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# Seed mixture X is 40 percent ryegrass and 60 percent

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Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink]  11 Nov 2013, 20:01
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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]  18 Apr 2014, 20:49
Another Approach:

X : 0.40 R and 0.60 B

Y: 0.25 R and 0.75 F

Mixture:

0.40 X + 0.25 Y = 0.30 (X+Y)

Y=2X

We need to know what is X/(X+Y)

1/3
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Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink]  03 Jun 2014, 20:45
Expert's post
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%

Quote:

In this my approach was that let weight of X be 100 and weight of Y be 100

Now For X, ryegrass is 40% of 100=40

and for total mixture it will be 30%of 200=60

To calculate the percentage weight from mixture X
why it is wrong 40/60 *100

Your first assumption is incorrect here: In this my approach was that let weight of X be 100 and weight of Y be 100

If you are assuming that the weights are 100 each and the combined weight is 200, what is left to find? X would be 1/2 of the mixture 100/200. What you have to find is the ratio of the weights in which they were mixed. The ratio may not be 1:1 as you have assumed here.

X has 40% ryegrass and Y has 25% ryegrass. Total mix has 30% ryegrass.

So X/Y = (25 - 30)/(30 - 40) = 1/2

So X by weight is 1 part (say 100 gms) and Y is 2 parts (say 200 gms). So X is 1/3 of the total mix i.e. 33.33%
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 25 Feb 2014 Posts: 12 Followers: 0 Kudos [?]: 2 [0], given: 2 Re: 223 Percentage [#permalink] 03 Jun 2014, 21:47 VeritasPrepKarishma wrote: 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%) Shortest way please. 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 Hence X is 33.33% in the mixture. Hi Karishma, So cann't we use plugging in for these types of questions like assuing the weight be anything etc. Like what i did was 100 and 100 for x and y which was wrong as we cannot assume both of the weights to be equal . Hence for the questions which require calculation for wieighted percentage, we will have to go by equations. SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1854 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 27 Kudos [?]: 1226 [1] , given: 193 Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink] 04 Jun 2014, 23:44 1 This post received KUDOS Using Alligation method Attachments alli.jpg [ 25.07 KiB | Viewed 1169 times ] _________________ Kindly press "+1 Kudos" to appreciate Manager Joined: 08 Feb 2014 Posts: 205 Location: United States Concentration: Finance GMAT 1: 650 Q39 V41 WE: Analyst (Commercial Banking) Followers: 2 Kudos [?]: 73 [0], given: 144 Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink] 28 Aug 2014, 08:23 This is similar to question 185 for those seeking a similar problem. That said, this question (about seed mixtures) is a bit more challenging. Intern Joined: 06 Oct 2013 Posts: 25 Location: United Kingdom WE: Engineering (Consulting) Followers: 0 Kudos [?]: 12 [0], given: 32 Seed mixture X is 40 percent ryegrass and 60 percent [#permalink] 28 Nov 2014, 09:17 Let resulting mixture is M. 30M=40x+25Y 70M=60X+75Y Solving above equations for X in terms of M is , 4M=12X so X=M/3 which is 33.33% Ans.B Intern Joined: 12 Jun 2014 Posts: 4 Followers: 0 Kudos [?]: 0 [0], given: 162 Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink] 25 Jan 2015, 03:08 tejal777 wrote: 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% Thanx tejal777. Personally I found Method 2 very simple to understand. Manager Joined: 06 Jul 2011 Posts: 132 Followers: 0 Kudos [?]: 36 [0], given: 240 Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink] 20 Apr 2015, 11:36 Use this amazing formula to answer faster - w1/w2 = (A2 – Aavg)/(Aavg – A1) A1 = 40% A2 = 25% Aavg = 30% Plugging in numbers, we get - w1/w2 = 1/2 so So mixture X is 1/3 i.e. 33.33% of the mix. Answer (B) Another such question can be found here - a-feed-store-sells-two-varieties-of-birdseed-brand-a-which-88125.html Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6062 Location: Pune, India Followers: 1599 Kudos [?]: 8954 [0], given: 195 Re: Seed mixture X is 40 percent ryegrass and 60 percent [#permalink] 09 Nov 2015, 01:03 Expert's post VeritasPrepKarishma wrote: 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%) Shortest way please. 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. Quote: Isn't the ratio for X:Y = 2:1 ? I do not understand simply how you are getting it as 1:2 ???? Because i was following all your posts for mixture problems, and the answer 1:2 seems to be contradicting the weighted average formula. How i am solving this is w1/ w2=(A2–Aavg)(Aavg–A1). Here i am taking Aavg as 30, A2= 25 A1 = 40 So 25-30/30-40 = 1/2 which is ratio for Y/X. so X/Y is 2/1. Its really really confusing for me which ratio to assign the equation to. I am getting many mixture problems wrong because of this. Can you please help clarify? Highlighted part is wrong. Use the formula as it is. X has 40% ryegrass and Y has 25% ryegrass to give 30% ryegrass in mixture w1/ w2=(A2–Aavg)(Aavg–A1) wX/wY = (AY - Aavg)/(Aavg - AX) wX/wY = (25 - 30)/(30 - 40) = 1/2 So wX/wY = 1/2. You get X:Y as 1:2 _________________ 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] 09 Nov 2015, 01:03

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