Word problem

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Imsukhi: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Thu Jun 20, 2013 7:58 pm; Thanked: 1 times

by Imsukhi » Sat Jun 29, 2013 2:30 am

A group at a hotel has 495$ to share.two person,s left without contributing. And each of those who were left had to pay 10 $ more to make the deficit .
How many we're these in the group originally .?
A 13

B 11
C 9
D 10
E 25

Pls explain

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Source: Beat The GMAT — Problem Solving | Sat Jun 29, 2013 2:30 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 » Sat Jun 29, 2013 3:01 am

Imsukhi wrote:A group of people is sharing a hotel room. The total price of the room is $495. After two members of the group leave without contributing, the cost per person for each of the remaining members increases by $10. How many people were in the group originally?

9, 10, 11, 13, 25

Pls explain

I've cleaned up the wording of the problem and reordered the answer choices as they would appear on the GMAT.

We can plug in the answers, which imply the following options for the ORIGINAL number of people:
9, 10, 11, 13, 25
These values imply the following options for the REMAINING number of people after 2 members leave:
7, 8, 9, 11, 23

Only the pair in red is composed of two factors of 495.

The correct answer is C.

Answer choice C: 11
For 11 people, the price per person = 495/11 = 45.
For 9 people, the price per person = 495/9 = 55.
Increase in the price per person = 55-45 = 10.
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aaggar7: Master | Next Rank: 500 Posts; Posts: 124; Joined: Sun Mar 11, 2012 8:48 pmFollowed by: 1 member; Thanked: 9 times

by aaggar7 » Sat Jun 29, 2013 4:34 am

Hi,

Let no of people = x
Share per head = y

So, xy = 495 --(1)

Next equation,

(x-2)(y+10) = 495

=> xy +10x - 2y -20 = 495

From 1 xy= 495

So 10x -2y -20 = 0

x = 495/y from 1

y^2 + 10y -2475 = 0

y = 45 , y = -55

so x = 11.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Jun 29, 2013 6:06 am

A group of people is sharing a hotel room. The total price of the room is $495. After two members of the group leave without contributing, the cost per person for each of the remaining members increases by $10. How many people were in the group originally?

A) 9
B) 10
C) 11
D) 13
E) 25

Let x = the original number of people in the group
So, x - 2 = number of people in the group after 2 leave

So, 495/x = original cost per person
And 495/(x-2) = cost per person after 2 leave

After two members of the group leave without contributing, the cost per person for each of the remaining members increases by $10.
In other words, (cost per person after 2 leave) - (original cost per person) = 10
So, 495/(x-2) - 495/x = 10

IMPORTANT: At this point, it might actually be fastest to plug in the answer choices to see which one works. Or, we can solve the equation for x . . .

495/(x-2) - 495/x = 10
Multiply both sides by (x)(x-2) to get: 495x - 495(x-2) = 10(x)(x-2)
Expand: 495x - 495x + 990 = 10x^2 - 20x
Simplify: 10x^2 - 20x - 990 = 0
Divide both sides by 10: x^2 - 2x - 99 = 0
Factor: (x - 11)(x + 9) = 0
So, x = 11 or x = -9
We can eliminate x = -9, so x must equal 11

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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