A Pi Day Problem

Algebra Level 2

What is wrong with this image?

$\textbf{Choices for the answer:}$

(A) The "TOTAL" value is wrong, it should be greater than the given value.

(B) Nothing is wrong with this picture.

(C) The "TIP" value should be $e$ and not $\pi$ for the given "TOTAL" value to be correct.

(D) The "TOTAL" value is wrong, it should be less than the given value.

$\textbf{Note:}$ The customer pays via credit card and pays the exact value that is to be paid (in short, do not round up the TOTAL that you get! The customer pays the amount accurately atleast upto $10$ decimal places).

C A B D

8 solutions

Abdur Rehman Zahid
Mar 14, 2015

If $16.86+\pi=20\rightarrow \pi=20-16.86=3.14$ .But 3.14 is only an $\text{approximation}$ for $\pi$ .It is not the exact value;in fact, $\pi$ has no exact value because it is irrational.It's value to 9 decimal places is $3.141592653$ .Which is greater than 3.14.Therefore when it is added to 16.86.The total will be greater than 20.So answer is $\boxed{A}$

But you can't have fractions of cents so it's rounded correctly. Answer (B) is correct.

Jonathan Roberts - 6 years, 2 months ago

He paid via credit card and was able to pay at accuracy of at least ten decimal places. Therefore A is correct as TOTAL should be more than 20.00

Faisal Islam - 6 years, 2 months ago

Pretty sure this question tests nothing. It is a fairly debatable answer.

Reuben Praveen - 5 years, 9 months ago

$\pi\approx 3.1415\ldots \gt 3.14\\ \implies 16.38+\pi\gt 16.38+3.14=20.00\implies \textbf{TOTAL}\gt 20.00$

Prasun Biswas - 6 years, 3 months ago

Like any waiter would expect to be paid $314.159265...$ cents.

Michael Mendrin - 6 years, 3 months ago

The customer paying the tip would be like, "Payment still in progress...." :P

Prasun Biswas - 6 years, 3 months ago

@Prasun Biswas – I would like to make the point that the total would be £20.00 because the answer comes out as £20.00159... which rounds to £20.00 to the nearest pence and you can't have part of a pence.

Curtis Clement - 6 years, 3 months ago

@Curtis Clement – In the world of my fictional problems, you can even have a nanopenny where,

$1\textrm{ penny }=10^{9} \textrm{ nanopennies }$

Nonetheless, I have edited the wording of the problem.

Prasun Biswas - 6 years, 3 months ago

@Prasun Biswas – You can't pay in nanopennies. The value of the total in the problem is correct for currency. The correct answer is B.

Rolo Mictlanetcuhtli - 6 years, 2 months ago

@Rolo Mictlanetcuhtli – That was not in the statement of the problem.

Rolo Mictlanetcuhtli - 6 years, 2 months ago

@Rolo Mictlanetcuhtli – Prasun Biswas mentioned in response to Curtis Clement "In the world of my fictional problems, you can even have a nanopenny"

samarth sangam - 6 years, 2 months ago

Answer B is correct. Significant figures do in fact matter. Pi=3.141 which rounds to 3.14. The totaling is correct. -_-

Sam Rozans - 6 years, 2 months ago

The problem is that the total can not have fractions of cents. The note of accurately up to 10 decimal places is absurd because the smallest unit of measure is only two decimal places. The most accurate payment possible is 20.00. If this were simply a math question and not formed into an argument of money then your answer would be correct.

Chris Hornsby - 6 years, 2 months ago

You do know that there's a separate section called "Quantitative Finance (Beta)" for problems on finance, right?

Prasun Biswas - 6 years, 2 months ago

there in question total is given only 20.00 but not 20.000000. so as per first two decimals it is correct . and total is 20.0015.... as 1 is less than 5 it can be rounded to 0. answer must be B

Priya Darshini - 6 years, 2 months ago

See the note I have added in the problem.

Prasun Biswas - 6 years, 2 months ago

"in fact, pi has no exact value because it is irrational"

Pi has an exact value...

Nick Schreiner - 4 years, 4 months ago

Joel Oduro-Afriyie
Mar 20, 2015

For TOTAL to be $20.00$ , TIP should be $20.00 -16.86=3.14$ .

Since the actual value of $\pi$ is greater than $3.14$ , TOTAL should actually be greater than $20.00$

Paola Ramírez
Mar 15, 2015

$16.86+\pi=20 \Rightarrow \pi=20-16.86=3.14?$ but $\pi$ is greater than $3.14$ becasue is $3.1415926535..$

$\boxed{A}$ is wrong

Himanshu Aggarwal
Mar 22, 2015

Question not worthy..It can have both the answers A and B, as according to maths we can consider the digits more than 2 decimal places, but in monetary/financially terms we just consider upto 2 decimal places.

Muhammad Hermawan
Apr 14, 2015

Yes, we can sure that 16.84+3.14=20.00, but remember, 22/7>3.14 because Pi is exactly 22/7, the decimal form (3.14) is lower than the actual Pi (22÷7).

Faisal Islam
Apr 2, 2015

Customer was able to pay TOTAL with accuracy of at least ten decimal places. This accuracy is greater than 2 decimal places, so A is answer

Jb Cunanan
Mar 23, 2015

Technically, correct answer is A. But in reality, there is nothing wrong with the image since currency is always rounded up to 2 decimal places. So the customer is actually correct since he is paying money. This answer will be accepted in any academic institution.

Aakash Singh
Mar 17, 2015

the total value is short by 0.00159265358979323..............

A Pi Day Problem

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