Arithmetic - ACT Math
Card 0 of 6453
How many different 5 letter computer passwords are possible, assuming that letters cannot be repeated?
How many different 5 letter computer passwords are possible, assuming that letters cannot be repeated?
26P5 = 26 x 25 x 24 x 23 x 22 = 7,893,600
26P5 = 26 x 25 x 24 x 23 x 22 = 7,893,600
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What is the difference between the LCM and GCF for the following set of numbers: 3, 12, and 30?
What is the difference between the LCM and GCF for the following set of numbers: 3, 12, and 30?
LCM = least common multiple = 2 x 2 x 3 x 5 = 60
GCF = greatest common factor = 3
Prime factor each number
3 = 3 x 1
12 = 3 x 4 = 3 x 2 x 2
30 = 5 x 6 = 5 x 2 x 3
LCM – GCF = 60 – 3 = 57
LCM = least common multiple = 2 x 2 x 3 x 5 = 60
GCF = greatest common factor = 3
Prime factor each number
3 = 3 x 1
12 = 3 x 4 = 3 x 2 x 2
30 = 5 x 6 = 5 x 2 x 3
LCM – GCF = 60 – 3 = 57
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Florida Clementines Corp sells only the best clementines. The inspector rejected 50% of January’s harvest. Unfortunately, 20% of the inspected clementines fell off the delivery truck. If the truck delivers 200 clementines, how many were harvested in January?
Florida Clementines Corp sells only the best clementines. The inspector rejected 50% of January’s harvest. Unfortunately, 20% of the inspected clementines fell off the delivery truck. If the truck delivers 200 clementines, how many were harvested in January?
We first obtain how many clementines were loaded on the delivery truck from 200 delivered clementines. Then we obtain how many clementines were inspected. 200 = (1-0.2)x gives us 250 loaded onto the delivery truck. 250 = (1-0.5)x gives us 500 harvested clementines.
We first obtain how many clementines were loaded on the delivery truck from 200 delivered clementines. Then we obtain how many clementines were inspected. 200 = (1-0.2)x gives us 250 loaded onto the delivery truck. 250 = (1-0.5)x gives us 500 harvested clementines.
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Ed eats 3 cookies every day. If he increases the total amount of cookies he has to begin with by 50%, it would take 21 days to finish all of his cookies. How many cookies does he have to begin with?
Ed eats 3 cookies every day. If he increases the total amount of cookies he has to begin with by 50%, it would take 21 days to finish all of his cookies. How many cookies does he have to begin with?
We let T be the total amount of cookies and D be the number of days it takes to eat all of the cookies before increasing by 50%, and A be the number of days after increasing by 50%. With the information given, we can write the expressions, T=3D and 1.5T=3A. For the second equation, we know A=21. We plug in and get T=42.
We let T be the total amount of cookies and D be the number of days it takes to eat all of the cookies before increasing by 50%, and A be the number of days after increasing by 50%. With the information given, we can write the expressions, T=3D and 1.5T=3A. For the second equation, we know A=21. We plug in and get T=42.
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Gwen has a collection of 1,000 books. The average thickness of each book is 1.25” thick. She wants to buy enough bookshelves that all of her books will fit on it.
What is the shortest length of bookshelf she should buy, in whole feet, to fit all her books?
Gwen has a collection of 1,000 books. The average thickness of each book is 1.25” thick. She wants to buy enough bookshelves that all of her books will fit on it.
What is the shortest length of bookshelf she should buy, in whole feet, to fit all her books?
Length of books = 1,000 books x 1.25” per book = 1,250”
Translate to feet
1” = 12’
1250” / 12 = 104.16 feet
Round up to 105 feet to be able to fit all the books.
Length of books = 1,000 books x 1.25” per book = 1,250”
Translate to feet
1” = 12’
1250” / 12 = 104.16 feet
Round up to 105 feet to be able to fit all the books.
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There are 8 blue balls in a bag. 40% of all the balls in the bag are blue. How many total balls are in the bag?
There are 8 blue balls in a bag. 40% of all the balls in the bag are blue. How many total balls are in the bag?
You evaluate 8/0.4 = 20.
You evaluate 8/0.4 = 20.
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95 is 20% of what number?
95 is 20% of what number?
multiply the part times 100 then divide by the percent.
(95 x 100) / 20 = 475
multiply the part times 100 then divide by the percent.
(95 x 100) / 20 = 475
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Bryan has white socks and blue socks in his drawer, in a ratio of 4 : 7. What percent of his socks are white?
Bryan has white socks and blue socks in his drawer, in a ratio of 4 : 7. What percent of his socks are white?
You divide the number of blue socks, 4, by the number of total socks, 11, giving you 36%.
You divide the number of blue socks, 4, by the number of total socks, 11, giving you 36%.
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There are 9 marbles in a box, and 4 of them are red.
What percentage of the marbles in the box are NOT red?
There are 9 marbles in a box, and 4 of them are red.
What percentage of the marbles in the box are NOT red?
There are 5 non-red marbles and 9 total marbles.
5/9 = 0.555, which is about 55%
There are 5 non-red marbles and 9 total marbles.
5/9 = 0.555, which is about 55%
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Ben and Sam are starting a furniture design business. In order to build their shop, they borrow $150,000 from their neighborhood bank. The interest rate on the loan is 6%. How much interest do they have to pay?
Ben and Sam are starting a furniture design business. In order to build their shop, they borrow $150,000 from their neighborhood bank. The interest rate on the loan is 6%. How much interest do they have to pay?
Simple interest = Amount borrowed x Interest rate =
150,000 x 6% = 150,000 x .06 = $9000
Simple interest = Amount borrowed x Interest rate =
150,000 x 6% = 150,000 x .06 = $9000
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Find the lowest common denominator of these four fractions:
Find the lowest common denominator of these four fractions:
All of the denominators must be able to divide into the same number. First, see if the three smaller numbers (3, 4, 12) divide into the largest number (15)—NO. Then check the multiples of the largest number to see if the lower numbers divide into it:
15 * 2 = 30 (NO)
15 * 3 = 45 (NO)
15 * 4 = 60 (YES!)
All of the denominators must be able to divide into the same number. First, see if the three smaller numbers (3, 4, 12) divide into the largest number (15)—NO. Then check the multiples of the largest number to see if the lower numbers divide into it:
15 * 2 = 30 (NO)
15 * 3 = 45 (NO)
15 * 4 = 60 (YES!)
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Which of the following is not a factor of 52?
Which of the following is not a factor of 52?
Listing all the factors of 52: 1,2,4,13,26,52.
3 is not one of the factors.
Listing all the factors of 52: 1,2,4,13,26,52.
3 is not one of the factors.
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There is a set of numbers. The mean of this set of numbers is equal to the median. If four of the numbers are 10, 15, 15, and 17, what is the fifth number?
There is a set of numbers. The mean of this set of numbers is equal to the median. If four of the numbers are 10, 15, 15, and 17, what is the fifth number?
Since the set contains two 15s, along with 10 and 17, the median can only be 15, no matter what the fifth number is. So now we know that the mean is equal to 15, since it is equal to the median. Now an equation can be set up to solve this problem. 15 = (10 + 15 + 15 + 17 + x)/5. Solving for x we get an answer of 18.
Since the set contains two 15s, along with 10 and 17, the median can only be 15, no matter what the fifth number is. So now we know that the mean is equal to 15, since it is equal to the median. Now an equation can be set up to solve this problem. 15 = (10 + 15 + 15 + 17 + x)/5. Solving for x we get an answer of 18.
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How many irrational numbers are there between 3 and 7?
How many irrational numbers are there between 3 and 7?
There is an infinite amount of irrational numbers between any two "real" (whole) numbers. 3 and 7 are both real numbers
There is an infinite amount of irrational numbers between any two "real" (whole) numbers. 3 and 7 are both real numbers
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How many prime numbers are between 20 and 50?
How many prime numbers are between 20 and 50?
Prime numbers are numbers that cannot be divided evenly by any numbers besides itself and 1. The prime numbers between 20 and 50 are: 23, 29, 31, 37, 41, 43, 47, yielding an answer of 6.
Prime numbers are numbers that cannot be divided evenly by any numbers besides itself and 1. The prime numbers between 20 and 50 are: 23, 29, 31, 37, 41, 43, 47, yielding an answer of 6.
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3 candy bars and 4 bags of potato chips cost $7, and 3 candy bars and 2 bags of potato chips cost $5. What is the price of 1 bag of potato chips?
3 candy bars and 4 bags of potato chips cost $7, and 3 candy bars and 2 bags of potato chips cost $5. What is the price of 1 bag of potato chips?
Increasing 2 bags of potato chips increases the cost by $2. Therefore, they cost $1 per bag.
Increasing 2 bags of potato chips increases the cost by $2. Therefore, they cost $1 per bag.
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Susie wants to make a sandwich for lunch. She has two types of breads, three types of meats, and two types of cheeses to choose from. How many different sandwiches can she make if she chooses only one of each ingredient?
Susie wants to make a sandwich for lunch. She has two types of breads, three types of meats, and two types of cheeses to choose from. How many different sandwiches can she make if she chooses only one of each ingredient?
Each item (bread, meat, and cheese) is chosen independently from the others, so the answer can be found in a tree diagram: Bread x Meat x Cheese or 2 x 3 x 2 or 12.
Each item (bread, meat, and cheese) is chosen independently from the others, so the answer can be found in a tree diagram: Bread x Meat x Cheese or 2 x 3 x 2 or 12.
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At a party with 9 guests, every guest shakes every other guest’s hand exactly once. How many handshakes are exchanged during the party?
When two people shake hands with each other, that counts as one handshake.
At a party with 9 guests, every guest shakes every other guest’s hand exactly once. How many handshakes are exchanged during the party?
When two people shake hands with each other, that counts as one handshake.
Each person shakes 8 people’s hands, so at first guess that’s 9x8=72 handshakes. However, this double counts the number of handshakes since we count the handshake between person A and B once when we count A’s 8 handshakes and a second time when we count B’s 8 handshakes. Therefore, we divide our estimate by 2 and get 36.
Each person shakes 8 people’s hands, so at first guess that’s 9x8=72 handshakes. However, this double counts the number of handshakes since we count the handshake between person A and B once when we count A’s 8 handshakes and a second time when we count B’s 8 handshakes. Therefore, we divide our estimate by 2 and get 36.
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A candy shop sells Valentine's Day gift baskets that consist of chocolates, a basket, and a card. If there are five different types of chocolate, three types of baskets, and ten options for cards, how many different gift basket combinations are there?
A candy shop sells Valentine's Day gift baskets that consist of chocolates, a basket, and a card. If there are five different types of chocolate, three types of baskets, and ten options for cards, how many different gift basket combinations are there?
The correct answer is 150. Since there are five types of chocolate, three types of baskets, and ten card choices, the correct answer can be found by multiplying 3 x 5 x 10, which is 150. If you got 15 or 1500, you may have made a multiplication error. If you got 18, you may have added instead of multiplying.
The correct answer is 150. Since there are five types of chocolate, three types of baskets, and ten card choices, the correct answer can be found by multiplying 3 x 5 x 10, which is 150. If you got 15 or 1500, you may have made a multiplication error. If you got 18, you may have added instead of multiplying.
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A student is taking a test consisting of six questions. It is a multiple choice test and each question has four answers labelled A, B, C, and D. How many ways can the student answer all six questions if he does not choose the same answer for any two consecutive questions?
A student is taking a test consisting of six questions. It is a multiple choice test and each question has four answers labelled A, B, C, and D. How many ways can the student answer all six questions if he does not choose the same answer for any two consecutive questions?
the student has four choices for the first question, but only three choices for each of the remaining questions since he does not choose answers with the same letter twice in a row. From the multiplicative counting principle, there are 4 × 3 × 3 × 3 × 3 x 3 = 972 ways Steve can answer the six questions.
the student has four choices for the first question, but only three choices for each of the remaining questions since he does not choose answers with the same letter twice in a row. From the multiplicative counting principle, there are 4 × 3 × 3 × 3 × 3 x 3 = 972 ways Steve can answer the six questions.
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