GED Math : Complex Operations
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Example Questions
Example Question #61 : Complex Operations
Lucy's weight increased from 180 pounds to 200 pounds. By what percent (nearest tenth, if applicable) did her weight increase?
In a percent of increase problem, the whole is the amount at the beginning of the time period, which here is 180 pounds. The part is the difference between the final and initial amounts, which here is 
Example Question #28 : Proportions And Percentages
To get on the ballot for the student body president at Parker High School, a student must turn in a petition with the signatures of 8% of the students from each of the three classes - sophomore, junior, and senior. There are 365 sophomores, 315 juniors, and 268 seniors enrolled at Parker.
Marisol has a petition with the signatures of 35 sophomores, 30 juniors, and 24 seniors. Can she get on the ballot with the signatures she has, and if not, why not?
Marisol cannot get on the ballot yet, because she needs more signatures from juniors.
Marisol has the signatures she needs to get on the ballot.
Marisol cannot get on the ballot yet, because she she needs more signatures from seniors.
Marisol cannot get on the ballot yet, because she needs more signatures from sophomores.
Marisol has the signatures she needs to get on the ballot.
In order to answer the question, we must find out the percent of each class that has signed Marisol's petition, and compare it to 8%.
Sophomores: 35 out of 365, which is 
Juniors: 30 out of 315, which is 
Seniors: 24 out of 268, which is 
Marisol has sufficient signatures from all three classs, and thus has the signatures she needs to get on the ballot.
Example Question #61 : Complex Operations
Members of a grocery co-operative can earn a discount by working at the grocery; for every full hour they work over a given week, they can take 4% off of their grocery bill the next week.
Michael is a member of this co-operative. He wants to work enough hours so that he can purchase the groceries he needs, which normally would cost him $140, for at most $100. How many hours must he work, at the very least, in order to get this discount?
Michael wants to save $40 on a $140, which is a discount of
Ha saves 4% per hour he works in the grocery, so if 
Since the discount is a function of a whole number of hours worked, Michael will need to work 8 hours to pay less than $100 for the groceries.
Example Question #30 : Proportions And Percentages
Refer to the above diagram. The circles are of equal size and the portions of each circle are of equal size.
If the shaded portion of the circle at lower right were to be unshaded, then by what percent would the area of the unshaded region increase?
At current, 5 regions of equal size are unshaded. If the remainder of the lower right circle were shaded, this would increase the size by 3 regions of the same size. Therefore, we need to calculate what percent 3 is of 5. This is an increase in area of
Example Question #31 : Proportions And Percentages
Currently, Brian pays $865 a month for his rent. Monthly rent is due to increase by 12% starting next month. Rounded to the nearest dollar, how much will he pay then?
12% of $865 is
Add that amount to the current rent:
This rounds to $969, the correct choice.
Example Question #32 : Proportions And Percentages
Thomas’s current yearly salary is $44,000 per year. After an 8% raise, what will his new salary be?
8% of Thomas's salary of $44,000 is
Add this to the original salary:
Example Question #33 : Proportions And Percentages
Refer to the above diagram. The circles are of equal size and the portions of each circle are of equal size.
If the unshaded portion of the above diagram were to be shaded, then, to the nearest tenth, by what percent would the area of the shaded region increase?
At current, 27 regions of equal size are shaded. If the remainder of the diagram were shaded, this would increase the size of the shaded portion by 5 regions of the same size. Therefore, we need to calculate what percent 5 is of 27. This is an increase in area of
Example Question #34 : Proportions And Percentages
Greg deposits $9,000 at 7% simple interest per year. How much will he have in this account after eighteen months, assuming he does not make any withdrawals or deposits?
Use the simple interest formula
with 
This is the simple interest earned. Add it to the original principal:
Example Question #35 : Proportions And Percentages
If 
of the circle is white.
Since 
this amount converts to 
Example Question #36 : Proportions And Percentages
Refer to the above diagram. The portions of the large rectangle are of equal size.
If the unshaded portions of the above diagram were to be shaded, then, to the nearest tenth, by what percent would the area of the shaded region increase?
At current, 14 regions of equal size are shaded. If the remainder of the squares were shaded, this would increase the size of the shaded portion by 6 regions of the same size. Therefore, we need to calculate what percent 6 is of 14. This is an increase in area of
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