parking garage

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Fri Oct 30, 2009 2:24 pm

A particular parking garage is increasing its rates by 15 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob's percentage reduction in the number of days he uses the garage each month?

Looking for easy ways to solve this problem..

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Source: Beat The GMAT — Problem Solving | Fri Oct 30, 2009 2:24 pm

sanjana: Master | Next Rank: 500 Posts; Posts: 182; Joined: Sun Aug 02, 2009 7:19 pm; Thanked: 18 times; GMAT Score:680

by sanjana » Sun Nov 01, 2009 10:04 pm

Whats the OA? is it 14%

Confirm and then I will let u know how I solved.

Made a mistake.. Got new days = 87% old days,hece 13% is correct.

Last edited by sanjana on Tue Nov 03, 2009 9:56 am, edited 1 time in total.

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NikolayZ: Master | Next Rank: 500 Posts; Posts: 124; Joined: Thu Jun 18, 2009 5:33 am; Thanked: 35 times

by NikolayZ » Sun Nov 01, 2009 11:31 pm

Hey there.

We need to introduce 3 variables here.
x- rate.
D- days prior to rate increase
n - days reducted.

so, if the monthly price have to be the same, we have an equation :
xD=1.15*x*(D-n), we need to know n, from this equation. "x" may be terminated

1.15 = 1 15/100, 1 3/20 or 23/20

so,

D-n=D*20/23, -n=(20D/23)-D, n=(3/23)D, or 12/92, would be less then 14% but greater than 13 %.
What is the OA?

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Mon Nov 02, 2009 5:20 am

you got it!13%

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life is a test: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon Mar 02, 2009 12:02 pm; Thanked: 15 times

by life is a test » Tue Nov 03, 2009 9:52 am

alternative way is just to plug in nums:

orig rate =100, new rate = 115
orig days = 2, new days = 200/115 = 40/23

% change = difference/original = (6/23) / 2 = 6/46 -> round it up to 6/48 -> ans is greater than 1/8 since we rounded the denominator up --> ans>12.5%

hope that helps.

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

by crackgmat007 » Tue Nov 03, 2009 1:48 pm

I guess the easiest way is to apply inversly prop rule

r * d = amount spent

amount spent is constant. if you increase r by 15%, to maintain the same constant #, we must multiply d by 100/115.

R = r * 115/100

Hence, R * 115/100 * D * 100/115 (must be multiplied to maintain constant) = amount spent

Balance is simple (old - new) / old formula

HTH

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ssuarezo: Master | Next Rank: 500 Posts; Posts: 126; Joined: Wed Jun 24, 2009 1:12 pm; Location: Montreal; Thanked: 2 times; GMAT Score:510

by ssuarezo » Tue Nov 03, 2009 5:35 pm

Hi:

What about this?
100 -- previous month
115 -- current month

in the current month, I need to save 15, the % to save is 15/115 = 13%

We can't count days 'cause it will change every month (28,29,30-31).

Is this correct? I know this formula is valid for the first month, but, as I see, all the other solutions are valid just for the first month, 13%, am I wrong?

Silvia

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