Basic Operations - PSAT Math
Card 0 of 112
Suppose you know the values of the variables in the expression
and you wish to evaluate it.
Which operation do you execute last?
Suppose you know the values of the variables in the expression
and you wish to evaluate it.
Which operation do you execute last?
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In the absence of grouping symbols, the first operations that should be carried out are exponentiations, followed by multiplications and divisions, followed by additions and subtractions.
The additions and subtractions are carried out from left to right. Since the addition is the one to the right, it is performed last.
In the absence of grouping symbols, the first operations that should be carried out are exponentiations, followed by multiplications and divisions, followed by additions and subtractions.
The additions and subtractions are carried out from left to right. Since the addition is the one to the right, it is performed last.
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?
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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.
32,000-26,000=6,000
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.
32,000-26,000=6,000
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” ?
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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.
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?
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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.
What number replaces the circle in the following sequence?
What number replaces the circle in the following sequence?
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The sequence is formed by starting with 1 and adding successive powers of 5. The numbers are obtained as follows:
- the correct response.
The sequence is formed by starting with 1 and adding successive powers of 5. The numbers are obtained as follows:
Refer to the above graph. Francie, a sixth grader at Polk, scored a 372 on the math portion of the SCAT. Which of the following could have been her rank among the students?
Refer to the above graph. Francie, a sixth grader at Polk, scored a 372 on the math portion of the SCAT. Which of the following could have been her rank among the students?
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By scoring a 372, Francie was outcored by all of the students who finished in the 401-800 ranges, which add up to:
students.
She was outscored by at most an additional 17 students (the other 17 in the 301-400 range), for a total of at most
students.
Francie finished between 97th and 114th place, making 100th place the only possible choice.
By scoring a 372, Francie was outcored by all of the students who finished in the 401-800 ranges, which add up to:
She was outscored by at most an additional 17 students (the other 17 in the 301-400 range), for a total of at most
Francie finished between 97th and 114th place, making 100th place the only possible choice.
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?
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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.
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?
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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.
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?
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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.
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?
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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.
If y is an integer, and 3 is the remainder when 7y+2 is divided by 5, then which of the following is a possible value of y?
If y is an integer, and 3 is the remainder when 7y+2 is divided by 5, then which of the following is a possible value of y?
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For this problem, you need to use process of elimination.
When y=8rightarrow 7times 8+2=58
The remainder of $\frac{58}{5}$ is 3 (the answer is 11, remainder 3), so y=8 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 y=8rightarrow 7times 8+2=58
The remainder of $\frac{58}{5}$ is 3 (the answer is 11, remainder 3), so y=8 is a possible answer choice. If you try the other answers they won't work.
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?
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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.
F=ma in physics whereForce=masstimes acceleration.
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?
F=ma in physics whereForce=masstimes acceleration.
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?
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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.
What property of arithmetic is demonstrated here?
What property of arithmetic is demonstrated here?
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The symbols express the idea that if three numbers are multiplied, the same product results regardless of which numbers are multiplied first. This is the associative property of multiplication.
The symbols express the idea that if three numbers are multiplied, the same product results regardless of which numbers are multiplied first. This is the associative property of multiplication.
What property of arithmetic is demonstrated below?
What property of arithmetic is demonstrated below?
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The statements demonstrates that the product of a number and a sum can be found by multiplying the number by each of the addends and adding the products. This is the distributive property of multiplication over addition.
The statements demonstrates that the product of a number and a sum can be found by multiplying the number by each of the addends and adding the products. This is the distributive property of multiplication over addition.
Multiply in modulo 8:
Multiply in modulo 8:
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In modulo 8 arithmetic, a number is congruent to the remainder of its division by 8.
and
so
making the correct response.
In modulo 8 arithmetic, a number is congruent to the remainder of its division by 8.
and
so
making the correct response.
Suppose you know the values of the variables in the expression
and you wish to evaluate it.
Which operation do you execute last?
Suppose you know the values of the variables in the expression
and you wish to evaluate it.
Which operation do you execute last?
Tap to see back →
In the absence of grouping symbols, the first operations that should be carried out are exponentiations, followed by multiplications and divisions, followed by additions and subtractions.
The additions and subtractions are carried out from left to right. Since the addition is the one to the right, it is performed last.
In the absence of grouping symbols, the first operations that should be carried out are exponentiations, followed by multiplications and divisions, followed by additions and subtractions.
The additions and subtractions are carried out from left to right. Since the addition is the one to the right, it is performed last.
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” ?
Tap to see back →
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.
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?
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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.
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?
![]()
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?
Tap to see back →
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.
32,000-26,000=6,000
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.
32,000-26,000=6,000