Integers - SAT Math
Card 0 of 2024
Four consecutive integers have a mean of 9.5. What is the largest of these integers?
Four consecutive integers have a mean of 9.5. What is the largest of these integers?
Four consecutive integers could be represented as n, n+1, n+2, n+3
Therefore, by saying that they have a mean of 9.5, we mean to say:
(n + n+1 + n+2 + n+ 3)/4 = 9.5
(4n + 6)/4 = 9.5 → 4n + 6 = 38 → 4n = 32 → n = 8
Therefore, the largest value is n + 3, or 11.
Four consecutive integers could be represented as n, n+1, n+2, n+3
Therefore, by saying that they have a mean of 9.5, we mean to say:
(n + n+1 + n+2 + n+ 3)/4 = 9.5
(4n + 6)/4 = 9.5 → 4n + 6 = 38 → 4n = 32 → n = 8
Therefore, the largest value is n + 3, or 11.
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The sum of three consecutive even integers is 108. What is the largest number?
The sum of three consecutive even integers is 108. What is the largest number?
Three consecutive even integers can be represented by x, x+2, x+4. The sum is 3x+6, which is equal to 108. Thus, 3x+6=108. Solving for x yields x=34. However, the question asks for the largest number, which is x+4 or 38. Please make sure to answer what the question asks for!
You could have also plugged in the answer choices. If you plugged in 38 as the largest number, then the previous even integer would be 36 and the next previous even integer 34. The sum of 34, 36, and 38 yields 108.
Three consecutive even integers can be represented by x, x+2, x+4. The sum is 3x+6, which is equal to 108. Thus, 3x+6=108. Solving for x yields x=34. However, the question asks for the largest number, which is x+4 or 38. Please make sure to answer what the question asks for!
You could have also plugged in the answer choices. If you plugged in 38 as the largest number, then the previous even integer would be 36 and the next previous even integer 34. The sum of 34, 36, and 38 yields 108.
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Four consecutive odd integers have a sum of 32. What are the integers?
Four consecutive odd integers have a sum of 32. What are the integers?
Consecutive odd integers can be represented as x, x+2, x+4, and x+6.
We know that the sum of these integers is 32. We can add the terms together and set it equal to 32:
x + (x+2) + (x+4) + (x+6) = 32
4x + 12 = 32
4x = 20
x = 5; x+2=7; x+4 = 9; x+6 = 11
Our integers are 5, 7, 9, and 11.
Consecutive odd integers can be represented as x, x+2, x+4, and x+6.
We know that the sum of these integers is 32. We can add the terms together and set it equal to 32:
x + (x+2) + (x+4) + (x+6) = 32
4x + 12 = 32
4x = 20
x = 5; x+2=7; x+4 = 9; x+6 = 11
Our integers are 5, 7, 9, and 11.
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The sum of three consecutive even integers equals 72. What is the product of these integers?
The sum of three consecutive even integers equals 72. What is the product of these integers?
Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.
x + (x + 2) + (x + 4) = 72
3x + 6 = 72
3x = 66
x = 22.
This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.
The answer is 13728.
Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.
x + (x + 2) + (x + 4) = 72
3x + 6 = 72
3x = 66
x = 22.
This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.
The answer is 13728.
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The sum of four consecutive odd integers is equal to 96. How many of the integers are prime?
The sum of four consecutive odd integers is equal to 96. How many of the integers are prime?
Let x be the smallest of the four integers. We are told that the integers are consecutive odd integers. Because odd integers are separated by two, each consecutive odd integer is two larger than the one before it. Thus, we can let x + 2 represent the second integer, x + 4 represent the third, and x + 6 represent the fourth. The sum of the four integers equals 96, so we can write the following equation:
x + (x + 2) + (x + 4) + (x + 6) = 96
Combine x terms.
4_x_ + 2 + 4 + 6 = 96
Combine constants on the left side.
4_x_ + 12 = 96
Subtract 12 from both sides.
4_x_ = 84
Divide both sides by 4.
x = 21
This means the smallest integer is 21. The other integers are therefore 23, 25, and 27.
The question asks us how many of the four integers are prime. A prime number is divisible only by itself and one. Among the four integers, only 23 is prime. The number 21 is divisible by 3 and 7; the number 25 is divisible by 5; and 27 is divisible by 3 and 9. Thus, 23 is the only number from the integers that is prime. There is only one prime integer.
The answer is 1.
Let x be the smallest of the four integers. We are told that the integers are consecutive odd integers. Because odd integers are separated by two, each consecutive odd integer is two larger than the one before it. Thus, we can let x + 2 represent the second integer, x + 4 represent the third, and x + 6 represent the fourth. The sum of the four integers equals 96, so we can write the following equation:
x + (x + 2) + (x + 4) + (x + 6) = 96
Combine x terms.
4_x_ + 2 + 4 + 6 = 96
Combine constants on the left side.
4_x_ + 12 = 96
Subtract 12 from both sides.
4_x_ = 84
Divide both sides by 4.
x = 21
This means the smallest integer is 21. The other integers are therefore 23, 25, and 27.
The question asks us how many of the four integers are prime. A prime number is divisible only by itself and one. Among the four integers, only 23 is prime. The number 21 is divisible by 3 and 7; the number 25 is divisible by 5; and 27 is divisible by 3 and 9. Thus, 23 is the only number from the integers that is prime. There is only one prime integer.
The answer is 1.
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The sum of three consecutive integers is 60. Find the smallest of these three integers.
The sum of three consecutive integers is 60. Find the smallest of these three integers.
Assume the three consecutive integers equal 
, 
, and 
. The sum of these three integers is 60. Thus,
Assume the three consecutive integers equal
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In the repeating pattern 9,5,6,2,1,9,5,6,2,1......What is the 457th number in the sequence?
In the repeating pattern 9,5,6,2,1,9,5,6,2,1......What is the 457th number in the sequence?
There are 5 numbers in the sequnce.
How many numbers are left over if you divide 5 into 457?
There would be 2 numbers!
The second number in the sequence is 9,5,6,2,1
There are 5 numbers in the sequnce.
How many numbers are left over if you divide 5 into 457?
There would be 2 numbers!
The second number in the sequence is 9,5,6,2,1
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If 
are consecutive, non-negative integers, how many different values of 
are there such that 
is a prime number?
If
Since 
are consecutive integers, we know that at least 2 of them will be even. Since we have 2 that are going to be even, we know that when we divide the product by 2 we will still have an even number. Since 2 is the only prime that is even, we must have:
What we notice, however, is that for 
, we have the product is 0. For 
, we have the product is 24. We will then never have a product of 4, meaning that 
is never going to be a prime number.
Since
What we notice, however, is that for
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If the tick marks are equally spaced on the number line above, what is the average (arithmetic mean) of x, y, and z?
If the tick marks are equally spaced on the number line above, what is the average (arithmetic mean) of x, y, and z?
First, we must find out by how much they are spaced by. It cannot be 1, since 4(4) = 16, which is too great of a step in the positive direction and exceeds the equal-spacing limit. 2 works perfectly, however, as 4(2) equals 8 and fits in line with the equal spacing.
Next, we can find the values of x and y since we are given a value of 6 for the third tick mark. As such, x (6 – 4) and y (6 – 2) are 2 and 4, respectively.
Finally, z is 4 steps away from y, and since each step has a value of 2, 2(4) = 8, plus the value that y is already at, 8 + 4 = 12 (or can simply count).
Finding the average of all 3 values, we get (2 + 4 + 12)/3 = 18/3 = 6.
First, we must find out by how much they are spaced by. It cannot be 1, since 4(4) = 16, which is too great of a step in the positive direction and exceeds the equal-spacing limit. 2 works perfectly, however, as 4(2) equals 8 and fits in line with the equal spacing.
Next, we can find the values of x and y since we are given a value of 6 for the third tick mark. As such, x (6 – 4) and y (6 – 2) are 2 and 4, respectively.
Finally, z is 4 steps away from y, and since each step has a value of 2, 2(4) = 8, plus the value that y is already at, 8 + 4 = 12 (or can simply count).
Finding the average of all 3 values, we get (2 + 4 + 12)/3 = 18/3 = 6.
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How many numbers 1 to 250 inclusive are cubes of integers?
How many numbers 1 to 250 inclusive are cubes of integers?
The cubes of integers from 1 to 250 are 1, 8, 27,64,125,216.
The cubes of integers from 1 to 250 are 1, 8, 27,64,125,216.
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On the number line above, the tick marks are equally spaced. Which of the following expresses 
in terms of 
?
On the number line above, the tick marks are equally spaced. Which of the following expresses
If 
is between 
and 
on the number line, then 
and 
.
So 
must be correct because
.
If
So
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Kacey works 5 hours per day on Monday, Tuesday, and Wednesday, as well as 9 hours on Thursday and Friday. She does not work on Saturday or Sunday. Her total earnings per week is $363. How much does she earn per hour in dollars?
Kacey works 5 hours per day on Monday, Tuesday, and Wednesday, as well as 9 hours on Thursday and Friday. She does not work on Saturday or Sunday. Her total earnings per week is $363. How much does she earn per hour in dollars?
Kacey works 5 hours a day for 3 days and 9 hours a day for 2 days. (5)(3) = 15 and (2)(9) = 18. 15 + 18 = 33 hours worked a week. $363/33 hours = $11/hr.
Kacey works 5 hours a day for 3 days and 9 hours a day for 2 days. (5)(3) = 15 and (2)(9) = 18. 15 + 18 = 33 hours worked a week. $363/33 hours = $11/hr.
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When k is divided by 2, the remainder is 1. If k is divided by 3, the remainder is 0. And if k is divded by 5, the remainder is 3. Which of the following is a possible value for k?
When k is divided by 2, the remainder is 1. If k is divided by 3, the remainder is 0. And if k is divded by 5, the remainder is 3. Which of the following is a possible value for k?
Since the remainder when k is divided by 2 is 1, this means that k is not an even number. Therefore, we can immediately eliminate 30 from our possible answer choices.
Because the remainder when k is divded by 3 is 0, we know that k must be a multiple of 3. This means we can eliminate 23 from our answer choices.
The only choices left are 63, 27, and 57. When 27 and 57 are divded by five, the remainder is two. Thus, only 63 works, because when 63 is divded by five, the remainder is three.
The answer is 63.
Since the remainder when k is divided by 2 is 1, this means that k is not an even number. Therefore, we can immediately eliminate 30 from our possible answer choices.
Because the remainder when k is divded by 3 is 0, we know that k must be a multiple of 3. This means we can eliminate 23 from our answer choices.
The only choices left are 63, 27, and 57. When 27 and 57 are divded by five, the remainder is two. Thus, only 63 works, because when 63 is divded by five, the remainder is three.
The answer is 63.
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The result of a number divided by 2 is the same as the result of that number divided by 10. What is that number?
The result of a number divided by 2 is the same as the result of that number divided by 10. What is that number?
0 is the only choice that yields the same answer (0) when divided by 2 and 10. You can check this easily by plugging a few of the answer choices into a fraction:
1/2 ≠ 1/10
2/2 ≠ 2/10 etc.
0 is the only choice that yields the same answer (0) when divided by 2 and 10. You can check this easily by plugging a few of the answer choices into a fraction:
1/2 ≠ 1/10
2/2 ≠ 2/10 etc.
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If x and y are positive integers and 2y = 16x, what is the value of y/x?
If x and y are positive integers and 2y = 16x, what is the value of y/x?
Making the equation even yields y = 4 and x = 1, since 24 = 16. This makes y/x = 4.
Making the equation even yields y = 4 and x = 1, since 24 = 16. This makes y/x = 4.
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If 
is an integer, and 3 is the remainder when 
is divided by 5, then which of the following is a possible value of 
?
If
For this problem, you need to use process of elimination.
When 
The remainder of 
is 3 (the answer is 11, remainder 3), so 
is a possible answer choice. If you try the other answers they won't work.
For this problem, you need to use process of elimination.
When
The remainder of
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In the given sequence, the first term is 3 and each term after is one less than three times the previous term.
What is the sixth term in the sequence?
In the given sequence, the first term is 3 and each term after is one less than three times the previous term.
What is the sixth term in the sequence?
The fourth term is: 3(23) – 1 = 69 – 1 = 68.
The fifth term is: 3(68) – 1 = 204 – 1 = 203.
The sixth term is: 3(203) – 1 = 609 – 1 = 608.
The fourth term is: 3(23) – 1 = 69 – 1 = 68.
The fifth term is: 3(68) – 1 = 204 – 1 = 203.
The sixth term is: 3(203) – 1 = 609 – 1 = 608.
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2, 8, 14, 20
The first term in the sequence is 2, and each following term is determined by adding 6. What is the value of the 50th term?
2, 8, 14, 20
The first term in the sequence is 2, and each following term is determined by adding 6. What is the value of the 50th term?
We start by multiplying 6 times 46, since the first 4 terms are already listed. We then add the product, 276, to the last listed term, 20. This gives us our answer of 296.
We start by multiplying 6 times 46, since the first 4 terms are already listed. We then add the product, 276, to the last listed term, 20. This gives us our answer of 296.
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Which of the following could not be a term in the sequence 5, 10, 15, 20...?
Which of the following could not be a term in the sequence 5, 10, 15, 20...?
All answers in the sequence must end in a 5 or a 0.
All answers in the sequence must end in a 5 or a 0.
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