Arithmetic - SAT Math
Card 0 of 7312
On a real number line, x1 = -4 and x2 = 14. What is the distance between these two points?
On a real number line, x1 = -4 and x2 = 14. What is the distance between these two points?
The distance between two points is always positive. We calculate lx2 - x1l, which will give us the distance between the points.
|14- (-4)| = |14+4| = |18| = 18
The distance between two points is always positive. We calculate lx2 - x1l, which will give us the distance between the points.
|14- (-4)| = |14+4| = |18| = 18
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During Laura and Anna’s bake sale, 35 brownies, 12 cupcakes and 23 glasses of lemonade were sold. These goods cost $44 for the raw ingredients, and they sold for $79. What is the average profit per item?
During Laura and Anna’s bake sale, 35 brownies, 12 cupcakes and 23 glasses of lemonade were sold. These goods cost $44 for the raw ingredients, and they sold for $79. What is the average profit per item?
Total profit ($35) divided by total items (70) yields the answer of $0.50 profit per item.
Total profit ($35) divided by total items (70) yields the answer of $0.50 profit per item.
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The population of Town A is 12,979 people in 1995. The population, when measured again in 2005, is 22,752. What was the change in population to the nearest whole percentage point?
The population of Town A is 12,979 people in 1995. The population, when measured again in 2005, is 22,752. What was the change in population to the nearest whole percentage point?
Since we are looking for the change, we must take the
(Ending Point – Starting Point)/Starting Point * 100%
(22752 – 12979)/12979 * 100%
9773/12979 * 100%
0.753 * 100%
75%
Since we are looking for the change, we must take the
(Ending Point – Starting Point)/Starting Point * 100%
(22752 – 12979)/12979 * 100%
9773/12979 * 100%
0.753 * 100%
75%
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Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?
Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?
Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.
Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.
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A factory produced 2500 units during the month of September. In order to increase production by 12% in the month of October, the factory hired more workers. How many units were produced in October?
A factory produced 2500 units during the month of September. In order to increase production by 12% in the month of October, the factory hired more workers. How many units were produced in October?
This is a percentage increase problem.
Easiest approach : 2500 x 1.12 = 2800
In this way you are adding 12% to the original.
Using the formula, find 12% of 2500
12/100 = x/2500,
30000 = 100x
300 = x
Now add that to the original to find the new production:
2500 + 300 = 2800
This is a percentage increase problem.
Easiest approach : 2500 x 1.12 = 2800
In this way you are adding 12% to the original.
Using the formula, find 12% of 2500
12/100 = x/2500,
30000 = 100x
300 = x
Now add that to the original to find the new production:
2500 + 300 = 2800
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Evaluate:
0.082
Evaluate:
0.082
0.08 * 0.08
First square 8:
8 * 8 = 64
Then move the decimal four places to the left:
0.0064
0.08 * 0.08
First square 8:
8 * 8 = 64
Then move the decimal four places to the left:
0.0064
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On average, professional poker player Ben wins 6 out of 10 games. If a win brings in $75, how many games should he play to cover his rent of $625?
On average, professional poker player Ben wins 6 out of 10 games. If a win brings in $75, how many games should he play to cover his rent of $625?
Put into an equation where x is the number of games, 0.6 * x * 75 = 625. X = 13.9, the answer is 14.
Put into an equation where x is the number of games, 0.6 * x * 75 = 625. X = 13.9, the answer is 14.
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An mp3 player costs $100 on day one. On day two, the shop owner decides to decrease the price by 10% of the day one price. However, on day three the owner changes her mind and raises the price by 10% of the day two price. What is the new price of the mp3 player?
An mp3 player costs $100 on day one. On day two, the shop owner decides to decrease the price by 10% of the day one price. However, on day three the owner changes her mind and raises the price by 10% of the day two price. What is the new price of the mp3 player?
10% of the day one price = 0.1(100) = $10.
Therefore the day two price = 100 - 10 = $90.
10% of the day two price = 0.1(90) = $9.
Therefore the day three price = 90 + 9 = $99.
10% of the day one price = 0.1(100) = $10.
Therefore the day two price = 100 - 10 = $90.
10% of the day two price = 0.1(90) = $9.
Therefore the day three price = 90 + 9 = $99.
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If the cost of 20 equally priced pencils cost $5.80, then at the same rate what is the greatest number of pencils you can purchase for $50?
If the cost of 20 equally priced pencils cost $5.80, then at the same rate what is the greatest number of pencils you can purchase for $50?
Remeber for this problem that you cannot spend more than $50. First find the price of each pencil by 5.80/20 = 29 cents. And then use this to do 50/0.29 = 172.41. So the greatest number of pencils you can purchase for $50 is 172 pencils.
Remeber for this problem that you cannot spend more than $50. First find the price of each pencil by 5.80/20 = 29 cents. And then use this to do 50/0.29 = 172.41. So the greatest number of pencils you can purchase for $50 is 172 pencils.
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A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
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Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
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If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
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A pair of shoes originally sells for $250. There is a sale, and the shoes are then sold for 20% off. The shoes are then marked down an additional 35%. If sales tax is 7%, what can you buy the pair of shoes for today, including tax?
A pair of shoes originally sells for $250. There is a sale, and the shoes are then sold for 20% off. The shoes are then marked down an additional 35%. If sales tax is 7%, what can you buy the pair of shoes for today, including tax?
The shoes are first marked down 20%.
20% of $250 = .2 x $250 = $50
Sales price = $250 - $50 = $200
The second markdown is 35%.
35% of $200 = .35 x $200 = $70
New price = $200 - $70 = $130
Calculate the sales tax:
7% of $130 = .07 x $130 = $9.10
Total price = $130 + $9.10 = $139.10
The shoes are first marked down 20%.
20% of $250 = .2 x $250 = $50
Sales price = $250 - $50 = $200
The second markdown is 35%.
35% of $200 = .35 x $200 = $70
New price = $200 - $70 = $130
Calculate the sales tax:
7% of $130 = .07 x $130 = $9.10
Total price = $130 + $9.10 = $139.10
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The price of a purse is reduced by 20%. It is then put on final sale with an additional 30% off. What is the total discount on the purse?
The price of a purse is reduced by 20%. It is then put on final sale with an additional 30% off. What is the total discount on the purse?
Let us assume that the original purse is $100. The price after the first reduction is $80. After the second reduction the price is now $56. The difference between 100 and 56 is 44, giving 44% off.
Let us assume that the original purse is $100. The price after the first reduction is $80. After the second reduction the price is now $56. The difference between 100 and 56 is 44, giving 44% off.
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When evaluating the expression
what is the third operation that should be performed?
When evaluating the expression
what is the third operation that should be performed?
The order of operations is:
Exponents
Multiplication and division (left to right)
Addition and subtraction (left to right)
The first operation to be performed is the exponent (the cubing). The next two operations to be performed are the multiplication and the division; since the division is first when read left to right, this is performed second, and the multiplication is performed third.
The order of operations is:
Exponents
Multiplication and division (left to right)
Addition and subtraction (left to right)
The first operation to be performed is the exponent (the cubing). The next two operations to be performed are the multiplication and the division; since the division is first when read left to right, this is performed second, and the multiplication is performed third.
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Julie goes shopping at Gap. There is a storewide sale of 30% off. She buys a sweater on clearance that gets an additional 50% off. If the sweater was originally $50, how much did she pay?
Julie goes shopping at Gap. There is a storewide sale of 30% off. She buys a sweater on clearance that gets an additional 50% off. If the sweater was originally $50, how much did she pay?
The original price was $50. First you take 30% off (50 * (100 - 30)/100 = $35). Then you take an additional 50% off the new price (35 * 50/100 = 17.50)
The original price was $50. First you take 30% off (50 * (100 - 30)/100 = $35). Then you take an additional 50% off the new price (35 * 50/100 = 17.50)
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Solve 6-(3+2)-4=
Solve 6-(3+2)-4=
The order of operations is PEMDAS: Parenthesis, exponents, division and multiplication (performed left to right), addition and subtraction (performed left to right). “Please Excuse My Dear Aunt Sally” is one way to remember the order. One key is that multiplication and division are equal and addition and subtraction are equal, so they are performed in order from left to right. Sowe get 6-5-4=-3
The order of operations is PEMDAS: Parenthesis, exponents, division and multiplication (performed left to right), addition and subtraction (performed left to right). “Please Excuse My Dear Aunt Sally” is one way to remember the order. One key is that multiplication and division are equal and addition and subtraction are equal, so they are performed in order from left to right. Sowe get 6-5-4=-3
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For all positive integers, let a ★b be defined by a ★b = a b 2. Which of the following is equal to 8★2?
For all positive integers, let a ★b be defined by a ★b = a b 2. Which of the following is equal to 8★2?
To solve this problem, we first evaluate 8★2 and then see which of the answer choices is equal to the resulting number. Using the definition of ★, we see that 8★2 = 8(22) = 8(4) = 32. The only answer choice that is equivalent to 32 is 2★4, which evaluates to 2(42) = 32.
(Tip: If we quickly scan the answer choices by squaring the number on the right of the symbol, we immediately see that 3★6 and 1★32 are too big to be 32, even before being multiplied by any of the integers on the left of the symbol.)
To solve this problem, we first evaluate 8★2 and then see which of the answer choices is equal to the resulting number. Using the definition of ★, we see that 8★2 = 8(22) = 8(4) = 32. The only answer choice that is equivalent to 32 is 2★4, which evaluates to 2(42) = 32.
(Tip: If we quickly scan the answer choices by squaring the number on the right of the symbol, we immediately see that 3★6 and 1★32 are too big to be 32, even before being multiplied by any of the integers on the left of the symbol.)
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Eight more than four is an unknown number less than a quarter of the same unknown number. What is the value of the unknown number?
Eight more than four is an unknown number less than a quarter of the same unknown number. What is the value of the unknown number?
Let x be the unknown number.
4 + 8 = 0.25x – x.
12 = –0.75x
x = 12/–0.75
x = –16
Let x be the unknown number.
4 + 8 = 0.25x – x.
12 = –0.75x
x = 12/–0.75
x = –16
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Let a * b be defined as the following:
a * b = b2 – a2 + ab
Find the value of 4 * (3 * (2 * 1)).
Let a * b be defined as the following:
a * b = b2 – a2 + ab
Find the value of 4 * (3 * (2 * 1)).
We are told that a * b = b2 – a2 + ab, and we need to calculate 4 * (3 * (2 * 1)).
We need to start at the innermost set of parantheses, which requires us to find 2 * 1.
2 * 1 = 12 – 22 + 2(1) = 1 – 4 + 2 = –1
We can replace 2 * 1 with negative one. Then our expression becomes.
4 * (3 * (–1))
Now, we must find 3 * (–1)
3 * (–1) = (–1)2 – 32 + (3)(–1) = 1 – 9 – 3 = –11
So we can replace 3 * (–1) with –11.
Lastly, we must find 4 * (–11)
4 * (–11) = (–11)2 –42 + 4(–11) = 121 – 16 – 44 = 61
The answer is 61.
We are told that a * b = b2 – a2 + ab, and we need to calculate 4 * (3 * (2 * 1)).
We need to start at the innermost set of parantheses, which requires us to find 2 * 1.
2 * 1 = 12 – 22 + 2(1) = 1 – 4 + 2 = –1
We can replace 2 * 1 with negative one. Then our expression becomes.
4 * (3 * (–1))
Now, we must find 3 * (–1)
3 * (–1) = (–1)2 – 32 + (3)(–1) = 1 – 9 – 3 = –11
So we can replace 3 * (–1) with –11.
Lastly, we must find 4 * (–11)
4 * (–11) = (–11)2 –42 + 4(–11) = 121 – 16 – 44 = 61
The answer is 61.
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