Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weig

First of all, we don't care at about bluegrass or whatever fescue is. If we combine the mixtures to arrive at 30 percent ryegrass, we can just keep track of how we mix them according simply to the ryegrass; whatever else is in the mixture will follow accordingly and work out as it will. We just need to see how a mixture with 40 percent ryegrass and a mixture with 25 percent ryegrass combine to land at 30 percent.

What if you poured these 2 mixtures in equal quantities? Where would the ryegrass percentage land? It would of course land right in the middle. Equal parts of a 40 percent solution and a 25 percent solution will land us right in the middle, at 32.5 percent. However, in this problem that isn't where we land; we land at 30 percent. Think to yourself: if we mixed them evenly, the result would be a 32.5 percent solution and here we have 30, so which must there be more of? Which of the two mixtures, 25 or 40 percent, is the result closer to?

The 25 percent solution! 30 is closer to 25 than it is to 40, so there is more of the 25 percent solution, mixture Y. Even if you had no idea where to go from here, you can eliminate answers d and e. There has to be less of mixture X.

Now, let's return to thinking about that average mixture (because when you mix liquids of different salience, you're arriving at an average salience). Because 30 is twice as close to 25 as it is to 40 (5 away versus 10 away), we can reliably infer that there will be twice as much of the 25 percent mixture. That means it will be 2/3 Mixture Y (the 25 percent mixture) and 1/3 Mixture X (40 percent). Our answer is B.

W1 and A1 need to represent the same quantity and W2 and A2 need to represent the same quantity. When using the weight average formula, you can take either to be ingredient 1.

Seed mixture X is 40 percent ryegrass by weight - Say this represents W1 and A1
seed mixture Y is 25 percent ryegrass - Say this represents W2 and A2

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (25 - 30)/(30 - 40) = 1:2

Whatever you do keep the name consistent. Check out this post to understand: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2017/1 ... -averages/

No, that will not be the correct way.
The weighted average is already given as 30%, so what is in choices is NOT weighted average but the % of X in mix of X+Y.
As a matter of fact, each of the choice will give you weighted average between 25 and 30.

Now, weighted average method will help you in getting the ratio of X to Total, which will be (30-25)/(40-25)=5/15=1/3=33.33%
_________________

Asad

In this question, the required output is not the percentage of ryegrass in mixture else you would have been correct. But what's given here as 30% is not to be caklculated.

Here the question is asking the percentage of X in mixture so it's important to find the ratio of x and y first which has less to do with the percentage range

You need to rather understand that 40 and 25 have made average 30

30 is at distance of 5 from 25
30 is at distance of 10 from 40

i.e. 25% ryegrass solution has double the weightage than 40% ryegrass solution

i.e. x:y = 1:2

i.e. x% = 1/3 = 33.33%

Hope that help!

Answer: Option B

Please check video solution for step by step explanation (TWO OUTSTANDING SOLUTIONS)

Subscribe to my YouTube Channel for FREE resource (1000+ Videos)

Subscribe Topic-wise UN-bundled Video course. CHECK FREE Sample Videos

We are provided information about rye grass, hence let's focus on the same.

\(\frac{0.40X + 0.25Y}{X + Y} = 0.30\)

\(40X + 25Y = 30X + 30Y\)

\(10X = 5Y\)

\(2X = Y\)

\(\frac{X}{Y} = \frac{1}{2}\)

\(\frac{X}{X+Y} = \frac{1}{1 + 2}\)

\(\frac{X}{X+Y} = \frac{1}{3}\) or \(33\frac{1}{3}\)%

Ans. B

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

Short video solution here, using the Teeter Totter Timesaver Method (2:06):




Teeter Totter Method Steps:

1) Draw the Endpoints and Weighted Average numbers on the Teeter Totter Diagram (the weighted average represents the final mixture, and goes above the triangle-shaped fulcrum)

2) Draw the weights on each side. The LARGER weight goes on the side with the SHORTER distance from the fulcrum

3) Draw the distances from the Endpoints to the Weighted Average

4) Solve the equation: (W2)/(W1) =(D1)/(D2)
(the weights and distances are in an INVERSE RATIO)­


Teeter Totter Basic Examples Playlist: https://www.youtube.com/playlist?list=PL2exXfCUscn8Hvafet5-IPH1eNNLSjQBP

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%

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

Here are a couple of video explanations for this question. The first goes over an algebraic approach. The second goes over a 'balance method' approach.

Algebraic Method:

Balance Method:

VeritasPrepKarishma niks18




I went through your blog post here
wherein you mentioned to put lower no of LHS on scale line. Accordingly if W1=40% and W2=25% and combined average is 25%
I am getting W1/W2 =10/5 or 2/1. Can you add your two cents?
_________________

How did u get 1-x?9

Hi S1937,

It turns out that [1-x] is an error, if x is meant to represent the fraction of the final mixture made up by X. Instead, [1-x] should be the fraction of the final mixture that is made up by Y, and the equation should read:

25[1-x] + 40x = 30

Then you get x = 1/3 = 33 1/3%, and arrive at the correct answer, B.

I also wanted to let everyone know that I'm starting a new project to go through all of the Quant questions in the 2019 Official Guide and share my suggested "GMAT Timing Tips" for each one: that is, what could you notice or do to be able to answer each question more efficiently? For this question, my GMAT Timing Tips are:

Weighted average mapping strategy (also known as the tug of war, and similar to the "Balance Method" also described in this thread): Use the weighted average mapping strategy to find the ratio of X to Y. This is a shortcut for the algebra, and can be a great way to save valuable time on the GMAT.

Calculate percent as part of a total: Once you have the ratio, calculate the percent by dividing the part that you are interested in (X) by the total (X+Y).

I'm also planning to create video solutions demonstrating how to use my GMAT Timing Tips for each of these questions. This will take a while, but I'll start with the those that I get requests for first. If you would me to create a video solution for this question, please go to the page that I have created for this question and vote for or share it: Seed mixture X is 40 percent ryegrass and 60 percent...

You can also ask me to answer a question about this GMAT practice question by asking it in this thread, or by using the question form on the page above. Please let me know if you have any questions!

Hello Experts.
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight, ccooley

In this question prompt, x=40% , y=25%. So, our weighted average should be between 25 and 40.
Can we cross out the choices A,C,D,E because they are not between 25 and 40?
Thanks__
_________________

JeffTargetTestPrep

Can I create one more expression as this below?
X + Y = 100

et x = the PERCENT of mixture X needed (in other words, x/100 = the proportion of mixture X needed)
So, 100-x = the PERCENT of mixture Y needed (in other words, (100-x)/100 = the proportion of mixture Y needed)

Weighted average of groups combined = 30%

Now take the above formula and plug in the values to get:
30 = (x/100)(40) + [(100-x)/100](25)
Multiply both sides by 100 to get: 30 = 40x + (100-x)(25)
Expand: 3000 = 40x + 2500 - 25x
Simplify: 3000 = 15x + 2500
So: 500 = 15x
Solve: x = 500/15
= 100/3
= 33 1/3

So, mixture X is 33 1/3 % of the COMBINED mi

Video solution from TGS - The GMAT® Strategy:

Want to reach your dream GMAT® score in half the normal time? Free resources to show you how: http://linktr.ee/thegmatstrategy

Came across the simpler- Alligation method- see attached image for method.
Reference link I found on youtube- https://www.youtube.com/watch?v=C81cWy_GQQM

Do check it out for mixtures type qs