Ratios Question

Expert replies

Nijo: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Thu Jun 12, 2014 8:41 pm; Thanked: 1 times

by Nijo » Wed Aug 13, 2014 1:24 am

A contractor combined x tons of a gravel mixture that contained 10% gravel by weight with y tons of a mixture that contained 2% gravel by weight to produce z tons of a mixture that was 5% gravel by weight.
What is the value of x?
1) y = 10
2) z = 16

OA is D

thanks

Like this post

Source: Beat The GMAT — Data Sufficiency | Wed Aug 13, 2014 1:24 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Aug 13, 2014 1:43 am

A contractor combined x tons of a gravel mixture that contained 10% gravel G, by weight, with y tons of a mixture that contained 2 percent of the gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x?

1) y = 10

2) z = 16

x = 10% gravel
y = 2% gravel.
z = the MIXTURE of x and y = 5% gravel.

To determine the required ratio of x to y, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for x and y on the ends and the percentage for mixture z in the middle.
x 10%-----------5%-----------2% y

Step 2: Calculate the distances between the percentages.
x 10%-----5-----5%----3-----2% y

Step 3: Determine the ratio in the mixture.
The required ratio of x to y is equal to the RECIPROCAL of the distances in red.
x:y = 3:5.

Since x:y = 3:5, and 3+5 = 8, every 8 tons of mixture z is composed of 3 tons of x and 5 tons of y.

Statement 1: y=10
Since x:y = 3:5 = 6:10, x=6.
SUFFICIENT.

Statement 2: z=16
Since x:y = 3:5 = 6:10, and 6+10 = 16, the 16 tons of mixture z must be composed of 6 tons of x and 10 tons of y.
SUFFICIENT.

The correct answer is D.

Check here for a similar problem:
https://www.beatthegmat.com/weighted-ave ... 74015.html

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Aug 13, 2014 9:41 pm

Hi Nijo,

This question is build around an interesting math shortcut: a "system" of equations.

The information in the prompt can be rewritten into 2 equations:

The first equation accounts for the mixture:
.1(X) + .02(Y) = .05(Z)

It can be simplified...

.1X + .02Y = .05Z
10X + 2Y = 5Z

and

The second equation accounts for the fact that when we mix X tons with Y tons, we get Z tons:
X + Y = Z

Since we're mixing two types of gravel, we don't have to think about using 0 or any negative numbers. The info in the prompt gives us 3 variables and 2 unique equations. If we are given another new equation, then we'll have a "system" of equations, which will allow us to solve for all 3 variables. We're asked for the value of X.

Fact 1: Y = 10

This is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X. We don't actually have to do the math though.
Fact 1 is SUFFICIENT.

Fact 2: Z = 16

This too is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Last edited by [email protected] on Thu Aug 14, 2014 10:19 am, edited 1 time in total.

Contact Rich at [email protected]

Like this post

akhilsuhag: Master | Next Rank: 500 Posts; Posts: 351; Joined: Mon Jul 04, 2011 10:25 pmFollowed by: 4 members; Thanked: 57 times

by akhilsuhag » Thu Aug 14, 2014 5:44 am

[email protected] wrote:Hi Nijo,

This question is build around an interesting math shortcut: a "system" of equations.

The information in the prompt can be rewritten into 2 equations:

The first equation accounts for the mixture:
[.1(X) + .02(Y)]/(X + Y) = .05(Z)

It can be simplified...

.1X + .02Y = .05XYZ
10X + 2Y = 5XYZ

and

The second equation accounts for the fact that when we mix X tons with Y tons, we get Z tons:
X + Y = Z

Since we're mixing two types of gravel, we don't have to think about using 0 or any negative numbers. The info in the prompt gives us 3 variables and 2 unique equations. If we are given another new equation, then we'll have a "system" of equations, which will allow us to solve for all 3 variables. We're asked for the value of X.

Fact 1: Y = 10

This is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X. We don't actually have to do the math though.
Fact 1 is SUFFICIENT.

Fact 2: Z = 16

This too is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Rich I used two equations as well but our first ones are different. Can you explain why and if I am incorrect

0.1X + .02Y = 0.05 Z

X + Y = Z

You use a little different version of the first equation I used. I mean to say that the amount of gravel in X + amount of gravel in Y is equal to the amount of gravel in Z - as thr is no other source of gravel.

You seem to divide the Left hand side by (X+Y) although.

Please press "thanks" if you think my post has helped you.. Cheers!!

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Aug 14, 2014 7:04 am

akhilsuhag wrote:
[email protected] wrote:Hi Nijo,

This question is build around an interesting math shortcut: a "system" of equations.

The information in the prompt can be rewritten into 2 equations:

The first equation accounts for the mixture:
[.1(X) + .02(Y)]/(X + Y) = .05(Z)

It can be simplified...

.1X + .02Y = .05XYZ
10X + 2Y = 5XYZ

and

The second equation accounts for the fact that when we mix X tons with Y tons, we get Z tons:
X + Y = Z

Since we're mixing two types of gravel, we don't have to think about using 0 or any negative numbers. The info in the prompt gives us 3 variables and 2 unique equations. If we are given another new equation, then we'll have a "system" of equations, which will allow us to solve for all 3 variables. We're asked for the value of X.

Fact 1: Y = 10

This is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X. We don't actually have to do the math though.
Fact 1 is SUFFICIENT.

Fact 2: Z = 16

This too is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Rich I used two equations as well but our first ones are different. Can you explain why and if I am incorrect

0.1X + .02Y = 0.05 Z

X + Y = Z

You use a little different version of the first equation I used. I mean to say that the amount of gravel in X + amount of gravel in Y is equal to the amount of gravel in Z - as thr is no other source of gravel.

You seem to divide the Left hand side by (X+Y) although.

Your equation is correct.

I believe that Rich's equation should read as follows:
(0.1X + 0.02Y)/Z = 0.05.
Translated into words:
(gravel in X + gravel in Y)/(Z tons of the mixture of X and Y) = 5 percent.

Simplifying the equation above, we get:
0.1X + 0.02Y = 0.05Z
10X + 2Y = 5Z.

As you can see, your equation and Rich's are the same.

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Aug 14, 2014 10:18 am

Hi akhilsuhag,

You are absolutely correct; I must have been typing too quickly to notice the mistake. I've gone back and corrected by original post.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Aug 15, 2014 11:28 am

Nijo wrote:A contractor combined x tons of a gravel mixture that contained 10% gravel by weight with y tons of a mixture that contained 2% gravel by weight to produce z tons of a mixture that was 5% gravel by weight.
What is the value of x?
1) y = 10
2) z = 16

OA is D

thanks

Solution :

Answer: Option D

Attachments

"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review