GRE Quantitative Question (Percents)

Question

GRAPH The following links are a graph question dealing with percents on a GRE Quant practice test.

Here are the figures I am given:

https://jasper.kaptest.com/content/media/07/341107.3.gredi105_17a.png

https://jasper.kaptest.com/content/media/07/341107.3.gredi105_17b.png

This paragraph is below both figures: "The first circle graph gives the percent distribution of products sold by a website in a given year. Total sales were $83 million. The second circle graph breaks out the percent distribution of just laptops sold in the same year by brand; this graph gives no total number of laptops."

THE QUESTION "In 2014, sales at website T of every product other than tablets were approximately how much greater than the sales from tablets?"

ANSWER $63.1 million

EXPLANATION The task is to find the approximate difference between the sales of tablets in dollars and the sales of all other products. The sales of different products appear in the first graph. Tablets are 12% of the total, so all other products are 100% – 12% = 88% of the total. Because both percents are of the same total, the difference in sales is 88% – 12% = 76% of the total sales.

MY QUESTION Why do we subtract 12 percent from 88 to receive our answer?

PS I know that .76 * 83 (million, in sales) == the answer.

Thanks.

Answer 1

I think it's more confusing to deal with percentages; let's deal with the actual money instead. Simply put, the question is

$$\text{How much more money came from selling everything else vs. just the tablets?}$$

Translated into math, this is

$$\text{ammount of money from everything else - amount of money from tablets }$$

What is the ammont of money from everything else? Well everything else is $88$% so the ammount of money is $.88 \times 83$.

How much money came from selling the tablets? $.12 \times 83$. Thus our answer is

$$.88 \cdot 83 - .12 \cdot 83$$

You could compute this and get the right answer. Aditionally, if you look more closely you can see that you can factor out the 83, leaving

$$83(.88-.12) = 83 \cdot .76$$

which is the same as taking $76$% of $83$

Answer 2

The question is asking the difference between the sales of other products and the sales of tablets. Since "other products" is $88$% of the sales and tablets are $12$% of the sales, the difference is $88\%-12\%=76\%$ of the sales.