Arithmetic - PSAT Math
Card 1 of 4032
What is the next number in the following series: 0, 3, 8, 15, 24 . . . ?
What is the next number in the following series: 0, 3, 8, 15, 24 . . . ?
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The series is defined by n2 – 1 starting at n = 1. The sixth number in the series then equal to 62 – 1 = 35.
The series is defined by n2 – 1 starting at n = 1. The sixth number in the series then equal to 62 – 1 = 35.
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A stove is regularly priced for $300. What is the difference one would pay when buying it at a 20% discount rather than a 10% discount, with an additional 10% discount off the sale price?
A stove is regularly priced for $300. What is the difference one would pay when buying it at a 20% discount rather than a 10% discount, with an additional 10% discount off the sale price?
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Buying the stove at a 20% discount would be $240. If one buys it at a sale of 10%, with another 10% off then the price would be $243, so the difference is $3
20% of 300 is 0.2 * 300 = 60 → 300 – 60 = 240
10% of 300 is 0.1 * 300 = 30 → 300 – 30 = 270
10% of 270 is 0.1 * 270 = 27 → 270 – 27 = 243
243 – 240 = 3
Buying the stove at a 20% discount would be $240. If one buys it at a sale of 10%, with another 10% off then the price would be $243, so the difference is $3
20% of 300 is 0.2 * 300 = 60 → 300 – 60 = 240
10% of 300 is 0.1 * 300 = 30 → 300 – 30 = 270
10% of 270 is 0.1 * 270 = 27 → 270 – 27 = 243
243 – 240 = 3
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Mark sells his car to Mike for 95% of the amount he originally paid. Mike then discounts the car 20% and sells it to Max. Max paid $300. How much did Mark buy his car for (rounded to the nearest dollar)?
Mark sells his car to Mike for 95% of the amount he originally paid. Mike then discounts the car 20% and sells it to Max. Max paid $300. How much did Mark buy his car for (rounded to the nearest dollar)?
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Apply your percentage knowledge. Starting value times percentage equals end value. $300/(1 – 0.2) = $375. $375/0.95 = $395.
Apply your percentage knowledge. Starting value times percentage equals end value. $300/(1 – 0.2) = $375. $375/0.95 = $395.
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Out of 85 students in a certain class, 42 own a laptop and 54 own an mp3 player. If 5 students don't own either, what fraction of the students own both a laptop and an mp3 player?
Out of 85 students in a certain class, 42 own a laptop and 54 own an mp3 player. If 5 students don't own either, what fraction of the students own both a laptop and an mp3 player?
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Once you subtract the 5 students that don't own either, there are 80 students left.
There's 96 total students when you add the number that own an mp3 and the number that own a laptop, meaning 16 own both.
Recall that the fraction will be number of students who have both laptop and mp3 divided by the total students in the class.
Once you subtract the 5 students that don't own either, there are 80 students left.
There's 96 total students when you add the number that own an mp3 and the number that own a laptop, meaning 16 own both.
Recall that the fraction will be number of students who have both laptop and mp3 divided by the total students in the class.
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If an airplane is flying 225mph about how long will it take the plane to go 600 miles?
If an airplane is flying 225mph about how long will it take the plane to go 600 miles?
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Speed = distance /time; So by solving for time we get time = distance /speed. So the equation for the answer is (600 miles)/ (225 miles/hr)= 2.67 hours; Remember to round up when the last digit of concern is 5 or more.
Speed = distance /time; So by solving for time we get time = distance /speed. So the equation for the answer is (600 miles)/ (225 miles/hr)= 2.67 hours; Remember to round up when the last digit of concern is 5 or more.
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Vikki is able to complete 4 SAT reading questions in 6 minutes. At this rate, how many questions can she answer in 3 1/2 hours?
Vikki is able to complete 4 SAT reading questions in 6 minutes. At this rate, how many questions can she answer in 3 1/2 hours?
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First, find how many minutes are in 3 1/2 hours: 3 * 60 + 30 = 210 minutes. Then divide 210 by 6 to find how many six-minute intervals are in 210 minutes: 210/6 = 35. Since Vikki can complete 4 questions every 6 minutes, and there are 35 six-minute intervals we can multiply 4 by 35 to determine the total number of questions that she can complete.
4 * 35 = 140 problems.
First, find how many minutes are in 3 1/2 hours: 3 * 60 + 30 = 210 minutes. Then divide 210 by 6 to find how many six-minute intervals are in 210 minutes: 210/6 = 35. Since Vikki can complete 4 questions every 6 minutes, and there are 35 six-minute intervals we can multiply 4 by 35 to determine the total number of questions that she can complete.
4 * 35 = 140 problems.
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The costs for Lizzie’s party are as follows: $6000 to cater, $1200 for the DJ, $2000 for decorating, and $2200 for the venue rental. Lizze can choose to apply a discount of 10% for the caterer and decorating but is then charged an additional 30% for the DJ and venue. What is the minimum price she will pay?
The costs for Lizzie’s party are as follows: $6000 to cater, $1200 for the DJ, $2000 for decorating, and $2200 for the venue rental. Lizze can choose to apply a discount of 10% for the caterer and decorating but is then charged an additional 30% for the DJ and venue. What is the minimum price she will pay?
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The discounts are not worth the extra cost. The answer is $11,400.
The discounts are not worth the extra cost. The answer is $11,400.
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Mr. Glatfelter trains hunting dogs for a price of $4000 per dog. If it costs him $15,000 per month to keep his business open and each dog costs $1000 to train, how many dogs per month must he train to make a profit?
Mr. Glatfelter trains hunting dogs for a price of $4000 per dog. If it costs him $15,000 per month to keep his business open and each dog costs $1000 to train, how many dogs per month must he train to make a profit?
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The answer is 6. 6 hunting dogs gives him a net profit of $3000. If you picked 5, that’s where Glatfelter breaks even (he doesn’t make a profit or a loss).
The answer is 6. 6 hunting dogs gives him a net profit of $3000. If you picked 5, that’s where Glatfelter breaks even (he doesn’t make a profit or a loss).
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A dress was originally priced at $70. In January, it was put on sale for 20% off. Then in February, the sale price was lowered an additional $10 off of January's price. How much is the dress currently being sold for?
A dress was originally priced at $70. In January, it was put on sale for 20% off. Then in February, the sale price was lowered an additional $10 off of January's price. How much is the dress currently being sold for?
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The dress started at $70. In January, it was marked down 20%. $70 * 0.2 = $14, so it was being sold for $70 – $14 = $56. Then we're told its price is again lowered, this time by $10. Now the price is $56 – $10 = $46.
The dress started at $70. In January, it was marked down 20%. $70 * 0.2 = $14, so it was being sold for $70 – $14 = $56. Then we're told its price is again lowered, this time by $10. Now the price is $56 – $10 = $46.
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The pie chart illustrates how Carla allocates her money each week.
If she spends $200 on groceries each week, how much does she spend on rent?
The pie chart illustrates how Carla allocates her money each week.
If she spends $200 on groceries each week, how much does she spend on rent?
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1. 20% of Carla's whole budget is equal to $200. With this information, one can find Carla's weekly budget.
Set up the equation: 0.2b = 200 (b = budget).
b = 200/0.2 = 1000 = Carla's weekly budget
2. To find the amount Carla spends for rent, one needs to find what 35% of $1000 is.
0.35 x 1000 = 350
3. Because Carla spends 35% of her total budget on rent, she spends $350 on rent.
1. 20% of Carla's whole budget is equal to $200. With this information, one can find Carla's weekly budget.
Set up the equation: 0.2b = 200 (b = budget).
b = 200/0.2 = 1000 = Carla's weekly budget
2. To find the amount Carla spends for rent, one needs to find what 35% of $1000 is.
0.35 x 1000 = 350
3. Because Carla spends 35% of her total budget on rent, she spends $350 on rent.
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Three salesmen, Gor, Levon, and Raffi, competed to sell the highest number of cars in the month of August. A total of 250 cars were sold.
Gor sold 100 cars. Levon sold 62% of the remaining cars, and Raffi sold the rest.
How many cars did Raffi sell?
Three salesmen, Gor, Levon, and Raffi, competed to sell the highest number of cars in the month of August. A total of 250 cars were sold.
Gor sold 100 cars. Levon sold 62% of the remaining cars, and Raffi sold the rest.
How many cars did Raffi sell?
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We first subtract the 100 cars that Gor sold from the total of 250 sold. We are left with 150 cars, and we know that Levon sold 62% of them. 100% – 62% = 38%. Hence, Raffi sold 38% of 150 cars. 150 * 0.38 = 57
We first subtract the 100 cars that Gor sold from the total of 250 sold. We are left with 150 cars, and we know that Levon sold 62% of them. 100% – 62% = 38%. Hence, Raffi sold 38% of 150 cars. 150 * 0.38 = 57
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The price of k kilograms of quartz is 50 dollars, and each kilogram makes s clocks. In terms of s and k, what is the price, in dollars, of the quartz required to make 1 clock?
The price of k kilograms of quartz is 50 dollars, and each kilogram makes s clocks. In terms of s and k, what is the price, in dollars, of the quartz required to make 1 clock?
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We want our result to have units of "dollars" in the numerator and units of "clocks" in the denominator. To do so, put the given information into conversion ratios that cause the units of "kilogram" to cancel out, as follows: (50 dollar/k kilogram)* (1 kilogram / s clock) = 50/(ks) dollar/clock.
Since the ratio has dollars in the numerator and clocks in the denominator, it represents the dollar price per clock.
We want our result to have units of "dollars" in the numerator and units of "clocks" in the denominator. To do so, put the given information into conversion ratios that cause the units of "kilogram" to cancel out, as follows: (50 dollar/k kilogram)* (1 kilogram / s clock) = 50/(ks) dollar/clock.
Since the ratio has dollars in the numerator and clocks in the denominator, it represents the dollar price per clock.
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Minnie can run 5000 feet in 15 minutes. At this rate of speed, how long will it take her to fun 8500 feet?
Minnie can run 5000 feet in 15 minutes. At this rate of speed, how long will it take her to fun 8500 feet?
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Find the rate of speed. 5000ft/15 min = 333.33 ft per min
Divide distance by speed to find the time needed
8500ft/333.33ft per min = 25.5
Find the rate of speed. 5000ft/15 min = 333.33 ft per min
Divide distance by speed to find the time needed
8500ft/333.33ft per min = 25.5
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If Kara drives a distance of m miles every h hours, how many hours will it take her to drive a distance of d miles, in terms of m, h, and d ?
If Kara drives a distance of m miles every h hours, how many hours will it take her to drive a distance of d miles, in terms of m, h, and d ?
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We need to convert d miles into hours. We do so by multiplying d miles by the conversion ratio of miles to hours given in the problem, (h hours / m miles), as follows:
d miles * (h hours / m miles) = (dh )/m hours.
From this conversion of miles into hours, we see that the number of hours it takes Kara to drive a distance of d miles is (dh )/m.
We need to convert d miles into hours. We do so by multiplying d miles by the conversion ratio of miles to hours given in the problem, (h hours / m miles), as follows:
d miles * (h hours / m miles) = (dh )/m hours.
From this conversion of miles into hours, we see that the number of hours it takes Kara to drive a distance of d miles is (dh )/m.
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Simplify the expression,
.
Simplify the expression,
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The numerator of the expression cannot be factored. Therefore, the denominator cannot divide into the numerator, and the expression is in its simplest form.
The numerator of the expression cannot be factored. Therefore, the denominator cannot divide into the numerator, and the expression is in its simplest form.
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Simplify:
Simplify:
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With this problem the first thing to do is cancel out variables. The x2 can all be divided by each other because they are present in each system. The equation will now look like this:
Now we can see that the equation can all be divided by y, leaving the answer to be:
With this problem the first thing to do is cancel out variables. The x2 can all be divided by each other because they are present in each system. The equation will now look like this:
Now we can see that the equation can all be divided by y, leaving the answer to be:
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Two two-digit numbers, 
and 
, sum to produce a three-digit number in which the second digit is equal to 
. The addition is represented below. (Note that the variables are used to represent individual digits; no multiplication is taking place).
What is 
?
Two two-digit numbers,
What is
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Another way to represent this question is:
In the one's column, 
and 
add to produce a number with a two in the one's place. In the ten's column, we can see that a one must carry in order to get a digit in the hundred's place. Together, we can combine these deductions to see that the sum of 
and 
must be twelve (a one in the ten's place and a two in the one's place).
In the one's column: 
The one carries to the ten's column.
In the ten's column: 
The three goes into the answer and the one carries to the hundred's place. The final answer is 132. From this, we can see that 
because 
.
Using this information, we can solve for 
.
You can check your answer by returning to the original addition and plugging in the values of 
and 
.
Another way to represent this question is:
In the one's column,
In the one's column:
The one carries to the ten's column.
In the ten's column:
The three goes into the answer and the one carries to the hundred's place. The final answer is 132. From this, we can see that
Using this information, we can solve for
You can check your answer by returning to the original addition and plugging in the values of
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Simplify:
Simplify:
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_x_2 – _y_2 can be also expressed as (x + y)(x – y).
Therefore, the fraction now can be re-written as (x + y)(x – y)/(x + y).
This simplifies to (x – y).
_x_2 – _y_2 can be also expressed as (x + y)(x – y).
Therefore, the fraction now can be re-written as (x + y)(x – y)/(x + y).
This simplifies to (x – y).
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Simplify the following expression:
Simplify the following expression:
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Following this equation, you divide 4 by 8 to get 1/2. When a variable is raised to an exponent, and you are dividing, you subtract the exponents, so 6 – 3 = 3.
Following this equation, you divide 4 by 8 to get 1/2. When a variable is raised to an exponent, and you are dividing, you subtract the exponents, so 6 – 3 = 3.
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Simplify the given fraction:
Simplify the given fraction:
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125 goes into 2000 evenly 16 times. 1/16 is the fraction in its simplest form.
125 goes into 2000 evenly 16 times. 1/16 is the fraction in its simplest form.
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