy is much too large to be correct, based on the overall weight of the mixture.

B) 33 1/3%

This tells us that the mixture is made up of 33 1/3% x and 66 2/3% y. This could be the answer.

C) 40%

This tells us that the mixture is made up of 40% x and 60% y. This could be the answer.

D) 50%

This tells us that the mixture is made up of 50% x and 50% y. Since we know that y is weighted more heavily in the mixture, we know this cannot be the answer.

E) 66.67%

This tells us that the mixture is made up of 66 2/3% x and 33 1/3% y. Since we know that y is weighted more heavily in the mixture, we know this cannot be the answer.

So now we have our answer choices narrowed down to B and C. However, there is something interesting about answer choice B. Notice that if we were to add together answer choice B (33 1/3%) and answer choice E (66 2/3%), our sum would be 100%. These are strategic answer choices, because the GMAT is hoping that if we make a mistake in our calculations we will determine that x represents 66 2/3% of the mixture rather than 33 1/3% of the mixture. Since answer choice C (40%) does not have a corresponding trap answer there is a higher likelihood that the answer is B (33 1/3%) than it is C (40%).

As mentioned at the beginning, the surest solution technique is to create an equation to solve it and actually complete the math. However, if you are short on time or have trouble setting up the equation, estimation is a method you can employ.

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Re: Seed mixture X is ryegrass and bluegrass [#permalink]

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13 Oct 2010, 02:11
Sorry, while I understand the explanation, I am bit perplexed on where I am making the mistake

RyeGrass Others
Mixture A 40lb 60lb 100lb
Mixture B 25lb 75lb 100lb
============================
65lb 135lb 200lb

Here 200lbs of mixture will have 65lb of RyeGrass.

In other words, 100lbs of mixture will have 32.5lbs of Ryegrass.

The question is saying - " What % of the weight of the mixture is X"
the mixture here is 100lb and Mixture A is 50lb, so why isn't it (50/100)*100=50%?

I know this is NOT a correct answer but what am I missing?
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Re: Seed mixture X is ryegrass and bluegrass [#permalink]

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26 Jan 2011, 08:18
one more way to solve this prob.

since mixture X has 40 percent ryegrass and 60 percent bluegrass i.e they are in ratio of ( 40/60) or ( 2/3)
similarly mixture y has 25 percent ryegrass and 75 percent fescue i.e they are in ratio of ( 25/75) or (1/3)
where as resultant is a mixture in which 30% is ryegrass i.e it is in ratio of ( 30/70) or ( 3/7)

then ryegrass in mixture x = 2/5
ryegrass in mixture y is =1/4

ryegrass in mixture(x+y)= 3/10

then they are mixed in ratio as
quantity of y/ quantity of x= ((2/5)-(3/10))/ ((3/10)-(1/4))= 2 /1

then quantity of x is 1/3 or 33.3%
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Seed mixture X is 40 percent ryegrass and 60 percent [#permalink]

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17 Jul 2012, 11:34
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of this mixture is X ?

(A) 10%
(B) 33.33 %
(C) 40%
(D) 50%
(E) 66.66 %

[Reveal] Spoiler:
1=X+Y --> Y=1-X

(4/10)X+(1/4)Y = (3/10)(X+Y)

(4/10)X+(1/4)(1-X) = (3/10)(x+(1-X))

get common denominator

(16x+(10-10x))/40 = (3/10)

6x+10=12

6x=2

x=2/6 = 1/3 => 33.3%

Can anyone pls expain me how they are taking 1=X+Y.

Pls response. Thanks a lot

Last edited by Bunuel on 26 Oct 2013, 03:23, edited 3 times in total.
Edited the question and added the OA. TOPIC LOCKED
Seed mixture X is 40 percent ryegrass and 60 percent   [#permalink] 17 Jul 2012, 11:34

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