GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 02:33 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In a hostel, the number of students decreased by 8% and the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern  Joined: 04 Mar 2012
Posts: 37
In a hostel, the number of students decreased by 8% and the  [#permalink]

Show Tags

1
13 00:00

Difficulty:   65% (hard)

Question Stats: 65% (02:43) correct 35% (02:51) wrong based on 193 sessions

HideShow timer Statistics

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%
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4773
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: In a hostel, the number of students decreased by 8% and the  [#permalink]

Show Tags

6
1
stonecold wrote:
Vyshak
Any Shortcuts here ?
took me 8 minutes to solve
i solved twice
actually thrice regards
Stone Cold

Yes bro possible

IMHO that we need to take three factors ( No of Students , Consumption per student and Cost of Food ) and create a table as below -
Attachment: 1.PNG [ 4.07 KiB | Viewed 3949 times ]

Where Total Cost = No of Students * Consumption per student * Cost of Food

So, from the above table find the new value of Consumption per student

Consumption per student = Total Cost / ( No of Students * Cost of Food )
=>Consumption per student = 10000 / 92 * 12
=>New Consumption per student = 9.06

Now find the last part -

Quote:
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?

Reduction in consumption required is 10 - 9.06 = 0.94

So, Percentage consumption of food be cut short by every student = 0.94/10 * 100 = 9.40%  _________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
General Discussion
SVP  P
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1883
GMAT 1: 780 Q51 V48 GRE 1: Q800 V740 In a hostel, the number of students decreased by 8% and the  [#permalink]

Show Tags

3
Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)

Originally,
C = FNP

When number of students decrease by 8%, and the price of food increases by 20%,
C = F(new) * (0.92N) * (1.2P)
=> F(new) = F/(0.92*1.2)
=> F(new) = 0.906F

Therefore the new cost of food must be 90.6% of the old cost, or the cost of food must decrease by 9.4% (option E)
_________________
GyanOne [www.gyanone.com]| Premium MBA and MiM Admissions Consulting

Awesome Work | Honest Advise | Outstanding Results

Reach Out, Lets chat!
Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services

Originally posted by GyanOne on 01 May 2012, 23:23.
Last edited by GyanOne on 27 Jun 2015, 00:21, edited 1 time in total.
Current Student B
Joined: 23 May 2013
Posts: 183
Location: United States
Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45 GPA: 3.5
Re: In a hostel, the number of students decreased by 8% and the  [#permalink]

Show Tags

1
I cannot see this being a GMAT problem - how is one supposed to calculate 1- [1/(.92*1.2)] without a calculator? Even with using fractions I get 13/138 which is also not easily solved.
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1749
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: In a hostel, the number of students decreased by 8% and the  [#permalink]

Show Tags

1
speedilly wrote:
I cannot see this being a GMAT problem - how is one supposed to calculate 1- [1/(.92*1.2)] without a calculator? Even with using fractions I get 13/138 which is also not easily solved.

Agree.. this calculation goes tough. Any simpler way to avoid that 92 & 12 factor?
_________________
Kindly press "+1 Kudos" to appreciate Retired Moderator Joined: 16 Jun 2012
Posts: 991
Location: United States
Re: In a hostel, the number of students decreased by 8% and the  [#permalink]

Show Tags

1
1
PareshGmat wrote:
speedilly wrote:
I cannot see this being a GMAT problem - how is one supposed to calculate 1- [1/(.92*1.2)] without a calculator? Even with using fractions I get 13/138 which is also not easily solved.

Agree.. this calculation goes tough. Any simpler way to avoid that 92 & 12 factor?

Hello

My approach is

Name:
S = number of students
P = Price
Q = Quantity of food consumption.
C = total cost

==> C = S*P*Q

One way to solve this kind of question is plug in numbers.
Assume: before we have 100 students, P = \$10 ==> C = 100*10*Q = 1000*Q
After: we have 92 students, P = \$12 ==> C' = 92*12*Q' = 1104*Q'

==> 1104*Q' = 1000*Q
==> Q' = 1000/1104*Q = (1 - 104/1104)*Q
==> Q' = Q - 104/1104*Q

The red part is the decrease of food consumption. We can guess 104/1104 ~ 9.4% (The ONLY option < 10%) --> E is answer.

Hope it helps.
_________________
Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Chris Bangle - Former BMW Chief of Design.
Current Student D
Joined: 12 Aug 2015
Posts: 2569
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: In a hostel, the number of students decreased by 8% and the  [#permalink]

Show Tags

Vyshak
Any Shortcuts here ?
took me 8 minutes to solve
i solved twice
actually thrice regards
Stone Cold
_________________
Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1685
Location: India
Re: In a hostel, the number of students decreased by 8% and the  [#permalink]

Show Tags

3
stonecold wrote:
Vyshak
Any Shortcuts here ?
took me 8 minutes to solve
i solved twice
actually thrice regards
Stone Cold

Hi,

Assume there are 100 students, price/student = 10, Consumption = 1unit --> Cost = 100*10*1 = 1000
Given scenario: 92 students, price/student = 12, Consumption = x, But cost = 1000

92*12*x = 1000
x = 1000/1104 = 125/138 = 0.9 (approx)
So consumption has reduced by (1 - 0.9)*100 = 10% (approx)

Senior Manager  P
Joined: 02 Apr 2014
Posts: 468
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34 GPA: 3.5
Re: In a hostel, the number of students decreased by 8% and the  [#permalink]

Show Tags

Let there be 100 students , price of each food student be 100\$
Now 8% number of students reduced = 92, price of food increased by 20% = 120\$
x(x is decimal less than 1) be reduced consumption of food, so price of reduced food = 120x

given 100 * 100 = 92 * 120 * x
x = 10000/(92*120) = 1000/1104 = 10/11 (approx)
so how much each student has to reduce = 1 - 10/11 = 1/11 = 9% approx => closest is (E)
Director  P
Joined: 24 Nov 2016
Posts: 578
Location: United States
Re: In a hostel, the number of students decreased by 8% and the  [#permalink]

Show Tags

GyanOne wrote:
Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)

Originally,
C = FNP

When number of students decrease by 8%, and the price of food increases by 20%,
C = F(new) * (0.92N) * (1.2P)
=> F(new) = F/(0.92*1.2)
=> F(new) = 0.906F

Therefore the new cost of food must be 90.6% of the old cost, or the cost of food must decrease by 9.4% (option E)

just to clear things up, what you did in the second part was:
C = F(new) * (0.92N) * (1.2P)
FNP = F(new) * (0.92N) * (1.2P)
F(new) = FNP / (0.92N) * (1.2P)
F(new) = F / (0.92) * (1.2)
F(new) = 0.906F

correct? Re: In a hostel, the number of students decreased by 8% and the   [#permalink] 23 Aug 2019, 05:07
Display posts from previous: Sort by

In a hostel, the number of students decreased by 8% and the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  