Solving 207/1.15 without a calculator

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tnkippen: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sun Sep 09, 2012 6:20 pm; Thanked: 1 times

by tnkippen » Sat Oct 27, 2012 9:24 pm

Problem #135 in the Official Guide 13th Edition (copied below) requires me to calculate 207/1.15 without a calculator. The explanation glosses over this, simply stating that 207/1.15 = 180

"135. The price of lunch for 15 people was $ 207.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?"

There is also a question in the diagnostic test that requires you to calculate 45/.12 without a calculator (answer is 375).

Is there any shortcut to solve these kinds of simple calculations? I can't find a way to do with this mental math.

Thank you!
Thomas

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Source: Beat The GMAT — Problem Solving | Sat Oct 27, 2012 9:24 pm

anuprajan5: Master | Next Rank: 500 Posts; Posts: 279; Joined: Mon Jun 25, 2012 10:56 pmFollowed by: 10 members; Thanked: 60 times

by anuprajan5 » Sat Oct 27, 2012 9:51 pm

Hey Thomas,

An easy way to handle this is through fractions.

You could convert 207/1.15 into (207*100)/115. Since you have 2 multiples of 5, you can simplify this into (207*20)/23. You might be able to recognize that 207 is a multiple of 23, which will help you solve the rest.

You could convert 45/0.12 into (45*100)/12. Since 45 and 12 are multiples of 3, you can simplify this into 15*25.

Regards
Anup

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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 » Sun Oct 28, 2012 3:05 am

There is no need to calculate 207/1.15 if we approach the problem differently.

The price of lunch for 15 people was $207.00,
including a 15 percent gratuity for service. What was
the average price per person, EXCLUDING the
gratuity?

(A) $11.73
(B) $12.00
(C) $13.80
(D) $14.00
(E) $15.87

We can plug in the answers, which represent the cost per person.
Given that the total cost is an INTEGER, the correct answer is almost certainly an integer itself.
Answer choice D is too great, since 15 people paying $14 each = 15*14 = 210 -- a value beyond the total cost of 207.

Answer choice B: $12 per person without gratuity
Total price for 15 people = 15*12 = 180.
Price + gratuity = 180 + .15(180) = 180+27 = 207.
Success!

The correct answer is B.

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tnkippen: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sun Sep 09, 2012 6:20 pm; Thanked: 1 times

by tnkippen » Sun Oct 28, 2012 12:28 pm

Mitch - Fantastic, thank you. That is exactly what I was looking for.

Thomas

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