Problem Solving

The price of lunch for 15 people was $207.00 including a 15 % 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

[spoiler]Ans = B [/spoiler]

If you consider 207.00 as 115% and solve then you get the correct answer . But if you take 15% of 207 and subtract that from 207 and divide the result by 15 you will get the answer as 11.73 which is not correct .

My question is why is the second approach not correct , when there should not be any difference in answers no matter what the approach . If we look at the two approaches we are basically doing the same thing so why different answers ?

Can any one please explain ?

Hi rockeyb,

This is a basic concept of percentages.

Say, if you add x% of a certain value onto that value to get y. Taking x% of y off from y will not get you back to the original value. Try it with an example.

Say 20% of 100. If you add 20% to 100 you get 120. On the other hand, 20% of 120 is 24. If you take away 20% from 120, you get 96 (and not 100!)

This is simply because 20% of 120 is larger than 20% of 100.

valleeny wrote:Hi rockeyb,

This is a basic concept of percentages.

Say, if you add x% of a certain value onto that value to get y. Taking x% of y off from y will not get you back to the original value. Try it with an example.

Say 20% of 100. If you add 20% to 100 you get 120. On the other hand, 20% of 120 is 24. If you take away 20% from 120, you get 96 (and not 100!)

This is simply because 20% of 120 is larger than 20% of 100.

Thanks for your reply valleeny ,

I got it , the reason the second approach dose not work is because 207 is 115% and not 100% so taking away 15% of 207 will not give me 100% but some thing less than 100% .

And answer option A is exactly the kind of trap answer that GMAT throws at you , well a lesson learnt . Thanks for explaining.

thank you both for revealing this trap, I also got 11.73