Problem Solving

Rastis wrote:# 135, pg 171

How is doing the calculation 207(.15), then subtracting that value from 207 and then dividing that value by 15 NOT the answer?

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

Cheers,
Brent

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

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

A nice fast approach is the test the answer choices.

Since the total cost ($207) is an INTEGER, it's quite likely that the correct answer also an INTEGER.
So, let's test B and D first.

Answer choice B
$12 each BEFORE the gratuity
So, total (PRE-GRATUITY) for 15 people = (15)($12) = $180
GRATUITY = 15% of $180 = $27
So, the TOTAL (INCLUDING GRATUITY) = $180 + $27 = $207
PERFECT!

Answer: B

Aside: Here's an article on calculating percents (like 15% of $180) in your head: https://www.beatthegmat.com/mba/2014/04/ ... rcent-of-y

Cheers,
Brent