Word Problem

This topic has expert replies
User avatar
Master | Next Rank: 500 Posts
Posts: 131
Joined: Thu Feb 21, 2008 7:13 pm
Location: Canada
Thanked: 3 times
GMAT Score:590

Word Problem

by carllecat » Tue Nov 17, 2009 8:12 am
In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 4% sales tax to the dealer's price per gallon d, in dollars, then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?

A) d = p - 0.22
B) d = p/1.22
C) d = (p/1.04) - 0.18
D) d = p - 0.18/1.04
E) d = p - 0.04/1.18

Answer to be posted later.

User avatar
Master | Next Rank: 500 Posts
Posts: 131
Joined: Thu Feb 21, 2008 7:13 pm
Location: Canada
Thanked: 3 times
GMAT Score:590

by carllecat » Tue Nov 17, 2009 8:41 am
D) D = p - 0.18/1.04

I do not understand why it is -0.18 instead of +0.18. Can someone please explain?

User avatar
GMAT Instructor
Posts: 80
Joined: Wed Aug 12, 2009 8:49 pm
Location: San Francisco, CA
Thanked: 16 times

by grockit_jake » Tue Nov 17, 2009 10:41 am
The easiest way to start is to set up the equation in terms of d and p in the way the stimulus presents the question:

p = 1.04d + 0.18

Now solve for d:

p - 0.18 = 1.04d

d = (p - 0.18) / d
Jake Becker
Academic Director
Grockit Test Prep
https://www.grockit.com

User avatar
Master | Next Rank: 500 Posts
Posts: 131
Joined: Thu Feb 21, 2008 7:13 pm
Location: Canada
Thanked: 3 times
GMAT Score:590

by carllecat » Tue Nov 17, 2009 11:11 am
What a silly mistake it was... My formula was:

p + 0.18 = d + 0.04d when it should have been p = d + 0.04d +0.18.


Thanks grockit_jake!

Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Sat Jul 18, 2009 10:26 am

by cabate2000 » Tue Nov 17, 2009 3:21 pm
Why is the answer not C?

If you assume gas costs $3.00 a gallon for the dealer (d), then you add tax and get $3.00 + $0.12 + 0.18 = $3.30 gallon (p)

Plugging into answer C

d = (p/1.04) - 0.18

$3.00 = ($3.30/$1.04) - $0.18
$3.00 = $3.17-$0.18
(close enough)

Trying a different price, the formula still holds.

$5.00 = ($5.38/$1.04) - $0.18

User avatar
GMAT Instructor
Posts: 80
Joined: Wed Aug 12, 2009 8:49 pm
Location: San Francisco, CA
Thanked: 16 times

by grockit_jake » Tue Nov 17, 2009 3:27 pm
Close enough doesn't count. Sorry.

The reason it's so close is that 0.18 is really small relative to $5 or $3.

You have to "undo" the equation you put forward.

If you set d, then multiply by 1.04 and then subtract, to "undo" you must add first, then divide the sum.

Try answer C with $1 and see what you get
Jake Becker
Academic Director
Grockit Test Prep
https://www.grockit.com

Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Sat Jul 18, 2009 10:26 am

by cabate2000 » Tue Nov 17, 2009 3:46 pm
grockit_jake wrote:Close enough doesn't count. Sorry.

The reason it's so close is that 0.18 is really small relative to $5 or $3.

You have to "undo" the equation you put forward.

If you set d, then multiply by 1.04 and then subtract, to "undo" you must add first, then divide the sum.

Try answer C with $1 and see what you get
You are right. But try $3.00 with answer D and see what you get.

d = p - 0.18/1.04

$3.00 = [($3.00*1.04)+.18] - 0.18/1.04
3.00 = $3.30 - 0.17 does not equal $3.00

User avatar
GMAT Instructor
Posts: 80
Joined: Wed Aug 12, 2009 8:49 pm
Location: San Francisco, CA
Thanked: 16 times

by grockit_jake » Tue Nov 17, 2009 3:49 pm
There's a typo on D in the original question that carlcat posted.

it should read.

D. d = (p - 0.18)/1.04
Jake Becker
Academic Director
Grockit Test Prep
https://www.grockit.com

User avatar
Master | Next Rank: 500 Posts
Posts: 131
Joined: Thu Feb 21, 2008 7:13 pm
Location: Canada
Thanked: 3 times
GMAT Score:590

by carllecat » Tue Nov 17, 2009 5:34 pm
grockit_jake wrote:There's a typo on D in the original question that carlcat posted.

it should read.

D. d = (p - 0.18)/1.04
You are right for the typo, apologies.

Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Sat Jul 18, 2009 10:26 am

by cabate2000 » Tue Dec 01, 2009 9:31 am
I guess I'll take close enough, thanks.