|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 08 Sep 2006
Posts: 39
|
A rabbit on a controlled diet is fed daily 300 grams of a
[#permalink]
Show Tags
 Updated on: 06 Jun 2014, 01:39
Question Stats:
81% (02:16) correct 19% (02:34) wrong based on 1741 sessions
HideShow timer Statistics
A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture. A. 100 B. 140 C. 150 D. 160 E. 200
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by tinman1412 on 26 Jul 2007, 08:45.
Last edited by Bunuel on 06 Jun 2014, 01:39, edited 1 time in total.
Edited the question and added the OA.
|
|
|
|
|
|
|
|
Director
Joined: 26 Feb 2006
Posts: 609
|
Re: Mixture Problem. Please explain
[#permalink]
Show Tags
26 Jul 2007, 09:17
tinman1412 wrote: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture. a)100 b)140 c)150 d)160 e)200 The answer is B)140, but I do not understand the OG explanation. Can someone provide their approach to this question in detail Thanks, in fact one eq is enough: .1x + .15(300-x) = 38
solve for x, x = 140
|
|
|
|
|
|
|
|
Manager
Joined: 22 May 2007
Posts: 83
|
Set up two equations.
We know that 10%x+15%y=38 grams or .1x+.15y=38
We also know that x+y=300 grams.
2 eq. with 2 variables. Solve them and you should get it.
|
|
|
|
|
|
Intern
Joined: 26 Aug 2006
Posts: 18
|
Re: Mixture Problem. Please explain
[#permalink]
Show Tags
26 Jul 2007, 09:35
tinman1412 wrote: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture. a)100 b)140 c)150 d)160 e)200 The answer is B)140, but I do not understand the OG explanation. Can someone provide their approach to this question in detail Thanks, Much simpler method is there...
38 gms means approx. 12.66%. Then use the mixture alligation formula to calculate the ratio of X to Y, ie,
X/Y= (15-12.66)/(12.66-10)=2.33/2.66.
Hence amt of X in total mixture is 300*2.33/(2.33+2.66)=139.2~140
Answer B.
|
|
|
|
|
|
Manager
Joined: 21 Jun 2006
Posts: 208
|
D
Assume x grams is of mixture A and 300-x is of mixture B
Eqn is:
(300-x)*.1 + .15x = 38 (10% and 15% protein in Mixtures A and B respectively)
Solve for x =160
|
|
|
|
|
|
CEO
Joined: 07 Jul 2004
Posts: 2917
Location: Singapore
|
0.1x + 0.15y = 38
x+y = 300
x = 300-y
so 0.1(300-y) + 0.15y = 38
30-0.1y + 0.15y = 38
0.05y = 8
y = 160 grams
then x = 140 grams.
Ans B
|
|
|
|
|
|
Intern
Joined: 26 Aug 2006
Posts: 18
|
tinman1412 wrote: I was just wondering. I know there are many different ways to solve math problems, but is there a prefer method when solving Mixture Problems?
Its wat you feel comfortable with or the one which you do faster and accurately. You have to develop that approach by practice.
Atleast I think so. I solved the problem using Mixtures & Alligation formula coz I feel comfortable with that.
Sunil
|
|
|
|
|
|
Manager
Joined: 02 Jul 2007
Posts: 95
|
Re: Mixture Problem. Please explain
[#permalink]
Show Tags
13 Aug 2009, 04:37
MGMAT has a great method that has really helped me to do these problems quickly. For mixture problems, set up a chart: the two different mixtures go on the right hand side, the quantities of each go on the top: Protein Other X Y The problem says the two mixtures are added together to produce a new mixture totaling 300 grams, so add to the chart: Protein Other Total X X Y Y X+Y 300 Now add the information about how much protein is in each mixture Protein Other Total X .1X X Y .15Y Y X+Y 38 300 Now there are two equations with 2 variables: .1X + .15Y=38 X + Y = 300 Simple method, but it really helps break down harder questions.
|
|
|
|
|
|
Intern
Joined: 22 Jun 2010
Posts: 6
|
Re: Mixture Problem. Please explain
[#permalink]
Show Tags
22 Jun 2010, 16:23
can someone explain the logic of the mixture and allegation formula?
the ratio of (difference between the high value and new percentage)
over
(diff b/t high and new) + (diff b/t new and low value)
what does this ratio represent and why, when multiplying the whole to it does it give you the amount in final.....
|
|
|
|
|
|
Intern
Joined: 20 Sep 2010
Posts: 2
|
Re: Mixture Problem. Please explain
[#permalink]
Show Tags
23 Sep 2010, 01:13
We know that
1.00x+1.00y=300
and that
0.10x+0.15y=38
so
0.10x+0.15y=38
*10=
1.00x+1.50y=380
Align them under eachother
1.00x+1.50y=380
1.00x+1.00y=300
Means 0.50y=80
80*2=160
y=160
x=300-y
x=300-160
x=140
|
|
|
|
|
|
Intern
Joined: 07 Sep 2010
Posts: 4
|
Re: Mixture Problem. Please explain
[#permalink]
Show Tags
24 Sep 2010, 02:21
let x= mixture A ,, then 300-x is Mixture B
.0.1 x + (300-x)0.15=38
after the solving the equation ,,x=140
|
|
|
|
|
|
Manager
Joined: 19 Dec 2010
Posts: 72
|
Re: Mixture Problem. Please explain
[#permalink]
Show Tags
11 Mar 2011, 04:15
This problem is relatively easy once you break it up the way it's supposed to be broken up...
they basically say X lbs +Y lbs = 300 lbs
Now, equate the protein levels together:
0.10 X + 0.15 Y = 38
Solve
|
|
|
|
|
|
Manager
Joined: 25 May 2011
Posts: 92
|
Re: A rabbit on a controlled diet is fed daily 300 grams of a
[#permalink]
Show Tags
07 Nov 2011, 02:47
just calculation:
0.1*X+0.15*(300-X)=38
X=140
|
|
|
|
|
|
Manager
Joined: 24 Nov 2013
Posts: 55
|
Re: A rabbit on a controlled diet is fed daily 300 grams of a
[#permalink]
Show Tags
17 Aug 2015, 00:40
we can solve by testing answers
lets start with B...
let qty of X be 140 gms. so Y will be 160 gms.
proteins from X = 14 gms
proteins from Y = 24 gms
add both, we get 38gms.
so X must be 140 gms.
|
|
|
|
|
|
Senior Manager
Joined: 12 Aug 2015
Posts: 277
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
|
Re: A rabbit on a controlled diet is fed daily 300 grams of a
[#permalink]
Show Tags
01 Feb 2016, 22:30
30 sec reasoning out: 38/300 - is a bit less than a 13% protein content. Hence 13% is closer to 15%Y than to 10%X - this means that there is just sligthly more Y component because should those 2 be equal the protein content would have been sharply 12.5% which is not the case.
Immediately we kick out 3 answer choices >= 150 and are left with A and B. A is too low for the aboe slight deviation - so B is much closer to truth.
|
|
|
|
|
|
Math Expert
Joined: 02 Aug 2009
Posts: 8602
|
A rabbit on a controlled diet is fed daily 300 grams of a
[#permalink]
Show Tags
01 Feb 2016, 22:53
shasadou wrote: 30 sec reasoning out: 38/300 - is a bit less than a 13% protein content. Hence 13% is closer to 15%Y than to 10%X - this means that there is just sligthly more Y component because should those 2 be equal the protein content would have been sharply 12.5% which is not the case.
Immediately we kick out 3 answer choices >= 150 and are left with A and B. A is too low for the aboe slight deviation - so B is much closer to truth. Hi, this weighted approach,if mastered, can actually make a difference in your Quant score.. Good approach and you should try this in almost all Q that asks for an average in a mixture, or for a quantity, when an average is given.. +1 kudos
_________________
|
|
|
|
|
|
Senior Manager
Joined: 12 Aug 2015
Posts: 277
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
|
Re: A rabbit on a controlled diet is fed daily 300 grams of a
[#permalink]
Show Tags
01 Feb 2016, 23:14
I am going through word problem types of questions because I think i bombed this type of q in my last gmat both time-wise and accuracy wise. And what i see from OG about 30% of all questions comprise the word problem type. During these 2 days I solved numerous word problems and here are my observations: - very time consuming because the intuitive approach is to apply algebra and form equations, on average easy question take almost the same time as hard ones - given my incline to make silly mistakes in algebraic calculations I should rely more on reasoning out the easy questions - majority of easy word problems employ weighted average or mean concepts which can be done by reasoning much faster than by doing algebra - ultimately this will save at least 30 secs on each such question -
|
|
|
|
|
|
Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 773
Location: United States (CA)
Age: 40
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47  GMAT 3: 750 Q50 V42
WE: Education (Education)
|
A rabbit on a controlled diet is fed daily 300 grams of a
[#permalink]
Show Tags
26 Mar 2016, 17:25
Here is a visual that should help.
Attachments
Screen Shot 2016-03-26 at 6.26.43 PM.png [ 108.49 KiB | Viewed 23307 times ]
|
|
|
|
|
|
Manager
Joined: 28 Apr 2016
Posts: 81
|
Re: A rabbit on a controlled diet is fed daily 300 grams of a
[#permalink]
Show Tags
23 May 2016, 11:29
The answer choices are wide enough to narrow down. Food X < average, therefore options C to D are out. Can't be 100 because it is to far away from the average, hence B. tinman1412 wrote: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture.
A. 100
B. 140
C. 150
D. 160
E. 200
|
|
|
|
|
|
Manager
Joined: 23 Feb 2015
Posts: 165
|
Re: A rabbit on a controlled diet is fed daily 300 grams of a
[#permalink]
Show Tags
23 May 2016, 11:52
\(.1x+.15(300-x)=38\)
\(10x+4500-15x=3800\)
\(5x=700\)
\(x=140\)
|
|
|
|
|
|
|
Re: A rabbit on a controlled diet is fed daily 300 grams of a
[#permalink]
23 May 2016, 11:52
|
|
|
|
|
Go to page
1 2
Next
[ 33 posts ]
|
|
close
