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OG - Quant Review - PS - Q135

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OG - Quant Review - PS - Q135

by vittovangind » Sun Jan 19, 2014 1:49 pm
Hello,

Is this problem we must divide $207/1.15.

In order to do so, my logic would be to do as follow: 115/1.15 + 92/1.15

The first term is easily calculate to equal 100, however to me it isn't easy to recognize that 92/1.15 = 80.

In general, I'm struggling with those types of calculation.

Any advise / tips to get better at them?

Many thanks,

Vitto
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by Brent@GMATPrepNow » Sun Jan 19, 2014 2:20 pm
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
NOTE: The GMAT often rewards people for using fractions rather than decimals. The reason for this is that most people are very uncomfortable working with fractions.

So, here's one way to calculate 207/1.15:
207/1.15 = 207/(1 3/20)
= 207/(23/20)
= 207 x (20/23)

IMPORTANT: At this point, the calculation looks very hard. But first notice that (23)(10) = 230. In other words, 230 = the sum of ten 23's
Also notice that 207 is 23 less than 230
So, 207 = the sum of nine 23's
In other words 207 = (23)(9)
So, we have . . .
= (23)(9) x (20/23)
= 9 x 20 [the 23's cancel out]
= 180

So, the pre-tax price is $180
This cost is divided by 15 people.

$180/15 = [spoiler]$12 = B[/spoiler]

Yes, these calculations look cumbersome, but that's only because I added a lot of extra information. In reality, students with strong fraction skills can perform most (if not all) of these calculations in their heads.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by GMATGuruNY » Sun Jan 19, 2014 2:22 pm
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 -- yields 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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