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
Let x = the total BEFORE the gratuity.
A 15% gratuity = 0.15x
So, the TOTAL cost = x + 0.15x
In other words, the TOTAL cost = 1.15x
So, we can write 1.15x = 207
So, x = 207/1.15
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......
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.
Since the total PRE-GRATUITY price = $180, the price PER PERSON = 180/15 = [spoiler]12 = B[/spoiler]
Cheers,
Brent
