place values compare. Column A can be written as 0.73(29) and Column B can
be written as 0.0029(7,300). 0.0029(7,300) = 0.73(29).- B 400 is double 200, but 65% is more than double 30%. Thus Quantity B is
greater. Note that you can use your calculator here. - B Plug in the numbers! The prompt gives you a in terms of b and b in terms of
c. Since you can express everything in terms of c, choose a value for c and work
backward to get values for a and b. In this case, you should choose a value for
c that will divide evenly by 4 twice. Why? Because b =^34 (c) and a =^14 (b). To get
integer values for a and b, you will be dividing by 4 and then dividing by 4
again, so a good value for c would be 16. If c = 16, then b = 12. If b = 12, then
a = 3. The value in Quantity A is thus^1612 × 100 = 133.3%. The value in Quantity
B is thus^123 × 100 = 400%. Quantity B is greater. - A Before doing any math, make sure to look at the columns. You are
comparing a $40 reduction in the price of the item to a 20% reduction. So you
need to determine how 20% of the price compares to $40. The difficulty here
is that you only have a range for the price of the item, so you will only be able
to arrive at a range for what 20% of the item would be. Let’s see how that range
compares to $40. First, assume that the item actually equaled $200. If that’s the
case, then a 20% reduction in the item would equal $40. But since the price of
the item is less than $200, a 20% reduction in the item would be less than $40.
Thus Quantity A is greater. - B Don’t calculate! Instead, figure out how the columns relate to each other.
First, notice that in both cases, the principal is the same ($10,000). In Column
A, the interest earned will be 0.05(10,000)4, which is the same as 20% of
10,000. How does Column B relate to 20% of $10,000? Compound interest
accrues on each successive period. For the first period, the interest is 10% of
$10,000. For the second period, the interest is 10% of a value that is more than
$10,000. The sum of these two quantities will be more than 20% of $10,000.
Thus Quantity B is greater. - B The fastest way to do this question is to choose values. When choosing
values for percent questions, always start by choosing a value for the whole,
which in this case is y. Let y = 100, and let x = 80. Now the comparison is
20% more than 80 versus 100. 20% more than 80 is the same as 1.2(80), which
equals 96. This value is less than 100. Thus Quantity B is greater.
Ratios
A ratio represents a relationship between two or more quantities. Examples of
ratios are
There are 3 boys for every 4 girls.
The preceding can be expressed as “The ratio of boys to girls is 3 to 4.”
A recipe requires 3 parts sugar, 2 parts salt, and 4 parts water.242 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 242 12/05/17 11:52 am