Percentage Problem

Expert replies

askaichin: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Fri May 28, 2010 3:59 am; Thanked: 1 times

by askaichin » Sun Jul 25, 2010 8:06 am

Concrete mixture A is composed of 35 percent cement, 40 pecent sand and 25 percent gravel; concrete mixture B is composed of 15 percent cement, 30 percent sand and 55 percent gravel. If a mixture of A and B contains 25 percent cement, what percent of the weight of the mixture is A?

A 20%
B 33 1/3%
C 45%
D 50%
E 55 1/3%

Like this post

Source: Beat The GMAT — Problem Solving | Sun Jul 25, 2010 8:06 am

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Sun Jul 25, 2010 1:23 pm

Hi askaichin

To solve this, you can safely ignore the sand and gravel.

A is 35% cement. B is 15% cement. The mixture is 25% cement.

If the mix had only A but no B, then the mix would have been 35% cement. On the other hand, if the mix had only B but no A, then the mix would have been 15% cement. Essentially, the % cement in the mix is determined by the ratio of A:B in the mix. Since the % of cement in the whole mix is 25 (exactly halfway between 35 and 15), so there must be equal quantities of A and B. in other words the mix is 50% A and 50% B.

Pick answer D

In general, in weighted average questions between 2 things, the ratio of the distances between each datapoint and the weighted average is the inverse of the ratio of the two quantities being averaged. For example, A is 35% cement and B is 15% cement. If the mix had been 30% cement instead, then the ratio of distances between each datapoint (A=35, B=15) and the weighted average (30) would have been 5:15. This would mean that the ratio of quantities (inverse of ratio of distances) would have been A:B >> 15:5 >> 3:1. In other words, if the mix had 30% cement, then the mixture would have been 75% A and 25% B.

To practice weighted avg questions in timed drills, set topic='Weighted Averages' and difficulty='600-700 & 700+' in the Drill Generator

Good luck,
-Patrick

Last edited by Patrick_GMATFix on Mon Jul 26, 2010 4:45 am, edited 1 time in total.

Check out my site: GMATFix.com

To prep my students I use this tool >> (screenshots, video)

Ask me about tutoring.

Like this post

indiantiger: Master | Next Rank: 500 Posts; Posts: 362; Joined: Fri Oct 02, 2009 4:18 amFollowed by: 1 member; Thanked: 26 times

by indiantiger » Sun Jul 25, 2010 1:56 pm

given in the mixture the weight of Cement is 25 % of the weight of mixture

Let wm is the weight of the mixture wm this gives us

the weight of cement mixture = 25wm/100-----(1)

let wA be weight of concrete mixture A
let wB be weight of concrete mixture B

now

cement weight in mixture in A is = 35wA/100----(2)
cement weight in mixture in A is = 15wB/100----(3)

adding (2) and (3) = (1)
25wm/100 = 35wA/100 + 15wB/100
25wm = 35wA + 15wB
5wm = 7wA + 3wB
now we know wm = wA + wB
5wA+5wB = 7wA + 3wB
2wA = 2wB
wA = wB

% of A in combined mixture = wA/(wm) = wA/(wA+wB) = 1/2 = 50 %

"Single Malt is better than Blended"

Like this post

dinesh19aug: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Thu Feb 21, 2008 9:05 am; Thanked: 7 times

by dinesh19aug » Sun Jul 25, 2010 8:20 pm

Take a look at this:

https://www.beatthegmat.com/mba/2009/12/ ... art-2-of-2

Like this post

gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Sun Jul 25, 2010 8:53 pm

Alligation principle :

Wa/Wb = ( Pa-Pm)/(Pm-Pb)
(35-25)/(25-15)
1:1
Wa=Wb

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

Like this post

outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 amFollowed by: 3 members; Thanked: 46 times

by outreach » Sun Jul 25, 2010 10:00 pm

(.35A+.15B)/(A+B)=25/100
solving we Get A=B

hence D

askaichin wrote:Concrete mixture A is composed of 35 percent cement, 40 pecent sand and 25 percent gravel; concrete mixture B is composed of 15 percent cement, 30 percent sand and 55 percent gravel. If a mixture of A and B contains 25 percent cement, what percent of the weight of the mixture is A?

A 20%
B 33 1/3%
C 45%
D 50%
E 55 1/3%

-------------------------------------
--------------------------------------
General blog
https://amarnaik.wordpress.com
MBA blog
https://amarrnaik.blocked/

Like this post

thebigkats: Senior | Next Rank: 100 Posts; Posts: 86; Joined: Mon Sep 13, 2010 2:36 pmFollowed by: 2 members; Thanked: 29 times; GMAT Score:710

by thebigkats » Tue Jan 04, 2011 5:21 pm

say x tons of A and y tons of B is mixed to give us z tons of mixture ==> z = x+y ---------(1)
==> x contains x*(35/100) tons of cement
==> y contains y*(15/100) tons of cement
==> z contains (35x+15y)/100 tons of cement which is 25% of z = 25 *z/100
==> 35x+15y=25z ------------ (2)

?given (1) - 15x + 15y = 15z (multiplying (1) with 15) --------- (3)
subtracting (3) from (2)
20x = 10z
x = z/2

So A is 50% of mixture

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 » Tue Jan 04, 2011 7:46 pm

askaichin wrote:Concrete mixture A is composed of 35 percent cement, 40 pecent sand and 25 percent gravel; concrete mixture B is composed of 15 percent cement, 30 percent sand and 55 percent gravel. If a mixture of A and B contains 25 percent cement, what percent of the weight of the mixture is A?

A 20%
B 33 1/3%
C 45%
D 50%
E 55 1/3%

Almost no math is needed here. Since the resulting percentage of cement (25) is the average of the two original percentages of cement (35 and 15), equal amounts of A and B must have been used. Thus, the resulting mixture will be 50% A and 50% B.

The correct answer is D.

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

lordzilla: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sat Nov 13, 2010 12:42 pm

by lordzilla » Wed Apr 27, 2011 4:08 am

This question is quite simple. Ignore all the details about sand and gravel and focus on cement.

Now subtract 35% cement content of mixture A from cement content of mixture A and B. Then subtract 15% cement content of mixture B from mixture A and B. Note: Use just absolute values. Now find the ratio of the results.

35-25=10

15-25=10

ratio= 1:1
so 50%

Like this post

vishnuchaithanya: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Jan 20, 2011 3:19 am

by vishnuchaithanya » Mon May 30, 2011 2:38 am

it is 50%

Like this post

sushantgupta: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Sun Mar 27, 2011 9:54 am; Thanked: 2 times

by sushantgupta » Mon Jul 04, 2011 10:42 pm

50%

Like this post

sushantgupta: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Sun Mar 27, 2011 9:54 am; Thanked: 2 times

by sushantgupta » Mon Jul 04, 2011 10:42 pm

50%

Like this post

prashant misra: Master | Next Rank: 500 Posts; Posts: 101; Joined: Thu Aug 25, 2011 9:39 pm

by prashant misra » Sat Oct 29, 2011 10:48 am

the answer to this question is D.i solved this question in following manner 35%of A + 15% of B=25% of (A+B) that gives us A/B=1/1 ratio

Like this post

Rastis: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Sep 21, 2011 7:06 amFollowed by: 2 members; Location: Washington, DC; Thanked: 6 times; GMAT Score:500

by Rastis » Tue Nov 29, 2011 12:44 pm

I'm having a difficult time understanding the logic behind the answer explanations people are providing. Can someone help please?

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 » Tue Nov 29, 2011 1:19 pm

Rastis wrote:I'm having a difficult time understanding the logic behind the answer explanations people are providing. Can someone help please?

A = 15% cement.
B = 35% cement.

If we combine EQUAL amounts of A and B, the percentage of cement in the mixture will be HALFWAY between 15 and 35.
To illustrate:
In 100 pounds of A, the amount of cement = 15 pounds.
In 100 pounds of B, the amount of cement = 35 pounds.
When the two are combined, the percentage of cement in the mixture = (15+35)/(100+100) = 50/200 = 25/100 = 25%.
25% is HALFWAY between 15% and 35%.

In the problem above, since the mixture is 25% cement -- HALFWAY between 15% and 35% -- EQUAL amounts of A and B must have been used.
Thus, the percentage of A in the mixture = 50%.

Like this post

Post new topic Post Reply

GMAT Course Reviews

559 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