Begin by isolating your variable.

Subtract  from both sides:

, or 

Next, subtract  from both sides:

, or 

Then, divide both sides by :

Recall that division of a negative by a negative gives you a positive, therefore:

 or 

To solve this equation, you need to isolate the variable on one side. We can accomplish this by dividing by  on both sides:

Anytime you divide, if the signs are the same (i.e. two positive, or two negative), you'll get a positive result.  If the signs are opposites (i.e. one positive, one negative) then you get a negative.  

Both of the numbers here are negative, so we will have a positive result:

To solve, you need to isolate the variable. We first subtract  then divide by :

When dividing, if the signs of the numbers are the same (i.e. both positive, or both negative), you yield a positive result.  If the signs of the numbers are opposites (i.e. one of each), then you yield a negative result.  

Therefore:

Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.

Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.

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.