In a hostel, the number of students decreased by 8% and the price of food
increased by 20% over the previous year.If each student consumes the same amount of food
then By how much should the consumption of food be cut short by every student,
so that the total cost of the food remains the same as that of the previous year?
A 19%
B 15%
C 25%
D 40%
E 9.4%
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
hostel students - food consumptions - percent increase
This topic has expert replies
-
mathbyvemuri
- Master | Next Rank: 500 Posts
- Posts: 142
- Joined: Thu Apr 26, 2012 3:24 am
- Location: India
- Thanked: 28 times
price is hiked by 20% => new price = 1.2 times the old price
number of students is decreased by 8% => new number = 0.92 times the old number
Finally the ratio of price to the number of students is changed by a factor 1.2/0.92
=> to keep the ratio constant, the food consumption shall be a changed by a factor 0.92/1.2 = 0.766
= 1-0.234 = 23.4% decrease in food consumption is required
Nearest answer is [spoiler]25%[/spoiler]
Answer option [spoiler]"C"[/spoiler]
number of students is decreased by 8% => new number = 0.92 times the old number
Finally the ratio of price to the number of students is changed by a factor 1.2/0.92
=> to keep the ratio constant, the food consumption shall be a changed by a factor 0.92/1.2 = 0.766
= 1-0.234 = 23.4% decrease in food consumption is required
Nearest answer is [spoiler]25%[/spoiler]
Answer option [spoiler]"C"[/spoiler]
RaviSankar Vemuri
Join my Google Group on Math:
https://groups.google.com/group/mathbyvemuri
My Blog on Math:
https://mathbyvemuri.blocked/
Some concepts for GMAT:
https://mathbyvemuri.blogspot.in/2012/05 ... -data.html
https://mathbyvemuri.blogspot.in/2012/05 ... dates.html
https://mathbyvemuri.blogspot.in/2012/05 ... es-of.html
Join my Google Group on Math:
https://groups.google.com/group/mathbyvemuri
My Blog on Math:
https://mathbyvemuri.blocked/
Some concepts for GMAT:
https://mathbyvemuri.blogspot.in/2012/05 ... -data.html
https://mathbyvemuri.blogspot.in/2012/05 ... dates.html
https://mathbyvemuri.blogspot.in/2012/05 ... es-of.html
-
aneesh.kg
- Master | Next Rank: 500 Posts
- Posts: 385
- Joined: Mon Apr 16, 2012 8:40 am
- Location: Pune, India
- Thanked: 186 times
- Followed by:29 members
Hi GMIHIR and mathbyvemuri - you got (C) as the answer because you did not consider 'consumption per student' parameter.
Solution:
Let N be the initial number of students, P the price and C the consumption per student.
N became 0.92N.
P becomes 1.2P.
C becomes xC.
Initial Total Cost = NPC
Final Total Cost = 1.104 NPCx
Initial Total Cost = Final Total Cost (required)
NPC = 1.104 NPCx
x = 0.906
if C becomes 0.906C then it means that C has decresed by [spoiler]9.4%[/spoiler].
[spoiler](E)[/spoiler] is the right answer.
Solution:
Let N be the initial number of students, P the price and C the consumption per student.
N became 0.92N.
P becomes 1.2P.
C becomes xC.
Initial Total Cost = NPC
Final Total Cost = 1.104 NPCx
Initial Total Cost = Final Total Cost (required)
NPC = 1.104 NPCx
x = 0.906
if C becomes 0.906C then it means that C has decresed by [spoiler]9.4%[/spoiler].
[spoiler](E)[/spoiler] is the right answer.
Aneesh Bangia
GMAT Math Coach
[email protected]
GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
GMAT Math Coach
[email protected]
GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
-
ihatemaths
- Master | Next Rank: 500 Posts
- Posts: 122
- Joined: Tue May 01, 2012 6:05 am
- Thanked: 3 times
@aneesh is it possible to do by percentages say no:of students from 100 to 108 and food from 100 to 120 something like that ?
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let the number of students = 100 and the original cost per student = 10.GMIHIR wrote:In a hostel, the number of students decreased by 8% and the price of food
increased by 20% over the previous year.If each student consumes the same amount of food
then By how much should the consumption of food be cut short by every student,
so that the total cost of the food remains the same as that of the previous year?
A 19%
B 15%
C 25%
D 40%
E 9.4%
Total cost = 100*10 = 1000.
The number of students decreased by 8% = 92.
The cost per student increased by 20% = 12.
New total cost = 92*12 = 1104.
For the amount spent this year to be the same as the amount spent the previous year, the new total cost must be reduced from 1104 to 1000 -- a decrease of about 10%.
Thus, each student must consume about 10% less food.
The correct answer is E.
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
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
-
ihatemaths
- Master | Next Rank: 500 Posts
- Posts: 122
- Joined: Tue May 01, 2012 6:05 am
- Thanked: 3 times
