Integers - ACT Math
Card 0 of 1710
On an airline flight of 250 people there is a choice of pasta, salad, or pizza for dinner. If 113 passengers choose pasta and 30% choose salad, how many passengers choose pizza?
On an airline flight of 250 people there is a choice of pasta, salad, or pizza for dinner. If 113 passengers choose pasta and 30% choose salad, how many passengers choose pizza?
30% of 250 is 75. Therefore, 250 – 75 – 113 = 62
30% of 250 is 75. Therefore, 250 – 75 – 113 = 62
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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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The sum of four consecutive integers is 42. What is the value of the greatest number?
The sum of four consecutive integers is 42. What is the value of the greatest number?
We can represent four consecutive integers using the following expressions:
Create an equation using the information in the problem.
Subtract 6 from both sides of the equation.
Divide both sides of the equation by 4.
The highest number in the series is the x-variable plus 3. We can write the following:
.
We can represent four consecutive integers using the following expressions:
Create an equation using the information in the problem.
Subtract 6 from both sides of the equation.
Divide both sides of the equation by 4.
The highest number in the series is the x-variable plus 3. We can write the following:
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Given the sequence of numbers:
1, 5, 9, _ , _ , 21 ....
What are the two missing terms of the arithmetic sequence?
Given the sequence of numbers:
1, 5, 9, _ , _ , 21 ....
What are the two missing terms of the arithmetic sequence?
The sequence is defined by an = 4_n –_ 3 for such n = 1,2,3,4....
The sequence is defined by an = 4_n –_ 3 for such n = 1,2,3,4....
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Find the sixth term in the following number sequence.
Find the sixth term in the following number sequence.
This question can be answered by analyzing the sequence provided and determining the pattern. The first term is 
, and the second term is 
The third term is 
Thus, 
has been added to 
in order to obtain 
, and 
has been added to 
in order to obtain 
This shows that 
is added to each preceding term in the sequence in order to obtain the next term. The complete sequence from terms one through six is shown below.
Thus, the sixth term is 
This question can be answered by analyzing the sequence provided and determining the pattern. The first term is
Thus, the sixth term is
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What is the next term of the series 
?
What is the next term of the series
Begin by looking at the transitions from number to number in this series:
From 
to 
: Add 
From 
to 
: Subtract 
From 
to 
: Add 
From 
to 
: Subtract 
From what you can tell, you can guess that the next step will be to add 
. Thus, the next value will be 
.
Begin by looking at the transitions from number to number in this series:
From
From
From
From
From what you can tell, you can guess that the next step will be to add
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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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A locker combination consists of three different numbers from the set of 30 different numbers on the face of the lock. Imagine that you have forgotten the combination. How many times do you have to try to find the right combination?
A locker combination consists of three different numbers from the set of 30 different numbers on the face of the lock. Imagine that you have forgotten the combination. How many times do you have to try to find the right combination?
It is said that the three numbers are different. So the number of lock combinations is 30_P_3 = 24 360.
It is said that the three numbers are different. So the number of lock combinations is 30_P_3 = 24 360.
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The game of euchre uses the 9s, 10s, jacks, queens, kings, and aces from a standard deck of 52 cards. How many 5-card euchre hands have at least 2 black cards?
The game of euchre uses the 9s, 10s, jacks, queens, kings, and aces from a standard deck of 52 cards. How many 5-card euchre hands have at least 2 black cards?
The hand could have 2, 3, 4, or 5 black cards. There are 12 black cards and 12 red cards, so the numbers of combinations for the four cases are as follows.
2 black cards: C(12, 2) × C(12, 3) = 14 520
3 black cards: C(12, 3) × C(12, 2) = 14 520
4 black cards: C(12, 4) × C(12, 1) = 5940
5 black cards: C(12, 5) × C(12, 0) = 792
The total number of euchre hands that have at least two black cards is the total of these four cases, 35 772.
The hand could have 2, 3, 4, or 5 black cards. There are 12 black cards and 12 red cards, so the numbers of combinations for the four cases are as follows.
2 black cards: C(12, 2) × C(12, 3) = 14 520
3 black cards: C(12, 3) × C(12, 2) = 14 520
4 black cards: C(12, 4) × C(12, 1) = 5940
5 black cards: C(12, 5) × C(12, 0) = 792
The total number of euchre hands that have at least two black cards is the total of these four cases, 35 772.
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You work as a health inspector and must visit each of the 15 restaurants in town once each week. In how many different orders can you make these inspections?
You work as a health inspector and must visit each of the 15 restaurants in town once each week. In how many different orders can you make these inspections?
15_P_15 = 15!
= 1.307 674 368 × 1012
15_P_15 = 15!
= 1.307 674 368 × 1012
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A car averages 29 miles per gallon. If gas costs $3.75 per gallon how much money would need to be spent on gas to travel 1464.5 miles?
A car averages 29 miles per gallon. If gas costs $3.75 per gallon how much money would need to be spent on gas to travel 1464.5 miles?
The question is asking for the amount of money that would need to be spent on gas. Using the value given for the miles per gallon of the car and the amount of miles traveled it is possible to determine the gallons of fuel that will be required. This will be set up as 1464.5 miles travelled divided by the 29 miles per gallon that the car gets. This leaves us with 50.5 gallons of fuel used. From this point we can multiply the amount of fuel used, 50.5 gallons, by the price of fuel per gallon, $3.75, to obtain the amount of money that will spent on fuel, $189.38.
The question is asking for the amount of money that would need to be spent on gas. Using the value given for the miles per gallon of the car and the amount of miles traveled it is possible to determine the gallons of fuel that will be required. This will be set up as 1464.5 miles travelled divided by the 29 miles per gallon that the car gets. This leaves us with 50.5 gallons of fuel used. From this point we can multiply the amount of fuel used, 50.5 gallons, by the price of fuel per gallon, $3.75, to obtain the amount of money that will spent on fuel, $189.38.
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Connie's car gets 35 miles per gallon of gas. How much gas will she need to take a 525 mile trip? Round to the nearest gallon.
Connie's car gets 35 miles per gallon of gas. How much gas will she need to take a 525 mile trip? Round to the nearest gallon.
This becomes a division problem: 525 miles ÷ 35 miles per gallon = 15 gallons
This becomes a division problem: 525 miles ÷ 35 miles per gallon = 15 gallons
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