GingerAle

Here’s a copy of the original question.

----

In this problem, a and b are positive integers.

When a is written in base 9, its last digit is 5.

When b is written in base 6, its last two digits are 53.

When a-b is written in base 3, what are its last two digits? Assume a-b is positive.

----

GA

Here’s a copy of the original question.

Find the remainder when \(33818^2 + 33819^2 + 33820^2 + 33821^2 + 33822^2\) is divided by 17

------

GA

Here’s a copy of the original question.

Given that \(m\) and \(n\) are positive integers such that \(m\equiv 6\pmod 9\) and \(n\equiv 0\pmod 9\), what is the largest integer that \(mn\) is necessarily divisible by?

----

GA

Here’s a copy of the original question.

If \(4x\equiv 8\pmod{20}\) and \(3x\equiv 16\pmod{20}\), then what is the remainder when \(x^2\) is divided by 20?

GA

Here’s a copy of the original question.

If x^2+bx+9 has two non-real roots, find all possible values of b. Express your answer in interval notation.

***************

You know you are not supposed to post AoPS questions. You chose to do so, anyway. You then delete your questions because you fear getting caught, or you do not want anyone else to benefit from the solution.  This makes you an APoS (A Piece of Shit) student.

Why did you repeat your question? Your example at the end is not correct –it’s absurd.

The total should shows four or five places beyond the decimal and you'll have to round up or down. You will explain who keeps the difference, the owner or employee after you round it back to 2-places beyond the decimal.  This is similar to the price you pay for gas 1/10 of a cent below a break point.  You won't find the tenths of a cent on your paycheck, so where does it go?

The quick answer to your question “where does it go,” “who keeps the difference,” is simple: The fractional payments are distributed in other pay checks. No single person or entity “keeps” the fractional parts of the payments.  To clarify, the payments rounded down are used for payments that are rounded up.

Converting US dollars to Pesos

The exchange rate is $0.0529 per Peso. So it’s necessary to divide the dollars by the exchange rate to convert to Pesos.

For your example: (40) * ($19.55/hour) = $782.00

($782.00) / (0.0529) = 14782.608 Pesos

In finance (payables), the value of the third decimal is used to determine if the second decimal is rounded up or remains the same. If the third decimal is five (5) or higher, then the second decimal is incremented. If third decimal is four (4) or lower, then the second decimal remains as it is. Using this criterion, the pay check for this employee is 14782.61 Pesos; it’s rounded up to the next centavo.

Theoretically, half the time this third decimal will range from (5) to (9) and the half the time it will range from (0) to (4).  Thought this is true, when the third decimal is zero (0), there is no fractional value, so it does not generate any excess. The fraction that is collected for 4, 3, 2, and 1, pays for 9, 8, 7, and 6; but the zero (0) does not pay for the five (5).  This sounds trivial, but after a million paychecks, the company pays an extra 1000 Pesos –about $52.92.   

This confirms the old maxim: Watch your centavos closely, the pesos will take care of themselves.  

GA

This is one of the Mr. BBs. I’m not sure which one, but it doesn’t really matter, because they all think alike. One trait they all have is to demonstrate pseudo mathematical prestidigitation –aka fake math.   

He presents a name for the method and the result, but he never actually presents the method. He uses pseudo mathematical prestidigitation for most of his solutions, but he always does it for the Euclidian Algorithm.

There are two Euclidian Algorithms in Euclid’s Elements:

One for rational numbers, in Book VII, and one for real numbers, in Book X.

GA