Operations - SAT Math
Card 0 of 17
Find the values of the variables 
and 
in the following sequence:
Find the values of the variables
Terms are obtained by alternately adding 5 and multiplying by 3:
The missing two elements are found by multiplying by 3, then by adding 5:
Multiplying by 3 confirms that this is correct:
Terms are obtained by alternately adding 5 and multiplying by 3:
The missing two elements are found by multiplying by 3, then by adding 5:
Multiplying by 3 confirms that this is correct:
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My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?
My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?
In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.
In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.
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What is the sum of multiples of 10 from 10 to 140 inclusive?
What is the sum of multiples of 10 from 10 to 140 inclusive?
Listing them all, 10-20-30-40-50-60-70-80-90-100-110-120-130-140 you see you can divide the numbers in half (7 pairs). Alternatively you can take (140-10+10)/2/10, adding that additional +10 in the numerator because it is inclusive, giving you 7. Just adding the top and bottom numbers gives you 10+140 for 150. 150*7 is 1050.
Listing them all, 10-20-30-40-50-60-70-80-90-100-110-120-130-140 you see you can divide the numbers in half (7 pairs). Alternatively you can take (140-10+10)/2/10, adding that additional +10 in the numerator because it is inclusive, giving you 7. Just adding the top and bottom numbers gives you 10+140 for 150. 150*7 is 1050.
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Examine the sequence:
Give the number that replaces the square.
Examine the sequence:
Give the number that replaces the square.
After the first term, the next four terms are obtained by adding, multiplying, subtracting, and dividing by 2, in order. The four terms after that are obtained by carrying out the same operations with 4. The next term is obtained by adding 6, so the operations can be expected to be repeated with 6, the next even number.
Observe the operations as carried out with 2:
Carrying out the same steps, in order, with 4:
Carrying out the same steps, in order, with 6:
, the number that replaces the circle;
, the number that replaces the square.
After the first term, the next four terms are obtained by adding, multiplying, subtracting, and dividing by 2, in order. The four terms after that are obtained by carrying out the same operations with 4. The next term is obtained by adding 6, so the operations can be expected to be repeated with 6, the next even number.
Observe the operations as carried out with 2:
Carrying out the same steps, in order, with 4:
Carrying out the same steps, in order, with 6:
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The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?
The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?
To solve this problem. First set up a mathematical equation that represents this scenario.
"The sum of three consecutive even numbers is 42."
Let
and recalling that each consecutive even number is two values greater that the previous even number, the mathematical equation becomes
From here isolate the variable on one side of the equations with all other constants on the other side.
Subtract six from both sides.
Now divide by three.
Since 
represents the beginning number in this sequence it also represents the smallest even number in this sequence. Therefore the smallest even number is 12.
To solve this problem. First set up a mathematical equation that represents this scenario.
"The sum of three consecutive even numbers is 42."
Let
and recalling that each consecutive even number is two values greater that the previous even number, the mathematical equation becomes
From here isolate the variable on one side of the equations with all other constants on the other side.
Subtract six from both sides.
Now divide by three.
Since
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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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An office wants to buy 22 computers at $900 each. The budget is $20,000 and the tax on computers is 9%. How many computers can the office afford?
An office wants to buy 22 computers at $900 each. The budget is $20,000 and the tax on computers is 9%. How many computers can the office afford?
The office can only afford 20 computers.
1.09 * 900 = $981 is the actual price of each computer, with tax.
Divide:
20,000/981 = 20.39
Since the office cannot purchase a partial computer, we round down to 20 computers.
The office can only afford 20 computers.
1.09 * 900 = $981 is the actual price of each computer, with tax.
Divide:
20,000/981 = 20.39
Since the office cannot purchase a partial computer, we round down to 20 computers.
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in physics where
.
If the mass is increased by 3 three times the original and the acceleration is increased by 7 times the original, how many times greater is the new force than the original force?
If the mass is increased by 3 three times the original and the acceleration is increased by 7 times the original, how many times greater is the new force than the original force?
We simply multiply the new mass by the new acceleration to obtain a new force that is 21 times greater than the original.
We simply multiply the new mass by the new acceleration to obtain a new force that is 21 times greater than the original.
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A paint crew can paint 
walls in 
hours. At this rate, how many walls can the paint crew paint in 
hours?
A paint crew can paint
First, divide 
by 
to determine how many walls the paint crew can paint in 
hour.
divided by 
is equal to 
.
Then, multiply this number by 
hours.
First, divide
Then, multiply this number by
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Calculate 
in the following series:
Calculate
Each element is obtained from the previous one by alternating the following operations: multiplying by 5 and adding 6.
If we let 
be the first element, then
Solve for 
:
Each element is obtained from the previous one by alternating the following operations: multiplying by 5 and adding 6.
If we let
Solve for
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Convert three yards to inches.
Convert three yards to inches.
To solve this problem, we need to know the conversions between yards to feet, and feet to inches. Write their correct conversions.
Convert three yards to feet.
Convert nine feet to inches.
To solve this problem, we need to know the conversions between yards to feet, and feet to inches. Write their correct conversions.
Convert three yards to feet.
Convert nine feet to inches.
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Janet can pick between 10 and 20 tomatoes in an hour. What is a possible amount of time for Janet to pick 120 tomatoes?
Janet can pick between 10 and 20 tomatoes in an hour. What is a possible amount of time for Janet to pick 120 tomatoes?
Since Janet can pick between 10 and 20 tomatoes in an hour, there is a range for which she can pick 120 tomatoes. Therefore, to find the possible amount of time it will take Janet to pick 120 tomatoes set up two fractions.
The first fraction will use the rate of 10 tomatoes an hour.
Therefore, identifying the variables are as follows.
Substituting these into the fraction results in a possible time
The second fraction will use the rate of 20 tomatoes an hour.
Therefore, identifying the variables are as follows.
Substituting these into the fraction results in a possible time
Of the answer selections 6 hours would be the correct answer.
Since Janet can pick between 10 and 20 tomatoes in an hour, there is a range for which she can pick 120 tomatoes. Therefore, to find the possible amount of time it will take Janet to pick 120 tomatoes set up two fractions.
The first fraction will use the rate of 10 tomatoes an hour.
Therefore, identifying the variables are as follows.
Substituting these into the fraction results in a possible time
The second fraction will use the rate of 20 tomatoes an hour.
Therefore, identifying the variables are as follows.
Substituting these into the fraction results in a possible time
Of the answer selections 6 hours would be the correct answer.
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The annual number of cellular phones purchased from a company is illustrated in the following graph. How many more phones were sold in 2009 than 2011?
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The annual number of cellular phones purchased from a company is illustrated in the following graph. How many more phones were sold in 2009 than 2011?
In 2009, 32,000 phones were sold (according the the label on the y-axis, each number is equal to 1,000 phones). In 2011, 26,000 phones were sold.
In 2009, 32,000 phones were sold (according the the label on the y-axis, each number is equal to 1,000 phones). In 2011, 26,000 phones were sold.
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