average price per person, EXCLUDING the gratuity?

[kamalj]

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

OAB

Hello Experts ,

Please advise where did i go wrong?

Gratuity Service = 207*15/100 = 31.05

So without gratuity service = 207 - 31.05 = 175.95

average price without gratuity service = 175.95 /15 = 11.73

Please explain.

Thanks...

[GMATGuruNY]

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 -- 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.

Hello Experts ,

Please advise where did i go wrong?

Gratuity Service = 207*15/100 = 31.05

So without gratuity service = 207 - 31.05 = 175.95

average price without gratuity service = 175.95 /15 = 11.73

Please explain.

Thanks...

The step in red is the equivalent of subtracting 15% OF THE FINAL PRICE.
But the gratuity is not equal to 15% of the final price; the gratuity is equal to 15% OF THE BASE PRICE.
The two values are not the same.

[Brent@GMATPrepNow]

Hello Experts ,

Please advise where did i go wrong?

Gratuity Service = 207*15/100 = 31.05

So without gratuity service = 207 - 31.05 = 175.95

average price without gratuity service = 175.95 /15 = 11.73

Please explain.

Thanks...

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

[Scott@TargetTestPrep]

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

An efficient way to solve this problem is to translate what is provided in the question into a mathematical equation. We know that the total bill for 15 people was 207 dollars, including the 15 percent tip. We use the value 1.15 in the equation below to account for the meal itself plus the gratuity, and x as the individual cost per person for the meal before the gratuity. Thus, we can say:

(1.15)(15)(x) = 207

(115)(15)(x) = 20700

Dividing both sides by 15, we have:

115x = 1380

x = 1380/115

x = 12

Answer: B