# 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?
OG 13th Edition PS question
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
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.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?
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
Last edited by Brent@GMATPrepNow on Sun May 03, 2015 5:47 am, edited 1 time in total.
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let x = the total BEFORE 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
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
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
A nice fast approach is the test the answer choices.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
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