Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.

Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.

This question tests your familiarity with the mathematical principles behind how negative numbers operate.  

 is possible because two negative numbers added together will always equal a negative number. 

 is possible because xy and -yx are inverses of each other, so they will combine to make 0.  

 is possible because you don't know what the values of x and y are.  If y is sufficiently larger than x, then subtracting the negative number resulting from 2y (aka adding 2y) to the negative number 3x could be a positive number, including 5.

 is possible because a negative (2x) times a negative (y) will always be positive.

Which, of course, means that  is impossible, because a negative times a negative will never equal a negative.

For the sum of 7 consecutive even integers to be zero, the only sequence possible is –6, –4, –2, 0, 2, 4, 6. This can be determined algebraically by assigning the lowest number in the sequence to be “y” and adding 2 for each consecutive even integer, and then setting this equal to zero.

y, y + 2, y + 4, y + 6 . . .

The product of any number and 0 is 0.

Therefore, column B must be greater.

If  and  are both even whole numbers, then their addition must be an even whole number as well. Although  is an even number, it is not a whole number and could therefore not be a solution. This means the only possible solution would be .

Plugging in the values given we arrive at the total fruit John has:

A good note about adding even numbers--any even numbers--is that if you add two even numbers, their sum will ALWAYS be an even number.  

To deal with a problem with this many digits, often the best strategy is to line up one number over the other, then add the places one at a time.  Don't forget to carry a one every time the addition goes over ten.  Also, note that any time you add two even numbers, their sum will ALWAYS be an even number. 

Since ,  must result in a positive whole number. The only answer that fits these requirements of being both positive and whole number is .

First, add the total number of passengers that got off BEFORE the fourth stop.  Three plus three is six, so you know that you've lost six total passengers before the fourth stop.  , so there are ten passengers remaining at the fourth stop, and that's how many get off there. 

If it's simpler for you, you can split this problem into two parts:  First, take  away from , and you're left with .  Then, take away  from  (you can even count backwards if necessary), and you'll be left with the final answer, .