A parking lot charges a flat rate of X dollars for any

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BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Thu May 10, 2018 2:58 pm

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A parking lot charges a flat rate of X dollars for any amount of time up to two hours, and X/6 hours each hour or fraction of an hour after the first two hours. How much does it cost to park for 5 hours and 15 minutes?

A. 3X
B. 2X
C. 5X/3
D. 3X/2
E. 7X/6

The OA is C.

Please, can anyone assist me with this PS question? I'm confused and I can't solve it. Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Thu May 10, 2018 2:58 pm

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by [email protected] » Thu May 10, 2018 8:09 pm

Hi All,

We're told that a parking lot charges a flat rate of X dollars for any amount of time UP to 2 hours, and X/6 hours each hour OR fraction of an hour AFTER the first two hours. We're asked for the cost to park for 5 hours and 15 minutes. This question can be solved by TESTing VALUES.

IF.... X=6
Then it costs $6 for the first 2 hours and...
$6/6 = $1 for each additional hour or fraction of an hour.

With a total time of 5 hours and 15 minutes, the cost would be $6 (for the first 2 hours) + $3 (for the next 3 hours) + $1 (for the fraction of the last hour) = $10. So we're looking for an answer that equals 10 when X=6. There's only one answer that matches...

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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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 » Fri May 11, 2018 6:30 am

BTGmoderatorLU wrote:A parking lot charges a flat rate of X dollars for any amount of time up to two hours, and X/6 hours each hour or fraction of an hour after the first two hours. How much does it cost to park for 5 hours and 15 minutes?

A. 3X
B. 2X
C. 5X/3
D. 3X/2
E. 7X/6

2 hours: cost = x dollars
3 hours: cost = x + x/6 dollars
4 hours: cost = x + x/6 + x/6 dollars
5 hours: cost = x + x/6 + x/6 + x/6 dollars
5.25 hours: cost = x + x/6 + x/6 + x/6 + x/6 dollars

We must now simplify: x + x/6 + x/6 + x/6 + x/6 dollars
Rewrite with common denominator: 6x/6 + x/6 + x/6 + x/6 + x/6 dollars
Combine numerators: 10x/6 dollars
Simplify: 5x/3 dollars

Answer: C

Cheers.
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon May 14, 2018 4:01 pm

BTGmoderatorLU wrote:A parking lot charges a flat rate of X dollars for any amount of time up to two hours, and X/6 hours each hour or fraction of an hour after the first two hours. How much does it cost to park for 5 hours and 15 minutes?

A. 3X
B. 2X
C. 5X/3
D. 3X/2
E. 7X/6

For the first 2 hours, we pay X dollars. For the next 3 hours, we pay X/6 dollars per hour, so we have to pay 3(X/6) = X/2 dollars. For the last 15 minutes, which is a fraction of an hour, we still have to pay X/6 dollars. Thus the total we have to pay is:

X + X/2 + X/6 = 6X/6 + 3X/6 + X/6 = 10X/6 = 5X/3 dollars

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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