Question 1 of 25
In 2012, a university received 150,249 applicants. In 2013, the same university received 190,201 applicants. By what percent did the total number of applicants increase from 2012 to 2013?
Basic Math
Practice Test 2 for Basic Math: real questions and explanations from the Varsity Tutors practice-test pool.
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Question 1 of 25
In 2012, a university received 150,249 applicants. In 2013, the same university received 190,201 applicants. By what percent did the total number of applicants increase from 2012 to 2013?
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In 2012, a university received 150,249 applicants. In 2013, the same university received 190,201 applicants. By what percent did the total number of applicants increase from 2012 to 2013?
Explanation: To find the percent change, use the following formula:
Our new number of applicants is 190,201, while the original number of applicants is 150,249.
In March, an athlete weighed pounds. In April, the same athlete weighed
pounds. What is the athlete's percentage of weight loss?
Explanation: The formula to find percentage change is
.
So for our athlete, our new weight is 170 pounds, and the original weight is 195 pounds.
Because the question already tells us that we need to find the percent lost, or percent decrease, we can drop the negative sign in the answer.
Henry has taken a lot of tests this semester in his biology class. In total, he has taken tests. His scores on the tests were
,
,
,
,
,
,
,
,
,
. What is the mode of all his test scores?
Explanation: The mode is the number that appears most often in a set of numbers.
If we order our number set we get the following:
In this case, because Henry scored 88 three times, that is the mode.
Multiply these fractions:
Explanation: When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:
Simplify the fraction to get the final answer:
Find the sum.
Explanation: First add the digits in the ones colume, this would be . Make sure to carry the 1 from the 17 to the tens colume.
Then add the digits in the tens colume, this would be
.
Lastly, add the digits in the hundrends colume, this would be
Therefore the result is as follows:

What is the least common denominator of the following fractions: ?
Explanation: The correct answer is 36. The best way to approach this problem is to take each denominator and list out its multiples. You can then find the common multiple between each denominator. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48 Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42 Multiples of 12: 12, 24, 36, 48, 60 Multiples of 36: 36, 72, 108 Multiples of 18: 18, 36, 54, 72 From the above multiples, we can see that the least common denominator is 36.
How many minutes are in a hours?
Explanation: Knowing that there are 60 minutes in an hour, multiply that amount by the total number of hours (3.5):
minutes
Determine the answer as a mixed number:
Explanation: 1. Find the least common denominator:
The lowest number that both 4 and 6 can go into is 12 meaning that it is the least common denominator.
2. Use the new least common denominator to create two equivalent fractions with a denominator of 12.
3. Add the two fractions together.
4. Convert the fraction to a mixed number:
In March, an athlete weighed pounds. In April, the same athlete weighed
pounds. What is the athlete's percentage of weight loss?
Explanation: The formula to find percentage change is
.
So for our athlete, our new weight is 170 pounds, and the original weight is 195 pounds.
Because the question already tells us that we need to find the percent lost, or percent decrease, we can drop the negative sign in the answer.
What is divided by
? Express your answer as a whole number with a remainder.
Explanation: is not evenly divisible by
. As such, you want to first find out how many whole
's can go into
.
, so
is too many.
, which is as close to
as you can get.
, so that's your remainder.
What is expressed as a percentage rounded to the nearest tenth?
Explanation: Percents are numbers expressing parts of :
means
part of
, or
.
The simplest way to convert a decimal to a percentage is to move the decimal place over two places to the right. We move the decimal point to after the hundredths place because we are rewriting the decimal as a portion of
. Therefore:
Now, we need to round the percentage to the nearest tenth. The number after the tenths place is a five, so we need to round up:
is therefore our final answer.
For a school project, Jonas asked his classmates how many siblings they had. of his classmates had
siblings,
had
sibling,
had
siblings, and
had
siblings. What is the mode of the number of siblings his classmates had?
Explanation: In a data set, the mode is the number that occurs most frequently. Because 18 of his classmates only had 1 sibling, 1 is the number that appears most often.
What is of
?
Explanation: Before multiplying, it's necessary to convert 0.25% to a decimal, which is 0.0025. Multiply this 0.0025, with 100. The correct answer is 0.25.
What is the reciprocal of ?
Explanation: To get the reciprocal of a fraction, you simply switch the numerator and the denominator.
In our case our numerator is and our denominator is
.
So
becomes
.
What is the result of the above equation?
Explanation: We first multiply the numerators:
Then we multiply the denominators:
The resulting fraction is:
We divide the numerator and denominator by 12.
The numerator is:
The denominator results in:
Our resulting fraction is:
Solve for x
Explanation: Start by adding 10 to both sides.
Multiply both side by 9 to get rid of the fraction.
Divide by 5
Since all the answer choices have mixed fractions, you will also need to reduce down to a mixed fraction
Determine the answer as a mixed number:
Explanation: 1. Find the least common denominator:
The lowest number that both 4 and 6 can go into is 12 meaning that it is the least common denominator.
2. Use the new least common denominator to create two equivalent fractions with a denominator of 12.
3. Add the two fractions together.
4. Convert the fraction to a mixed number:
Solve:
Explanation: The answer is . The goal is to isolate the variable,
, on one side of the equation sign and have all numerical values on the other side of the equation.
Since
is a negative number, you must add
to both sides.
Then, divide both sides of the equation by
:
Paul had video games. On Monday, he gave
video games to his friend Chris. On Tuesday, he sold
of his video games to the local video game shop. On Wednesday, Paul accidentally broke
video games and threw them away. How many video games does Paul have left?
Explanation: This is a simple subtraction problem.
First, subtract the number of video games Paul gave to Chris on Monday.
Now, subtract the number of video games Paul sold from the number he has left.
Finally, subtract the number of video games Paul broke and threw away.
What is the perimeter of a semicircle with an area of ?
Explanation: This is a multi-step problem. The perimeter of a semicircle is the sum of the circumference and diameter. First, since we are given the area, we will need to find the radius.
For the area of a semicircle:
Since the area is
, substitute this into A to find radius r.
Since the radius is 2, the diameter is 4.
The circumference for a semicircle is:
The perimeter is the sum of the circumference and diameter:
Factor the following expression completely
Explanation: First, we need to factor the numerator and the denominator separately.
To factor an expression with the form , we will need to find factors of
that add up to be.
For the numerator,
,
and
.
Write down the factors of
and add them up.
Since
and
add up to
,
Now, do the same thing with the denominator,
.
Since
and
add up to
,
.
Now, stack these factors up as fractions:
Since both the numerator and denominator have the factors (x+6), they cancel each other out because they divide to 1.
Then,
Round to the nearest hundredth:
Explanation: The hundredth place is the 2nd number after the decimal. Because the thousandth place is great than 5, we will need to round up to
Subtract.
Explanation: To subtract two fractions, they need to both share the same denominator. Since 81 is a multiple of 9, we only need to change the 1st fraction.
Now subtract the two fractions.
Billy earned for shoveling his driveway. He wants to buy a new toy and a candy bar, and then add the rest to his piggy bank. The new toy costs
and the candy bar costs
How much money will Billy have left over to add to his piggy bank?
Explanation: Billy had . After buying the toy he had
left over:
.
After buying the candy bar he then had
left for his piggy bank,
.
Round to the nearest ten.
Explanation: To round to the nearest ten, you need to take a look at the ones' place. Since the ones' place is greater than , you will need to round the tens' place up.
So then
is rounded up to
.