MENSA IQ Test and rules of maths In a Mensa calendar, A daily challenge - your daily brain workout. I got this and put a challenge up at work.

The Challenge starts with..

Assume you are using a basic calculator and press the numbers in the order shown,
replacing each question mark ...continues... What is the highest number you can 
possibly score?


Basically, only using $+,-, * ,\div$, once in place of a question mark.


  $5 ? 4 ? 7 ? 3 ? 2 =$


We all worked out the operators to be 


  $5 + 4 $ x $ 7 - 3/2 =$


Except that I calculated the answer to be $31.5$ and the others argued $30$. THe answer sheet from MENSA says the calculated total is 30.

Nobody actually understood the first part about using a basic calculator. I initially thought the challenge was all about the rules of maths.
And when I asked why nobody else applied the rules of maths, they all forgot about it, not because the challenge said to use some "basic calculation" 

I emailed MENSA and queried them about the challenge and they replied,

Thank you for your email.

On a basic calculator it will be:
5 + 4 = 9
9 x 7 = 63
63 – 3 = 60
60 ÷ 2 = 30

Kind regards,
Puzzle Team


My Reply,

 Thank you for your reply. 

 Could you please define what a basic calculator is? I tried 4 pocket,
 £1 calculators, and all gave me 31.5.


And finally their definition.

I guess what the question really means, whether you do the sum manually or on a 
calculator,  is don’t change the order of the numbers. The Casio calculators we have in 
the office allow you to do the sum as it appears:

5 + 4 = 9
9 x 7 = 63
63 – 3 = 60
60 ÷ 2 = 30

Kind regards,
Puzzle Team


So they guess the challenge meant to do it that way. Why not just say ignore rules of maths. What is the point of this anyway?



My original question, on Maths Stack (this one) was why MENSA used 30 instead of 31.5. And initially I did not understand that using a basic calculator meant calculating left to right by pressing equals after each operation.

So what is going on here? If they wanted us the ignore rules of math they should of said taht. Because my basic calculator gives me 31.5 and not 30.0 (I dont have a special. Casio MENSA calculator though)

Windows standard calculator gives me 30. Why? None of my pocket, office, el cheapo calculators do this.



Google, or Windows Scientific give me 31.5 - As do ally my elelctornic calculators.
In response to edit of initial post, then answer is clearly $30$. Basic calculators are assumed to evaluate in order from left to right.



Original post I responded to

In a Mensa calander, IQ dialy challenge I got this and put a challenge up at work.

Using +,-,time and divide only once. Use the math operator only once to get the highest answer.


  5 ? 4 ? 7 ? 3 ? 2 =


We all worked out


  5 + 4 x 7 - 3 / 2 = 30


Except that my result answer was 31.5 and not 30, like in the answers of the MENSA calendar.

Why was I the only one that applied the rules of maths on this? ANd when I asked why nobody else applied the rule of maths, I got the weirdest looks. Nobody knew about multiplication before division, subtraction before adding?  I thought that was why the question was marked as the most difficutl to test if you knew this.



Response to original post

Sadly, many people forget the basic rules of arithmetic as they (a) don't view them as affecting their lives, (b) didn't like maths, and/or (c) know technology can handle the problem for them. The issue with the last point is that different technologies handle things differently. The Google calculator (much like most graphing calculators) will handle order of operations for you correctly. The standard Windows calculator appears to be operating like an old 4 function calculator which evaluates after every operation is completed as opposed to correct order of operations. Though this can also happen when users hit enter after every operation is finished as opposed to when the whole expression is finished. (Don't have access to a Windows calculator right now so can't tell which is the reason for the wrong answer.)
the answer is 31.5. you know it but you messed up the math.
with subtraction and addition it shouldnt matter which is carried out first; they can both be considered to be identical functions (addition of a positive and a negative no or vice versa)

the answer is therefore 28+5-1.5; whichever way you look at it.