Counting / Sets - PSAT Math
Card 1 of 84
How many prime numbers are between 1 to 25?
How many prime numbers are between 1 to 25?
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A prime numbers is a number greater than 1 that can only be divided by 1 and itself. Simply count from 1 to 25 and see how many values fit the criteria.
2, 3, 4, 5, 6, 7 , 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
Prime numbers are underlined. Nine prime numbers are in this set interval.
A prime numbers is a number greater than 1 that can only be divided by 1 and itself. Simply count from 1 to 25 and see how many values fit the criteria.
2, 3, 4, 5, 6, 7 , 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
Prime numbers are underlined. Nine prime numbers are in this set interval.
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Four consecutive odd integers sum to 40. How many of these numbers are prime?
Four consecutive odd integers sum to 40. How many of these numbers are prime?
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Let x equal the smallest of the four numbers. Therefore:
x + (x+2)+(x+4)+(x+6)=40
4x +12 = 40
4x + 28
x=7
Therefore the four odd numbers are 7, 9, 11, and 13. Since all are prime except 9, three of the numbers are prime.
Let x equal the smallest of the four numbers. Therefore:
x + (x+2)+(x+4)+(x+6)=40
4x +12 = 40
4x + 28
x=7
Therefore the four odd numbers are 7, 9, 11, and 13. Since all are prime except 9, three of the numbers are prime.
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A custom-made ruler is 30 cm long and for every 2 cm there's a tick mark. How many tick marks are there on the ruler?
A custom-made ruler is 30 cm long and for every 2 cm there's a tick mark. How many tick marks are there on the ruler?
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There will be 15 gaps of 2 cm long but 16 tick marks because there will be a tick mark on each end of the ruler.
There will be 15 gaps of 2 cm long but 16 tick marks because there will be a tick mark on each end of the ruler.
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Find the median of this set of numbers
Find the median of this set of numbers
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To find the median of a set of numbers, we must first order them from smallest to greatest.
Next, we must find the number directly in the middle, which has an equal number of numbers to the right and to the left.
Therefore, our answer is 
.
To find the median of a set of numbers, we must first order them from smallest to greatest.
Next, we must find the number directly in the middle, which has an equal number of numbers to the right and to the left.
Therefore, our answer is
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Which number completes the following series: 1, 2, 4, 8, 16, 32, 64, _?
Which number completes the following series: 1, 2, 4, 8, 16, 32, 64, _?
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All of the numbers in this series are 2n-1. The number that we are looking for is the eighth number. So 28–1 = 27 = 128.
All of the numbers in this series are 2n-1. The number that we are looking for is the eighth number. So 28–1 = 27 = 128.
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Alhough Danielle’s favorite flowers are tulips, she wants at least one each of three different kinds of flowers in her bouquet. Roses are twice as expensive as lilies and lilies are 25% of the price of tulips. If a rose costs $20 and Danielle only has $130, how many tulips can she buy?
Alhough Danielle’s favorite flowers are tulips, she wants at least one each of three different kinds of flowers in her bouquet. Roses are twice as expensive as lilies and lilies are 25% of the price of tulips. If a rose costs $20 and Danielle only has $130, how many tulips can she buy?
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She can only buy 2 tulips at $80, because if she bought 3 she wouldn’t have enough to afford the other 2 kinds of flowers. She has to spend at least 30 dollars (20 + 10) on 1 rose and 1 lily.
She can only buy 2 tulips at $80, because if she bought 3 she wouldn’t have enough to afford the other 2 kinds of flowers. She has to spend at least 30 dollars (20 + 10) on 1 rose and 1 lily.
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Find the missing number in the following set:
Find the missing number in the following set:
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The rule is as follows: add 2 to the previous number then multiply times 2.
The answer is (16 + 2) * 2 = 36.
The rule is as follows: add 2 to the previous number then multiply times 2.
The answer is (16 + 2) * 2 = 36.
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Which of the following is not a rational number?
Which of the following is not a rational number?
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A rational number is a number that can be written in the form of a/b, where a and b are integers, aka a real number that can be written as a simple fraction or ratio. 4 of the 5 answer choices can be written as fractions and are thus rational.
5 = 5/1, 1.75 = 7/4, .001 = 1/1000, 0.111... = 1/9
√2 cannot be written as a fraction because it is irrational. The two most famous irrational numbers are √2 and pi.
A rational number is a number that can be written in the form of a/b, where a and b are integers, aka a real number that can be written as a simple fraction or ratio. 4 of the 5 answer choices can be written as fractions and are thus rational.
5 = 5/1, 1.75 = 7/4, .001 = 1/1000, 0.111... = 1/9
√2 cannot be written as a fraction because it is irrational. The two most famous irrational numbers are √2 and pi.
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If four different integers are selected, one from each of the following sets, what is the greater sum that these four integers could have?
W = {4, 6, 9, 10}
X = {4, 5, 8, 10}
Y = {3, 6, 7, 11}
Z = {5, 8, 10, 11}
If four different integers are selected, one from each of the following sets, what is the greater sum that these four integers could have?
W = {4, 6, 9, 10}
X = {4, 5, 8, 10}
Y = {3, 6, 7, 11}
Z = {5, 8, 10, 11}
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By observing each of these sets, we can easily determine the largest number in each; however, the problem is asking for us to find the greatest possible sum if we select four different integers, one from each set. The largest number is 11. We will either select this number from set Y or set Z.
We will select set
Y for the 11
because the next larger number in set
Z is 10, which is greater than the next largest number is set Y, 7.
We can use set Z for 10.
Because the 10 has already been selected, choosing the integer from W and X should be easy because 9 is the next largest integer from set W
and
8 is the next largest integer from set X.
11 + 10 + 9 + 8 = 38
By observing each of these sets, we can easily determine the largest number in each; however, the problem is asking for us to find the greatest possible sum if we select four different integers, one from each set. The largest number is 11. We will either select this number from set Y or set Z.
We will select set
Y for the 11
because the next larger number in set
Z is 10, which is greater than the next largest number is set Y, 7.
We can use set Z for 10.
Because the 10 has already been selected, choosing the integer from W and X should be easy because 9 is the next largest integer from set W
and
8 is the next largest integer from set X.
11 + 10 + 9 + 8 = 38
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A team has a win-loss ratio of 4:1. If the team wins six games in a row, the win-loss ratio will now be 6:1. How many losses did the team have initially?
A team has a win-loss ratio of 4:1. If the team wins six games in a row, the win-loss ratio will now be 6:1. How many losses did the team have initially?
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If a team's ratio of wins to losses increases from 4:1 to 6:1 by winning six games, they must have 12 wins initially and 3 losses.
If a team's ratio of wins to losses increases from 4:1 to 6:1 by winning six games, they must have 12 wins initially and 3 losses.
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If the average of Set 
is 
, what is the average of Set 
?
If the average of Set
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We know the average of Set A is 5. Therefore:
Now let's solve for 
:
We can now plug this value of 
into Set B and solve for the average:
Set B = {0, 2, 4}
The average of Set B is 2.
We know the average of Set A is 5. Therefore:
Now let's solve for
We can now plug this value of
Set B = {0, 2, 4}
The average of Set B is 2.
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Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
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The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
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Which of the following is not a rational number?
Which of the following is not a rational number?
Tap to reveal answer
A rational number is a number that can be written in the form of a/b, where a and b are integers, aka a real number that can be written as a simple fraction or ratio. 4 of the 5 answer choices can be written as fractions and are thus rational.
5 = 5/1, 1.75 = 7/4, .001 = 1/1000, 0.111... = 1/9
√2 cannot be written as a fraction because it is irrational. The two most famous irrational numbers are √2 and pi.
A rational number is a number that can be written in the form of a/b, where a and b are integers, aka a real number that can be written as a simple fraction or ratio. 4 of the 5 answer choices can be written as fractions and are thus rational.
5 = 5/1, 1.75 = 7/4, .001 = 1/1000, 0.111... = 1/9
√2 cannot be written as a fraction because it is irrational. The two most famous irrational numbers are √2 and pi.
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Find the missing number in the following set:
Find the missing number in the following set:
Tap to reveal answer
The rule is as follows: add 2 to the previous number then multiply times 2.
The answer is (16 + 2) * 2 = 36.
The rule is as follows: add 2 to the previous number then multiply times 2.
The answer is (16 + 2) * 2 = 36.
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Which number completes the following series: 1, 2, 4, 8, 16, 32, 64, _?
Which number completes the following series: 1, 2, 4, 8, 16, 32, 64, _?
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All of the numbers in this series are 2n-1. The number that we are looking for is the eighth number. So 28–1 = 27 = 128.
All of the numbers in this series are 2n-1. The number that we are looking for is the eighth number. So 28–1 = 27 = 128.
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Alhough Danielle’s favorite flowers are tulips, she wants at least one each of three different kinds of flowers in her bouquet. Roses are twice as expensive as lilies and lilies are 25% of the price of tulips. If a rose costs $20 and Danielle only has $130, how many tulips can she buy?
Alhough Danielle’s favorite flowers are tulips, she wants at least one each of three different kinds of flowers in her bouquet. Roses are twice as expensive as lilies and lilies are 25% of the price of tulips. If a rose costs $20 and Danielle only has $130, how many tulips can she buy?
Tap to reveal answer
She can only buy 2 tulips at $80, because if she bought 3 she wouldn’t have enough to afford the other 2 kinds of flowers. She has to spend at least 30 dollars (20 + 10) on 1 rose and 1 lily.
She can only buy 2 tulips at $80, because if she bought 3 she wouldn’t have enough to afford the other 2 kinds of flowers. She has to spend at least 30 dollars (20 + 10) on 1 rose and 1 lily.
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If four different integers are selected, one from each of the following sets, what is the greater sum that these four integers could have?
W = {4, 6, 9, 10}
X = {4, 5, 8, 10}
Y = {3, 6, 7, 11}
Z = {5, 8, 10, 11}
If four different integers are selected, one from each of the following sets, what is the greater sum that these four integers could have?
W = {4, 6, 9, 10}
X = {4, 5, 8, 10}
Y = {3, 6, 7, 11}
Z = {5, 8, 10, 11}
Tap to reveal answer
By observing each of these sets, we can easily determine the largest number in each; however, the problem is asking for us to find the greatest possible sum if we select four different integers, one from each set. The largest number is 11. We will either select this number from set Y or set Z.
We will select set
Y for the 11
because the next larger number in set
Z is 10, which is greater than the next largest number is set Y, 7.
We can use set Z for 10.
Because the 10 has already been selected, choosing the integer from W and X should be easy because 9 is the next largest integer from set W
and
8 is the next largest integer from set X.
11 + 10 + 9 + 8 = 38
By observing each of these sets, we can easily determine the largest number in each; however, the problem is asking for us to find the greatest possible sum if we select four different integers, one from each set. The largest number is 11. We will either select this number from set Y or set Z.
We will select set
Y for the 11
because the next larger number in set
Z is 10, which is greater than the next largest number is set Y, 7.
We can use set Z for 10.
Because the 10 has already been selected, choosing the integer from W and X should be easy because 9 is the next largest integer from set W
and
8 is the next largest integer from set X.
11 + 10 + 9 + 8 = 38
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A team has a win-loss ratio of 4:1. If the team wins six games in a row, the win-loss ratio will now be 6:1. How many losses did the team have initially?
A team has a win-loss ratio of 4:1. If the team wins six games in a row, the win-loss ratio will now be 6:1. How many losses did the team have initially?
Tap to reveal answer
If a team's ratio of wins to losses increases from 4:1 to 6:1 by winning six games, they must have 12 wins initially and 3 losses.
If a team's ratio of wins to losses increases from 4:1 to 6:1 by winning six games, they must have 12 wins initially and 3 losses.
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If the average of Set is , what is the average of Set ?
If the average of Set
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We know the average of Set A is 5. Therefore:
Now let's solve for :
We can now plug this value of into Set B and solve for the average:
Set B = {0, 2, 4}
The average of Set B is 2.
We know the average of Set A is 5. Therefore:
Now let's solve for
We can now plug this value of
Set B = {0, 2, 4}
The average of Set B is 2.
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Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Tap to reveal answer
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
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