Arithmetic - PSAT Math
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If Johnny buys two comic books, priced at $1.50 each, and a candy bar, priced at $0.75, he'll have three quarters and two dimes left over. How much money does he have right now?
If Johnny buys two comic books, priced at $1.50 each, and a candy bar, priced at $0.75, he'll have three quarters and two dimes left over. How much money does he have right now?
Add what he can purchase to what he has left over:
Two comic books and the candy bar: $1.50 + $1.0 + $0.75 = $3.75
Three quarters and two dimes: $0.75 + $0.20 = $0.95
Therefore his total amount of money is $3.75 + $0.95 = $4.70.
Add what he can purchase to what he has left over:
Two comic books and the candy bar: $1.50 + $1.0 + $0.75 = $3.75
Three quarters and two dimes: $0.75 + $0.20 = $0.95
Therefore his total amount of money is $3.75 + $0.95 = $4.70.
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.3 can be written as .30. Now we can add the two more easily:
__________
.3 can be written as .30. Now we can add the two more easily:
__________
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Above is the menu at a coffee shop.
Delia has a coupon that entitles her to a free butter croissant with the purchase of one large drink of any kind. The coupon says "limit one per coupon".
She decides to purchase two small espressos, two small cappucinos, and four butter croissants. Disregarding tax, how much will Delia spend?
Above is the menu at a coffee shop.
Delia has a coupon that entitles her to a free butter croissant with the purchase of one large drink of any kind. The coupon says "limit one per coupon".
She decides to purchase two small espressos, two small cappucinos, and four butter croissants. Disregarding tax, how much will Delia spend?
Delia will not use the coupon, since all four of her drinks are small. She will pay full price for:
Two small espressos: 
Two small cappucinos: 
Four butter croissants: 
The total price: 
Delia will not use the coupon, since all four of her drinks are small. She will pay full price for:
Two small espressos:
Two small cappucinos:
Four butter croissants:
The total price:
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Find the sum.
Find the sum.
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Find the sum.
Find the sum.
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If x represents an even integer, which of the following expressions represents an odd integer?
If x represents an even integer, which of the following expressions represents an odd integer?
Pick any even integer (2, 4, 6, etc.) to represent x. The only value that is odd is 3_x_ + 1. Any number multiplied by an even integer will be even. When an even number is added and subtracted to that product, the result will be even as well. 3_x_ + 1 is the only choice that adds an odd number to the product.
Pick any even integer (2, 4, 6, etc.) to represent x. The only value that is odd is 3_x_ + 1. Any number multiplied by an even integer will be even. When an even number is added and subtracted to that product, the result will be even as well. 3_x_ + 1 is the only choice that adds an odd number to the product.
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Jesse has a large movie collection containing X movies. 1/3 of his movies are action movies, 3/5 of the remainder are comedies, and the rest are historical movies. How many historical movies does Jesse own?
Jesse has a large movie collection containing X movies. 1/3 of his movies are action movies, 3/5 of the remainder are comedies, and the rest are historical movies. How many historical movies does Jesse own?
1/3 of the movies are action movies. 3/5 of 2/3 of the movies are comedies, or (3/5)*(2/3), or 6/15. Combining the comedies and the action movies (1/3 or 5/15), we get 11/15 of the movies being either action or comedy. Thus, 4/15 of the movies remain and all of them have to be historical.
1/3 of the movies are action movies. 3/5 of 2/3 of the movies are comedies, or (3/5)*(2/3), or 6/15. Combining the comedies and the action movies (1/3 or 5/15), we get 11/15 of the movies being either action or comedy. Thus, 4/15 of the movies remain and all of them have to be historical.
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If x = 1/3 and y = 1/2, find the value of 2_x_ + 3_y_.
If x = 1/3 and y = 1/2, find the value of 2_x_ + 3_y_.
Substitute the values of x and y into the given expression:
2(1/3) + 3(1/2)
= 2/3 + 3/2
= 4/6 + 9/6
= 13/6
Substitute the values of x and y into the given expression:
2(1/3) + 3(1/2)
= 2/3 + 3/2
= 4/6 + 9/6
= 13/6
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Solve 
.
Solve
Finding the common denominator yields 
. We can then evaluate leaving 
.
Finding the common denominator yields
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What is the solution, reduced to its simplest form, for 
?
What is the solution, reduced to its simplest form, for
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What is the sum of 
and 
?
What is the sum of
We can begin by eliminating the obviously wrong answers. We know that the sum of the two fractions will be more than 1, so the answer choices 
and 
are out. Now, let's add the two fractions:
Begin by converting 
to 
.
Now find the common denominator of 
and 
. The least common multiple of 5 and 6 is 30, so 30 is the common denominator. Now alter both fractions so that they use the common denominator:
Now we can easily add the two fractions together:
The answer is 
.
We can begin by eliminating the obviously wrong answers. We know that the sum of the two fractions will be more than 1, so the answer choices
Begin by converting
Now find the common denominator of
Now we can easily add the two fractions together:
The answer is
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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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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?
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.
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What number replaces the circle in the following sequence?
What number replaces the circle in the following sequence?
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:
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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?
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.
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a, b, c are integers.
abc < 0
ab > 0
bc > 0
Which of the following must be true?
a, b, c are integers.
abc < 0
ab > 0
bc > 0
Which of the following must be true?
Let's reductively consider what this data tells us.
Consider each group (a,b,c) as a group of signs.
From abc < 0, we know that the following are possible:
(–, +, +), (+, –, +), (+, +, –), (–, –, –)
From ab > 0, we know that we must eliminate (–, +, +) and (+, –, +)
From bc > 0, we know that we must eliminate (+, +, –)
Therefore, any of our answers must hold for (–, –, –)
This eliminates immediately a > 0, b > 0
Likewise, it eliminates a – b > 0 because we do not know the relative sizes of a and b. This could therefore be positive or negative.
Finally, ac is a product of negatives and is therefore positive. Hence ac < 0 does not hold.
We are left with a + b < 0, which is true, for two negatives added must be negative.
Let's reductively consider what this data tells us.
Consider each group (a,b,c) as a group of signs.
From abc < 0, we know that the following are possible:
(–, +, +), (+, –, +), (+, +, –), (–, –, –)
From ab > 0, we know that we must eliminate (–, +, +) and (+, –, +)
From bc > 0, we know that we must eliminate (+, +, –)
Therefore, any of our answers must hold for (–, –, –)
This eliminates immediately a > 0, b > 0
Likewise, it eliminates a – b > 0 because we do not know the relative sizes of a and b. This could therefore be positive or negative.
Finally, ac is a product of negatives and is therefore positive. Hence ac < 0 does not hold.
We are left with a + b < 0, which is true, for two negatives added must be negative.
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How many elements of the set 
are less than 
?
How many elements of the set
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set 
are less than this positive number.
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set
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The sum of three consecutive odd integers is 93. What is the largest of the integers?
The sum of three consecutive odd integers is 93. What is the largest of the integers?
Consecutive odd integers differ by 2. If the smallest integer is x, then
x + (x + 2) + (x + 4) = 93
3x + 6 = 93
3x = 87
x = 29
The three numbers are 29, 31, and 33, the largest of which is 33.
Consecutive odd integers differ by 2. If the smallest integer is x, then
x + (x + 2) + (x + 4) = 93
3x + 6 = 93
3x = 87
x = 29
The three numbers are 29, 31, and 33, the largest of which is 33.
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