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OG 13 - PS 135

by gdshamain » Sat May 03, 2014 12:11 pm
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?

(A) $11.73
(B) $12.00
(0 $13.80
(D) $14.00
(E) $15.87

My answer is (A), but the correct answer is (B) :(
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by Brent@GMATPrepNow » Sat May 03, 2014 12:15 pm
gdshamain wrote: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?

(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,
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by gdshamain » Sat May 03, 2014 12:26 pm
Thanks Brent for the reply.

It is clear now.
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by GMATGuruNY » Sat May 03, 2014 4:55 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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by Azizakaria » Thu Aug 06, 2015 11:07 am
sorry, but i don't understand, why you didn't multiply 207*0.15 to get the gratuity amount and then exclude them from 207 and divide by 15. which would yield 11.73
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by Brent@GMATPrepNow » Thu Aug 06, 2015 11:17 am
Azizakaria wrote:sorry, but i don't understand, why you didn't multiply 207*0.15 to get the gratuity amount and then exclude them from 207 and divide by 15. which would yield 11.73
The 15% gratuity is based on the amount BEFORE the gratuity was added.
$207 represents the cost of the lunch PLUS the gratuity.
So, 15% of $207 does not tell us the gratuity amount.


Your reasoning is that, since $207 is 15% GREATER than the pre-tip total, then the pre-tip total must be 15% LESS than $207.
This is a common misconception that goes something like this: If A is k percent greater than B, then B must be k percent less than A.

The truth of the matter is as follows: If A is k percent greater than B, then B is NOT k percent less than A.

I wrote an article about this misconception: https://www.gmatprepnow.com/articles/com ... 93-part-ii

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by nikhilgmat31 » Tue Aug 11, 2015 9:34 pm
115 % of x = 207

x = 207 *100/115

x = 9 * 100/5 = 9 * 20 = 180

cost of 15 persons = 180

1 person food cost = 180/15 = 12.
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by [email protected] » Wed Aug 12, 2015 9:22 am
Hi gdshamain,

In these types of situations, we have to think about the "timeline".... And if you're going to take an algebraic approach, then you have to follow the 'rules' of math:

Here, we had a bill, THEN the 15% gratuity was added, then we had a total....

X + .15X = 207

1.15X = 207

This is the equation that will get us the value of X...

X = 207/1.15

Solving this type of calculation is not 'fun' for most Test Takers, which is why TESTing THE ANSWERS (the approach that Mitch used) is preferable.

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