Could You Pass This Toughest SAT Math Practice Questions Test? Trivia Quiz

1. If Pete can run five miles in one hour, how many hours would it take him to run 25 miles?

3

4

5

10

15

5 miles / 1 hr = 5 mph
25 miles / 5 mph / 5 miles.

Explanation

5 miles / 1 hr = 5 mph
25 miles / 5 mph / 5 miles.

2. 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?

4

8

12

16

20

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 = 12

Explanation

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 = 12

3. John is older than Maria. Maria is younger than Sue. Terry is the oldest of the four of them. Who is the youngest?

John

Maria

Sue

Terry

They are all the same age

J > M
M T > (J,M, and S)
So,
M Maria is the youngest.

Explanation

J > M
M T > (J,M, and S)
So,
M Maria is the youngest.

4. Solve for x: 2x + 3 = 4x - 3

0

1

3

5

7

2x + 3 = 4x - 3
3 = 2x - 3
6 = 2x
3 = x

Explanation

2x + 3 = 4x - 3
3 = 2x - 3
6 = 2x
3 = x

5. If x = y, which of the follow is necessarily true?

X^2 = y^2

|x| = y

|y| = x

X^2 = y

Y^2 = x

x = y. You can square both sides of an equation and retain equality, so

x^2 = y^2

Explanation

x = y. You can square both sides of an equation and retain equality, so

x^2 = y^2

6. Let f(x) = x^2 - 2x. What is the value of f(2)?

0

2

4

8

16

Substitute 2 for x in the original function:

2^2 - 2 * 2 = f(2)
4 - 4 = 0
f(2) = 0

Explanation

Substitute 2 for x in the original function:

2^2 - 2 * 2 = f(2)
4 - 4 = 0
f(2) = 0

7. A set of integers includes: 44, 66, 88, and x. If the mean of the scores is 80, what is x?

12

104

120

122

200

(44 + 66 + 88 + x)/4 = 80
44 + 66 + 88 + x = 320
x = 320-88-66-44
x = 122

Explanation

(44 + 66 + 88 + x)/4 = 80
44 + 66 + 88 + x = 320
x = 320-88-66-44
x = 122

8. What is the slope of the line given by 5x - 2y = 0?

2/5

5/2

1/5

5

0

Put it Slope intercept form, so:

5x - 2y = 0
2y = 5x
y = (5/2)x
y = mx + b
m = 5/2

Explanation

Put it Slope intercept form, so:

5x - 2y = 0
2y = 5x
y = (5/2)x
y = mx + b
m = 5/2

9. 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?

21

22

23

24

25

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.

Explanation

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.

10. (5 * 5 + 3) / 2 + 7 / 7 = ?

1

7

14

15

35

5 * 5 = 25 + 3 = 28
28/2 = 14
14 + 1 = 15

Explanation

5 * 5 = 25 + 3 = 28
28/2 = 14
14 + 1 = 15

11. If a block has dimensions of 3, 4, and 5 units, how many 2 by 2 by 3 blocks can fit in the block?

5

6

8

12

15

V(big block) = 3*4*5 = 60
V(small block) = 2*2*3 = 12

V(big)/V(small) = 5 small blocks.

Explanation

V(big block) = 3*4*5 = 60
V(small block) = 2*2*3 = 12

V(big)/V(small) = 5 small blocks.

12. If |x| = |y|, which of the following is necessarily true?

X = y

X = -y

X + y = 0

X - y = 0

|x| - |y| = 0

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.

Explanation

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.

13. 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?

50 mph

75 mph

100 mph

150 mph

200 mph

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.

Explanation

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.

14. If |x| = |y| and |x| = z, which of the following is always true?

Z = |x| + |y|

Z = |y|

|z| = |y|

Z = 0

Z < 0

Only choice B will always be true by the transitive property.

Since |x| = |y|, and |x| = z, |y| = z.

Explanation

Only choice B will always be true by the transitive property.

Since |x| = |y|, and |x| = z, |y| = z.

15. If |x| > |y|, and x < y, which of the following is always true?

Y is negative

X is positive

Y is positive

X is negative

X is zero

For |x| > |y| and x

Explanation

For |x| > |y| and x

16. How many ways can the letters in the word "WORD" be arranged?

16

20

24

28

32

The number of ways that four things can be arranged is 4! = 4*3*2*1 = 24.

Explanation

The number of ways that four things can be arranged is 4! = 4*3*2*1 = 24.

17. 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?

X*z

X^2*z

(2x^2)/z

(4z)/x

(4*z^2)/(3*x^2)

(x^2*y)/2z = 2x
x^2 * y = 4xz
y = (4z)/x

Explanation

(x^2*y)/2z = 2x
x^2 * y = 4xz
y = (4z)/x

18. 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?

3

4

5

6

7

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.

Explanation

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.

19. If a number is divisible by 2 but not divisible by 3, what can be concluded about the number?

It is a multiple of 6

It is a prime number

It is a multiple of 7

It will leave a remainder when divided by 6

It does not have a square root

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.

Explanation

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.

20. 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?

12

25

50

65

100

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.

Explanation

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.

21. 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?

2a+b = (1/3)*(a*b)^2

2a+2b = (1/3)a*b^2

2(a+b) = (1/3)a*b^2

2a+2b = (1/3)a^2*b^2

2a + b = a^2*b^2/3

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.

Explanation

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.

22. A fair coin is flipped three times. What is the chance that no head will appear?

1/8

1/4

1/3

1/2

0

The chance of no heads appearing is the same as the chance of all tails appearing, which is: (1/2)^3 or 1/8

Explanation

The chance of no heads appearing is the same as the chance of all tails appearing, which is: (1/2)^3 or 1/8

23. X $$ Y is defined as (X + Y)*(X - Y). Which of the following represents X^2 $$ Y^2

X^2 + 2XY + Y^2

X^4 - Y^4

(X-Y)^3

X^4 + 4X^3 + 2XY + Y^3

X^2 - Y^2

Since X $$ Y = X^2 - Y^2, X^2 $$ Y^2 = (X^2)^2 - (Y^2)^2 = X^4 - Y^4

Explanation

Since X $$ Y = X^2 - Y^2, X^2 $$ Y^2 = (X^2)^2 - (Y^2)^2 = X^4 - Y^4

24. Solve for x: 2^(x+4) = 4^(x-2)

0

1

4

6

8

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 = 8

Explanation

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 = 8

25. If the length of the sides of a cube is tripled, by what factor is the volume of the cube increased?

3

6

9

15

27

V = s^3
so V of the new cube = (3s)^3 = 3^3*s^3 = 27s^3

27s^3/s^3 = 27

Explanation

V = s^3
so V of the new cube = (3s)^3 = 3^3*s^3 = 27s^3

27s^3/s^3 = 27

26. 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?

F(x) - g(x) = h(x)

2*f(x) = 2*g(x) + 2*h(x)

F( f(x) ) = f ( g(x) ) + f( h(x) )

F(x) - g(x) - h(x) = 0

F(x)/2 = g(x)/2 + h(x)/2

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.

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.

27. If a @ b = 2(a + |b|), what is the value of 2 @ (-2 @ -1)?

-8

4

0

4

8

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 = 8

Explanation

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 = 8

28. If y = x^2 + 3, at how many points does y=0?

0

1

2

3

Infinitely many

Since x^2 is positive always, x^2 + 3 is always positive, so y will never be 0.

Explanation

Since x^2 is positive always, x^2 + 3 is always positive, so y will never be 0.

29. A six-sided dice is rolled twice. What is the chance that the sum of the two rolls will be exactly 10?

1/12

1/16

3/7

1/6

3/8

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.

Explanation

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.

30. If f(x - 3) = g(x + 3), what does f(x) equal?

3

G(3)

G(x)

G(x+3)

G(x+6)

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)

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)

31. 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?

|x| = |y|

Y = z

X = z

Z = x - y

Y = x - z

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 - 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 - y

32. What is the value of n! divided by (n-3)! ?

N! - 3!

N!3!

(3n)!

N*(n-1)*(n-2)

N*(n-1)*(n-2)*(n-3)

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)

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)

33. If n is an integer, q is a rational number, and r is an irrational number, which of the following statements is incorrect?

N + q is a rational number

N * r is an irrational number

N / r is an irrational number

R - q is a rational number

R / q is an irrational number

If a rational is subtracted from an irrational, the result is always an irrational. So, D is not true.

Explanation

If a rational is subtracted from an irrational, the result is always an irrational. So, D is not true.

34. Which of the following numbers is not a possibility value of the function f(x) = x^2 - 1

3

2

1

-1

-2

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

Explanation

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

35. Which of the following number is in the domain of f(x) = squareroot(x-2)/(x-7)

0

1

1.5

2

7

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.

Explanation

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.

36. 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?

1/12

1/6

1/3

2/9

4/9

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.

Explanation

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.

37. If x < |y|, which of the following is always true?

2x < y

2x > y

X = y

-y < x < y

X < y^2

By definition of absolute value x x x -y
-y

Explanation

By definition of absolute value x x x -y
-y

38. 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?

6

7

8

9

10

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.

Explanation

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.

39. John is 4 years older than Marie. In ten years, he will be twice as old as Marie. How old is Marie now?

6

8

10

12

14

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 = M

Explanation

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 = M

40. 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?

1

2

4

6

8

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 banana

Explanation

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 banana

41. How many ways can four students sit around a circular table?

2

4

6

8

24

The number of arrangements in a circle is given by (n-1)!, so (4-1)! = 3! = 3*2*1 = 6.

Explanation

The number of arrangements in a circle is given by (n-1)!, so (4-1)! = 3! = 3*2*1 = 6.

42. Which of the following will be equal to the 1 times the sign (positive or negative) of x?

|x|

X

X/x

|x|/x

|x|/|x|

The quotient |x|/x is equal to one times the sign of x.

Explanation

The quotient |x|/x is equal to one times the sign of x.

43. Which of the following is not a true statement?

Every even number is divisible by two

Every number divisible by two is an even number

Every number not divisible by two is not odd

Every number that is odd is not divisible by two

Every number not divisible by two is composite

3 is not divisible by 2, but 3 is neither even nor composite.

Explanation

3 is not divisible by 2, but 3 is neither even nor composite.