SAT Math Quiz
SAT Math Hard Practice Quiz
5. How many integers between 10 and 500 begin and end in
3?
Numbers and Operations
1. A bag contains tomatoes that are either green or red.
The ratio of green tomatoes to red tomatoes in the bag is 4 to 3. When five green tomatoes and five red tomatoes are removed, the ratio becomes 3 to 2. How many red tomatoes were originally in the bag?
(A)
(B)
(C)
(D)
(E)
6. A particular integer N is divisible by two different prime numbers p and q. Which of the following must be true?
12
15
18
24
30
I.
N is not a prime number.
II. N is divisible by pq.
III. N is an odd integer.
2. If each digit in an integer is greater than the digit to the left, the integer is said to be “monotonic”. For example, …show more content…
B
x
4
x
4
x
4
x
4
D
E
G
Now, use the third-side rule for triangles: The length of the third side of a triangle is less than the sum of the lengths of the other two sides and greater than the positive difference of the lengths of the other two sides.
When the rule is applied to EG as the third side, we get: 0 < EG < x/2. If y is the perimeter of the triangle, then y = x/4 + x/4 + EG = x/2 + EG. Solving for EG gives EG = y − x/2. Substituting into the inequality gives 0 < y − x/2 < x/2 so that x/2 < y < x, making answer C the correct one. To make this problem less abstract, it may help to make up a number for the perimeter of the square. (A good choice might be 4 so that x = 1. You’ll find 1/2 < y < 1, the same as answer
C when x = 1.)
12. 2 < x < 3
(Estimated Difficulty Level: 5)
In order to determine at what point two lines intersect, set the equations of the lines equal to one another. In this case, we have: 2x − 1 = x + c so that x = c + 1.
In other words, x = c + 1 is the x-coordinate of P , the point where the lines intersect. Now, if c is between 1 and 2, then c + 1 is between 2 and 3. Any value for the x-coordinate of P between 2 and 3 is correct.
pg.
5. How many integers between 10 and 500 begin and end in
3?
Numbers and Operations
1. A bag contains tomatoes that are either green or red.
The ratio of green tomatoes to red tomatoes in the bag is 4 to 3. When five green tomatoes and five red tomatoes are removed, the ratio becomes 3 to 2. How many red tomatoes were originally in the bag?
(A)
(B)
(C)
(D)
(E)
6. A particular integer N is divisible by two different prime numbers p and q. Which of the following must be true?
12
15
18
24
30
I.
N is not a prime number.
II. N is divisible by pq.
III. N is an odd integer.
2. If each digit in an integer is greater than the digit to the left, the integer is said to be “monotonic”. For example, …show more content…
B
x
4
x
4
x
4
x
4
D
E
G
Now, use the third-side rule for triangles: The length of the third side of a triangle is less than the sum of the lengths of the other two sides and greater than the positive difference of the lengths of the other two sides.
When the rule is applied to EG as the third side, we get: 0 < EG < x/2. If y is the perimeter of the triangle, then y = x/4 + x/4 + EG = x/2 + EG. Solving for EG gives EG = y − x/2. Substituting into the inequality gives 0 < y − x/2 < x/2 so that x/2 < y < x, making answer C the correct one. To make this problem less abstract, it may help to make up a number for the perimeter of the square. (A good choice might be 4 so that x = 1. You’ll find 1/2 < y < 1, the same as answer
C when x = 1.)
12. 2 < x < 3
(Estimated Difficulty Level: 5)
In order to determine at what point two lines intersect, set the equations of the lines equal to one another. In this case, we have: 2x − 1 = x + c so that x = c + 1.
In other words, x = c + 1 is the x-coordinate of P , the point where the lines intersect. Now, if c is between 1 and 2, then c + 1 is between 2 and 3. Any value for the x-coordinate of P between 2 and 3 is correct.
pg.