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by Gurpinder » Fri Aug 20, 2010 10:56 am
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

207(.15)=31.05.
207-31.05=175.95
175.95/15 = 11.73, so (A).

How is this wrong?

OA: [spoiler](B)[/spoiler]
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by beatthegmatinsept » Fri Aug 20, 2010 12:14 pm
Gurpinder wrote: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

207(.15)=31.05.
207-31.05=175.95
175.95/15 = 11.73, so (A).

How is this wrong?

OA: [spoiler](B)[/spoiler]
This is EXACTLY what i did when I attempted this OG question 2 days ago. When I reattempted it, I figured out the error i was making.
1.15x = 207
NOT 207 * 0.15 = 31.05
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by beatthegmatinsept » Fri Aug 20, 2010 12:19 pm
A detailed answer:
1.15x = 207
Solve for x = 180 (price excluding tip)
180/15 = $12/person.
This question for sure got me too.
Hope this helps!
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by 4GMAT_Mumbai » Fri Aug 20, 2010 12:19 pm
Hi,

No wonder 11.73 is choice A !

Think about it ... If a service costs $207 (after gratuity is imposed), then the service originally costs 207 / 1.15, right ?

The service by itself would have costed $180. A gratuity of 15% is calculated off $180 (which comes to $27) so that a customer pays 180 + 27 = 207 for the service.

In this case, 180 / 15 = $12 per head.

This is same as saying that P% is ALWAYS calculated with CP as the base and never with SP as the base.

If SP is $207 and P% is 15%, what is CP ... Is it not 207 / 1.15 ...

Hope this helps. Thanks.
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by MBAD » Sun Jan 15, 2012 7:17 pm
Does anybody have any tricks for calculating 207/1.15? That is a step that seems to be assumed, but could take a bit of time to calculate alone.
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by ronnie1985 » Sun Jan 15, 2012 7:24 pm
(B)
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by GMATGuruNY » Mon Jan 16, 2012 8:07 am
All the issues discussed above -- the careless errors, the tedious arithmetic -- are easy to avoid if we plug in the answers, which represent the price per person without the gratuity.
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
Given that the total cost is an INTEGER, the correct answer choice almost certainly is B or D, the only integer values offered.

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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by LalaB » Tue Jan 17, 2012 12:47 am
total+0.15*total=207
total=180

180/15=12

12 usd per person
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by emz » Tue Jul 23, 2013 3:07 pm
MBAD wrote:Does anybody have any tricks for calculating 207/1.15? That is a step that seems to be assumed, but could take a bit of time to calculate alone.
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by GMATGuruNY » Tue Jul 23, 2013 3:56 pm
emz wrote:
MBAD wrote:Does anybody have any tricks for calculating 207/1.15? That is a step that seems to be assumed, but could take a bit of time to calculate alone.
Let x = the cost per person WITHOUT gratuity.

Cost per person WITH gratuity = 207/15.
Since this value is equal to 115% of x, we get:
(115/100)x = (207/15)
x = (207 * 100) / (115 * 15).

Here is one way to simplify:

Divide both 100 and 15 by 5:
(207 * 100) / (115 * 15)
(207 * 20) / (115 * 3).

Divide 3 into 207; divide both 20 and 115 by 5:
(207 * 20) / (115 * 3)
(69 * 4) / 23.

Divide 23 into 69:
(69 * 4) / 23
3 * 4
12.
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by Matt@VeritasPrep » Tue Jul 23, 2013 4:49 pm
MBAD wrote:Does anybody have any tricks for calculating 207/1.15? That is a step that seems to be assumed, but could take a bit of time to calculate alone.
This is a great question. My approach:

First, make it so that the numerator and the denominator have the same number of decimal places, then simply eliminate the decimal point.

207
---
1.15

= 207.00 / 1.15

= 20700 / 115

Now start dividing both the top and the bottom by common factors. Each number divides by 5, so 20700/115 becomes 4140/23. Now you KNOW this must simplify, or it wouldn't be on the GMAT, so divide 4140 by 23 longhand ... and you'll get 180. Now you just divide this by 15 (the number of people) and get 12.

This will work for most division on the GMAT, especially with decimals. Just factor out what you know you can factor out, cancel, and keep plugging away until you get an integer or a simple fraction (on the GMAT, this stuff "always" simplifies to something nice).
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by Brent@GMATPrepNow » Wed Jul 24, 2013 7:18 am
MBAD wrote:Does anybody have any tricks for calculating 207/1.15? That is a step that seems to be assumed, but could take a bit of time to calculate alone.
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 more 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

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,
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