Could You Pass This Toughest SAT Math Practice Questions Test? Trivia Quiz
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SAT Math practice questions: This is an extensive, 50 SAT Math practice question quiz that is comprehensive over the subjects of algebraic manipulation, absolute value, inequalities, counting principles, logical reasoning, probability, and simple word problems. It is modelled on actual SAT Math section questions. So, let's try out the quiz. All the best!
- 1.
If (x^2 * y) / (2z) = 2x, what is y in terms of x and z if x, y, and z are non-zero real numbers?
- A.
X*z
- B.
X^2*z
- C.
(2x^2)/z
- D.
(4z)/x
- E.
(4*z^2)/(3*x^2)
Correct Answer
D. (4z)/xExplanation
(x^2*y)/2z = 2x
x^2 * y = 4xz
y = (4z)/xRate this question:
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- 2.
A number is given as 3513N, where N is a positive integer that fills in the units digit. Which of the following values of N would result in 3513N being a multiple of 9?
- A.
3
- B.
4
- C.
5
- D.
6
- E.
7
Correct Answer
D. 6Explanation
For a number to be a multiple of 9, the sum of its digits must be a multiple of 9. Since 3 + 5 + 1 + 3 = 12, N must be 6.Rate this question:
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- 3.
X $$ Y is defined as (X + Y)*(X - Y). Which of the following represents X^2 $$ Y^2
- A.
X^2 + 2XY + Y^2
- B.
X^4 - Y^4
- C.
(X-Y)^3
- D.
X^4 + 4X^3 + 2XY + Y^3
- E.
X^2 - Y^2
Correct Answer
B. X^4 - Y^4Explanation
Since X $$ Y = X^2 - Y^2, X^2 $$ Y^2 = (X^2)^2 - (Y^2)^2 = X^4 - Y^4Rate this question:
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- 4.
Which of the following number is in the domain of f(x) = squareroot(x-2)/(x-7)
- A.
0
- B.
1
- C.
1.5
- D.
2
- E.
7
Correct Answer
D. 2Explanation
Since the denominator is (x-7), x cannot be 7.
Also, since the numerator is a square root function, x-2 must necessarily be greater than or equal to 0, so x must be >= 2. Therefore, only 2 applies.Rate this question:
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- 5.
If |x| = |y|, which of the following is necessarily true?
- A.
X = y
- B.
X = -y
- C.
X + y = 0
- D.
X - y = 0
- E.
|x| - |y| = 0
Correct Answer
E. |x| - |y| = 0Explanation
Since |x| = |y|, x could be equal to y or -y. Therefore, choices A-D cannot apply because only one case can hold true to the equation.
Choice E, |x| - |y| = 0 is obvious because if |x| = |y|, it is like saying: |x| - |x| = 0, which is always true.Rate this question:
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- 6.
Let X be the number of prime numbers on [1,10]. Let Y be the number of composite numbers on [1,10]. What is X+Y?
- A.
6
- B.
7
- C.
8
- D.
9
- E.
10
Correct Answer
D. 9Explanation
Since [1,10] includes the numbers from 1 to 10, you must simply count all the primes and composites on 1 to 10; that is, you count all the numbers on 1 to 10 except for 1, because 1 is neither prime nor composite. Therefore, 10-1 = 9.Rate this question:
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- 7.
Solve for x: 2x + 3 = 4x - 3
- A.
0
- B.
1
- C.
3
- D.
5
- E.
7
Correct Answer
C. 3Explanation
2x + 3 = 4x - 3
3 = 2x - 3
6 = 2x
3 = xRate this question:
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- 8.
If a @ b = 2(a + |b|), what is the value of 2 @ (-2 @ -1)?
- A.
-8
- B.
4
- C.
0
- D.
4
- E.
8
Correct Answer
E. 8Explanation
First, find the value included in the parentheses first.
-2 @ -1 = 2(-2 + |-1|) = 2(-2 + 1) = 2(-1) = -2
Second, find the value of 2 @ (...)
2 @ -2 = 2(2 + |-2|) = 2(2 + 2) = 2*4 = 8Rate this question:
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- 9.
John is 4 years older than Marie. In ten years, he will be twice as old as Marie. How old is Marie now?
- A.
6
- B.
8
- C.
10
- D.
12
- E.
14
Correct Answer
A. 6Explanation
Set up a system of equations:
J + 4 = M
J + 10 = 2 * M
Substitute equation 1 for J in 2
(M - 4) + 10 = 2 * M
M + 6 = 2 * M
6 = MRate this question:
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- 10.
Let f(x) = x^2 - 2x. What is the value of f(2)?
- A.
0
- B.
2
- C.
4
- D.
8
- E.
16
Correct Answer
A. 0Explanation
Substitute 2 for x in the original function:
2^2 - 2 * 2 = f(2)
4 - 4 = 0
f(2) = 0Rate this question:
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- 11.
Which of the following is not a true statement?
- A.
Every even number is divisible by two
- B.
Every number divisible by two is an even number
- C.
Every number not divisible by two is not odd
- D.
Every number that is odd is not divisible by two
- E.
Every number not divisible by two is composite
Correct Answer
D. Every number that is odd is not divisible by twoExplanation
3 is not divisible by 2, but 3 is neither even nor composite.Rate this question:
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- 12.
If f(x - 3) = g(x + 3), what does f(x) equal?
- A.
3
- B.
G(3)
- C.
G(x)
- D.
G(x+3)
- E.
G(x+6)
Correct Answer
E. G(x+6)Explanation
Let x - 3 = u
Then x + 3 = u + 6 (x + 3 + 3)
f(u) = g(u+3) in general.
So f(x) = g(x+3+3) = g(x+6)Rate this question:
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- 13.
If |x| = |y| and |x| = z, which of the following is always true?
- A.
Z = |x| + |y|
- B.
Z = |y|
- C.
|z| = |y|
- D.
Z = 0
- E.
Z < 0
Correct Answer
B. Z = |y|Explanation
Only choice B will always be true by the transitive property.
Since |x| = |y|, and |x| = z, |y| = z.Rate this question:
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- 14.
If x/y = z^2 and y/(xz) = z, and x, y, and z are not equal to 0, which of the following must be true?
- A.
|x| = |y|
- B.
Y = z
- C.
X = z
- D.
Z = x - y
- E.
Y = x - z
Correct Answer
A. |x| = |y|Explanation
Equation 1: x/y = z^2
Equation 2: y/(xz) = z
x / y = z^2
y / x = z^2
So x / y = y / x
So the two have the same absolute value:
x^2 = y^2
x = + or - yRate this question:
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- 15.
(5 * 5 + 3) / 2 + 7 / 7 = ?
- A.
1
- B.
7
- C.
14
- D.
15
- E.
35
Correct Answer
D. 15Explanation
5 * 5 = 25 + 3 = 28
28/2 = 14
14 + 1 = 15Rate this question:
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- 16.
How many ways can four students sit around a circular table?
- A.
2
- B.
4
- C.
6
- D.
8
- E.
24
Correct Answer
C. 6Explanation
The number of arrangements in a circle is given by (n-1)!, so (4-1)! = 3! = 3*2*1 = 6.Rate this question:
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- 17.
Solve for x: 2^(x+4) = 4^(x-2)
- A.
0
- B.
1
- C.
4
- D.
6
- E.
8
Correct Answer
E. 8Explanation
First, we want the bases to be the same:
2^(x+4) = 2^2^(x-2) = 2^(2(x-2))
2^(x+4) = 2^(2x-4)
x + 4 = 2x - 4
4 = x - 4
x = 8Rate this question:
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- 18.
A set of integers includes: 44, 66, 88, and x. If the mean of the scores is 80, what is x?
- A.
12
- B.
104
- C.
120
- D.
122
- E.
200
Correct Answer
D. 122Explanation
(44 + 66 + 88 + x)/4 = 80
44 + 66 + 88 + x = 320
x = 320-88-66-44
x = 122Rate this question:
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- 19.
John is older than Maria. Maria is younger than Sue. Terry is the oldest of the four of them. Who is the youngest?
- A.
John
- B.
Maria
- C.
Sue
- D.
Terry
- E.
They are all the same age
Correct Answer
B. MariaExplanation
J > M
M < S
T > (J,M, and S)
So,
M < (J, S, T)
Maria is the youngest.Rate this question:
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- 20.
If y = x^2 + 3, at how many points does y=0?
- A.
0
- B.
1
- C.
2
- D.
3
- E.
Infinitely many
Correct Answer
A. 0Explanation
Since x^2 is positive always, x^2 + 3 is always positive, so y will never be 0.Rate this question:
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- 21.
If the length of the sides of a cube is tripled, by what factor is the volume of the cube increased?
- A.
3
- B.
6
- C.
9
- D.
15
- E.
27
Correct Answer
E. 27Explanation
V = s^3
so V of the new cube = (3s)^3 = 3^3*s^3 = 27s^3
27s^3/s^3 = 27Rate this question:
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- 22.
If x = y, which of the follow is necessarily true?
- A.
X^2 = y^2
- B.
|x| = y
- C.
|y| = x
- D.
X^2 = y
- E.
Y^2 = x
Correct Answer
A. X^2 = y^2Explanation
x = y. You can square both sides of an equation and retain equality, so
x^2 = y^2Rate this question:
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- 23.
If f(x) = g(x) + h(x), which of the following is not always true for all f, g, and h that are defined at x?
- A.
F(x) - g(x) = h(x)
- B.
2*f(x) = 2*g(x) + 2*h(x)
- C.
F( f(x) ) = f ( g(x) ) + f( h(x) )
- D.
F(x) - g(x) - h(x) = 0
- E.
F(x)/2 = g(x)/2 + h(x)/2
Correct Answer
C. F( f(x) ) = f ( g(x) ) + f( h(x) )Explanation
Although f,g,h are defined at x, f(f), f(g), and f(h) are not always defined at x. The answer is C.Rate this question:
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- 24.
Which of the following will be equal to the 1 times the sign (positive or negative) of x?
- A.
|x|
- B.
X
- C.
X/x
- D.
|x|/x
- E.
|x|/|x|
Correct Answer
D. |x|/xExplanation
The quotient |x|/x is equal to one times the sign of x.Rate this question:
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- 25.
A fair coin is flipped three times. What is the chance that no head will appear?
- A.
1/8
- B.
1/4
- C.
1/3
- D.
1/2
- E.
0
Correct Answer
A. 1/8Explanation
The chance of no heads appearing is the same as the chance of all tails appearing, which is: (1/2)^3 or 1/8Rate this question:
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- 26.
A train leaves the train station at 10:00 AM travelling 100 mph due west. Another train leaves another station along the track travelling the opposite direction. If the trains meet at 11:00 AM and travelled 100 miles, what is the speed of the other train?
- A.
50 mph
- B.
75 mph
- C.
100 mph
- D.
150 mph
- E.
200 mph
Correct Answer
C. 100 mpHExplanation
The total time is 1 hr. The trains meet in 1 hr and both travel 100 miles, so the speed of both is 100 mph.Rate this question:
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- 27.
If a block has dimensions of 3, 4, and 5 units, how many 2 by 2 by 3 blocks can fit in the block?
- A.
5
- B.
6
- C.
8
- D.
12
- E.
15
Correct Answer
A. 5Explanation
V(big block) = 3*4*5 = 60
V(small block) = 2*2*3 = 12
V(big)/V(small) = 5 small blocks.Rate this question:
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- 28.
If x < |y|, which of the following is always true?
- A.
2x < y
- B.
2x > y
- C.
X = y
- D.
-y < x < y
- E.
X < y^2
Correct Answer
D. -y < x < yExplanation
By definition of absolute value x < + or - y
x < y or x < - y
x < y or x > -y
-y < x < yRate this question:
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- 29.
A six-sided dice is rolled twice. What is the chance that the sum of the two rolls will be exactly 10?
- A.
1/12
- B.
1/16
- C.
3/7
- D.
1/6
- E.
3/8
Correct Answer
A. 1/12Explanation
10 = 5 + 5, 4 + 6, 6 + 4
The probability of any given combination is (1/6)^2 = 1/36
There are three combinations
3*1/36 = 3/36 = 1/12.Rate this question:
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- 30.
In a class election between Ricky, Susie, and Mikey, Ricky earns 20% of the vote and Mikey earns 30% of the vote. There are 24 members of the class. How many votes did Susie receive?
- A.
4
- B.
8
- C.
12
- D.
16
- E.
20
Correct Answer
C. 12Explanation
First, you will need to know Susie's percentage: 100% - 30% - 20% = 50%
Second, you should multiply that percentage by the total number of votes: 50% * 24 = .5 * 24 = 12Rate this question:
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- 31.
If n is an integer, q is a rational number, and r is an irrational number, which of the following statements is incorrect?
- A.
N + q is a rational number
- B.
N * r is an irrational number
- C.
N / r is an irrational number
- D.
R - q is a rational number
- E.
R / q is an irrational number
Correct Answer
D. R - q is a rational numberExplanation
If a rational is subtracted from an irrational, the result is always an irrational. So, D is not true.Rate this question:
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- 32.
What is the slope of the line given by 5x - 2y = 0?
- A.
2/5
- B.
5/2
- C.
1/5
- D.
5
- E.
0
Correct Answer
B. 5/2Explanation
Put it Slope intercept form, so:
5x - 2y = 0
2y = 5x
y = (5/2)x
y = mx + b
m = 5/2Rate this question:
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- 33.
The letters of the word: "alphabet" are placed into a hat and scrambled. What is the probability of choosing a vowel at random from the hat?
- A.
1/12
- B.
1/6
- C.
1/3
- D.
2/9
- E.
4/9
Correct Answer
C. 1/3Explanation
The vowels are: a,e,i,o, and u. "alphabet" has 2 a's and 1 e, or 3 vowels total out of 9 letters. 3/9 = 1/3.Rate this question:
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- 34.
If Mike can buy four apples for one pear and four pears for one peach, and if one peach is equal to eight bananas, how many bananas will Mike receive for one apple?
- A.
1
- B.
2
- C.
4
- D.
6
- E.
8
Correct Answer
A. 1Explanation
4 apples = 1 pear
4 pears = 1 peach
1 peach = 8 bananas
So,
1 apple = 1/4 pear
1/4 pear = 1/8 peach
1/8 peach = 1 banana.
So,
1 apple = 1 bananaRate this question:
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- 35.
If Pete can run five miles in one hour, how many hours would it take him to run 25 miles?
- A.
3
- B.
4
- C.
5
- D.
10
- E.
15
Correct Answer
C. 5Explanation
5 miles / 1 hr = 5 mph
25 miles / 5 mph / 5 miles.Rate this question:
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- 36.
Which of the following numbers is not a possibility value of the function f(x) = x^2 - 1
- A.
3
- B.
2
- C.
1
- D.
-1
- E.
-2
Correct Answer
E. -2Explanation
x^2 is always positive, so the minimum point of f is at f(x) = -1 or x = 0. So, f can never be less than -1, so E is not possible as -2 < -1Rate this question:
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- 37.
If a number is divisible by 2 but not divisible by 3, what can be concluded about the number?
- A.
It is a multiple of 6
- B.
It is a prime number
- C.
It is a multiple of 7
- D.
It will leave a remainder when divided by 6
- E.
It does not have a square root
Correct Answer
D. It will leave a remainder when divided by 6Explanation
A number that is only divisible by 2 and not 3 is not divisible by 6. Therefore, it leaves a remainder when divided by 6.Rate this question:
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- 38.
In football, a team earns 6 points for a touchdown and can earn 0, 1, or 2 extra points after each touchdown. Which of the following scores is not possible after earning three touchdowns?
- A.
21
- B.
22
- C.
23
- D.
24
- E.
25
Correct Answer
E. 25Explanation
A team can earn between 6 and 8 points per touchdown. So, after three, they could score between 18 points and 24 points. 25, however, is not possible.Rate this question:
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- 39.
A teacher tells her students that on a 100-question test, the answer to every third question is C and the answer to every fourth question is B. Based on this, how many questions can be answered using her suggestion?
- A.
12
- B.
25
- C.
50
- D.
65
- E.
100
Correct Answer
C. 50Explanation
Since every third and fourth question is covered, two out of every four questions are covered. That means 1/2 of 100 or 50 questions total are answerable with her suggestion.Rate this question:
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- 40.
Twice the sum of two different numbers is equal to one-third of the product of the squares of the numbers. Which of the following equations represent this statement?
- A.
2a+b = (1/3)*(a*b)^2
- B.
2a+2b = (1/3)a*b^2
- C.
2(a+b) = (1/3)a*b^2
- D.
2a+2b = (1/3)a^2*b^2
- E.
2a + b = a^2*b^2/3
Correct Answer
D. 2a+2b = (1/3)a^2*b^2Explanation
The sum of two different numbers is a + b
Twice that sum is 2(a+b) = 2a+2b
Product of the squares of two different numbers = a^2*b^2 = (ab)^2
One-third of the product = (1/3)(ab)^2
Only D works out.Rate this question:
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- 41.
If |x| > |y|, and x < y, which of the following is always true?
- A.
Y is negative
- B.
X is positive
- C.
Y is positive
- D.
X is negative
- E.
X is zero
Correct Answer
D. X is negativeExplanation
For |x| > |y| and x < y, the magnitude of x must be greater than y but x must be less than y. This can only occur where x is negative.Rate this question:
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- 42.
How many ways can the letters in the word "WORD" be arranged?
- A.
16
- B.
20
- C.
24
- D.
28
- E.
32
Correct Answer
C. 24Explanation
The number of ways that four things can be arranged is 4! = 4*3*2*1 = 24.Rate this question:
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- 43.
What is the value of n! divided by (n-3)! ?
- A.
N! - 3!
- B.
N!3!
- C.
(3n)!
- D.
N*(n-1)*(n-2)
- E.
N*(n-1)*(n-2)*(n-3)
Correct Answer
D. N*(n-1)*(n-2)Explanation
n! = n*(n-1)*(n-2)*(n-3)...
(n-3)! = (n-3)*(n-4)*(n-5)...
by division: n!/(n-3)! = n*(n-1)*(n-2)Rate this question:
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Mar 21, 2022Quiz Edited by
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Mar 01, 2007Quiz Created by
Vaibhav Agarwal