SAT Math Questions: Quiz! Trivia

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| By Vaibhav Agarwal
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Vaibhav Agarwal
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  • 1/24 Questions

    If (a-b)^2 = (a+b)^2, what is the value of ab?

    • -4
    • -2
    • 0
    • 2
    • 4
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About This Quiz

Challenge your math skills with this SAT Math Questions Quiz! Featuring diverse problems, test your understanding in algebra, geometry, and number theory.

SAT Math Questions: Quiz! Trivia - Quiz

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  • 2. 

    How many numbers less than 1000 are divisble by 3?

    • 300

    • 310

    • 311

    • 333

    • 500

    Correct Answer
    A. 333
    Explanation
    Every multiple of three is divisible by 3, so divide 1000 by 3 and take the whole part = 333.3333 = 333

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  • 3. 

    If a^b = c^d, which of the following is not necessarily true?

    • A^b - c^d = 0

    • A^b + c^d = 2 * (a^b)

    • (a^b)/(c^d) = 1

    • A = c

    • A^b * c^d = a^(2*b)

    Correct Answer
    A. A = c
    Explanation
    A, B, C, and E can be proven by substituting a^b for c^d. However, D is not always true. For example, 2^3 = 8^1, but 2 is not equal to 8.

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  • 4. 

    If a + b = y, what is a^2 + 2ab + b^2?

    • Y

    • 2y

    • Y^2

    • 2y^2

    • 4y^2

    Correct Answer
    A. Y^2
    Explanation
    a^2+2ab+b^2 = (a+b)^2 = y^2

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  • 5. 

    If 2 ^ (4x + 3) = 4 ^ (x - 1), what is x?

    • -3

    • -5/2

    • -1

    • 2

    • 4/3

    Correct Answer
    A. -5/2
    Explanation
    If a ^ b = a ^ c, then b = c. However, 2 does not equal 4, so we should make the two equal. 4 = 2 ^ 2, so 4 ^ (x - 1) = (2 ^ 2) ^ (x - 1) = 2 ^ 2(x-1) by exponent rules. So since 2 = 2, 4x + 3 = 2(x-1) -> 4x + 3 = 2x - 2 -> 2x = - 5 -> x = -5/2

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  • 6. 

    A square, X, has sides of length n. Another square, Y, has sides of length 1.5n. How many X can fit into a single Y?

    • 1

    • 1.5

    • 2

    • 2.25

    • 4

    Correct Answer
    A. 2.25
    Explanation
    The number of X's that fit into Y is equal to the ratio of area of Y to that of X. Area of Y = (1.5n)^2 = 2.25. The area of X = n^2. 2.25n^2/n^2 = 2.25

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  • 7. 

    A cubic box, X, has sides of length n. Another cubic box, Y, has sides of length 2n. How many boxes X could fit into a single box Y?

    • 2

    • 4

    • 8

    • 16

    • 32

    Correct Answer
    A. 8
    Explanation
    The volume of Y is equal to (2n)^3 = 8n^3. The volume of X is equal to n^3. So, to find the number of X's that could fit into Y, you should divide the volume of Y by that of X, or 8n^3/n^3, which is equal to 8.

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  • 8. 

    A triangle has sides of length 7, 11, and X. Which of the following cannot be X?

    • 2

    • 4

    • 8

    • 12

    • 18

    Correct Answer
    A. 2
    Explanation
    The sum of lengths of two sides of a triangle cannot be less than the length of the third side. So, 2 + 7 = 9, but 9 < 11

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  • 9. 

    Which of the following lines does not intersect y = 5 x + 2?

    • -5x + 2y = 4

    • -2x + 5y = -3

    • 10x - y = 1

    • 3x + y = 17

    • 5x - y = -29

    Correct Answer
    A. 5x - y = -29
    Explanation
    You are looking for a line whose slope is equal to the slope of the given line, or 5. Slope in standard form = -A/B, so E is the answer (-5/-1 = 5 = slope)

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  • 10. 

    If A $ B = A * B - ( A + B), what is 3 $ (2 $ 1)?

    • -5

    • -3

    • 0

    • 1

    • 4

    Correct Answer
    A. -5
    Explanation
    First, use the order of operations to find the parenthetical value of (2 $ 1), which is 2*1-3 or -1

    Next, plug in -1 for (2 $ 1) to find 3 $ -1 = 3 *-1 - (3 - 1) = -3 - 2 = -5

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  • 11. 

    In physics, force = mass * acceleration. Suppose you have an original force F and new force G in which the mass is increased by a factor of two and the acceleration is increased by a factor of four. What is the ratio of G:F?

    • 1:8

    • 1:4

    • 1:1

    • 4:1

    • 8:1

    Correct Answer
    A. 8:1
    Explanation
    F = ma, G = (2m)(4a) = 8ma; 8ma:ma simplifies to 8:1

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  • 12. 

    A regular polygon has 9 sides. What is the degree measure of the angle, within the polygon, between any two sides?

    • 60

    • 90

    • 120

    • 140

    • 165

    Correct Answer
    A. 140
    Explanation
    First, you must figure the sum of the measures of the internal angles, which is equal to (n-2)180 or (9-2)180 = 7 * 180. Then, you should divide this measure by the number of sides to find the length of each angle. (7 * 180)/9 = 7 * (180/9) = 7 * 20 = 140 degrees

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  • 13. 

    Six children sit at a circular table. In how many orders can they sit at the table?

    • 6

    • 18

    • 64

    • 118

    • 120

    Correct Answer
    A. 120
    Explanation
    At a circular (ring) table, the order ABCDEF = BCDEFA = CDEFAB, and so on. So, you need to find the total number of orders and divide this number by 6 to recognize the fact that the table is circular. The total number of orders is 6!, and 6!/6 = 5! = 5*4*3*2*1 = 120.

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  • 14. 

    Which of the following values of x is not in the domain of the function y = x / (x^2-2x+1)

    • -3

    • -2

    • -1

    • 0

    • 1

    Correct Answer
    A. 1
    Explanation
    Any time the denominator is equal to 0, that value of x is not included in the functional value. So, x / (x^2-2x+1) = x / (x-1)^2. (x-1)^2 = 0 only when x = 1.

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  • 15. 

    If a^2 = b^2, which of the following is/are always true? I. a = b II. |a| = |b| III. |a - b| = 0

    • I only

    • II only

    • I and II

    • I and III

    • I, II, and III

    Correct Answer
    A. II only
    Explanation
    If a^2 = b^2, then a = + or - b.

    So, I is not true because a could be = -b
    II is true because |-b| = |b|
    III is false because |b - (-b)| = |2b| = 2|b| is not equal to 0.

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  • 16. 

    A number is called "round" if it contains at least one zero as a digit. How many three-digit numbers are "round?"

    • 153

    • 171

    • 178

    • 179

    • 215

    Correct Answer
    A. 171
    Explanation
    An easy strategy here is to just count the number of "round" numbers between 100 and 199 and multiply that number by 9 for every hundreds digit (100, 200, 300... to 900). So, there are 19 "round" numbers through 100-199 (100, 101, 102 ... 109 = 10 + and 110, 120, 130... 190 = 9). 19 * 9 = 171

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  • 17. 

    If m & n = (m + n)^(m - n), what is 2 & (2 & 2)?

    • 2

    • 3

    • 4

    • 6

    • 8

    Correct Answer
    A. 3
    Explanation
    First, do what is in the ( )'s. (2 & 2) = (2 + 2) ^ ( 2 - 2) = 4^0 = 1.

    Next, plug in 1 for (2 & 2) to get 2 & 1 = (2 + 1)^(2 - 1) = 3^1 = 3.

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  • 18. 

    A three-digit number is called "big" if any two of its digits are equal. How many three-digit numbers are "big?"

    • 112

    • 146

    • 214

    • 252

    • 316

    Correct Answer
    A. 252
    Explanation
    Start with 100-199 and then multiply the result by 9 for each hundreds digit. 100, 101, 110, 111, 112, 113, ... 119, 121, 122, 131, 133, 141, 144, 151, 155... = 2 + 10 + 2(8) = 12 + 16 = 28. 28 * 9 = 252

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  • 19. 

    Which of the following statements is always true?

    • |(a+b)^2| < |a^2| + |b^2|

    • |a^2 + b^2| > (a+b)^2

    • |a^2 + b^2| >= |a+b|^2

    • |a^2 + b^2 - 1|

    • |a + b^2| > |a^2 - b|

    Correct Answer
    A. |a^2 + b^2 - 1|
    Explanation
    Since |X + Y| is always less than or equal to |X| + |Y|, substitute a^2 for X and b^2 for Y to find |a^2 + b^2| is less than or equal to |a^2| + |b^2|

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  • 20. 

    The number 100 has two trailing zeros. How many trailing zeros does 100! have?

    • 12

    • 15

    • 18

    • 24

    • 28

    Correct Answer
    A. 24
    Explanation
    Every trailing zero indicates a factor of 10 or 5 * 2. Since there are many more factors of 2 than 5's, you should count the number of factors of 5 there are in 100! Since it is one big product (100 * 99 * 98...), count: 5, 10, 15, 20, 25 (5 * 5), 30, 35, 40, 45, 50 (5*5), 55, 60, 65, 70, 75 (5*5), 80, 85, 90, 95, 100 (5*5). The total number of 5's is 24.

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  • 21. 

    If |a| < |b|, and a > b, which of the following is necessarily true?

    • |a + b| > |b| + |a|

    • |a + b| < a - b

    • |a| + |b| > 2|b|

    • |a - b| > a + b

    • None of the above

    Correct Answer
    A. None of the above
    Explanation
    None of the given options are necessarily true under the conditions that the absolute value of a is less than the absolute value of b, and a is greater than b. Each statement can be disproven with counterexamples. These conditions do not support the conclusions drawn in the statements about absolute values and arithmetic operations.

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  • 22. 

    If a two-sided coin is flipped three times, what is the probability that at least one head will show up?

    • 1/8

    • 3/8

    • 1/2

    • 2/3

    • 7/8

    Correct Answer
    A. 7/8
    Explanation
    The probability of one head showing up is equal to 1 - P(All tails), and the probability of all tails is (1/2)^3 = 1/8, so 1- 1/8 = 7/8

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  • 23. 

    How many ways can Pete, Mary, Sue, and Joe stand in a line if Joe and Sue cannot stand next to each other?

    • 4

    • 6

    • 12

    • 16

    • 18

    Correct Answer
    A. 12
    Explanation
    Step 1: Total Arrangements
    There are 4 people, so without any restrictions, they can be arranged in 4 factorial (4 x 3 x 2 x 1) ways, which equals 24 ways.
    Step 2: Arrangements Where Joe and Sue Are Together
    Treat Joe and Sue as one unit. This changes the problem to arranging 3 units: {Joe-Sue}, Pete, and Mary.
    These 3 units can be arranged in 3 factorial (3 x 2 x 1) ways, which equals 6 ways.
    Joe and Sue can switch places within their unit, and this can happen in 2 factorial (2 x 1) ways, which equals 2 ways.
    Therefore, Joe and Sue can be together in 6 x 2 = 12 ways.
    Step 3: Valid Arrangements (Joe and Sue Not Together)
    Subtract the number of ways Joe and Sue are together from the total arrangements: 24 (total ways) - 12 (Joe-Sue together) = 12 ways

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  • 24. 

    A rectangle's length is twice its width. If the perimeter of the rectangle is 30 meters, what is the area of the rectangle?

    • 20 square meters

    • 36 square meters

    • 40 square meters

    • 50 square meters

    Correct Answer
    A. 50 square meters
    Explanation
    First, let's define the width of the rectangle as w meters. According to the problem, the length (l) is twice the width, so we can express this as: l = 2w
    The formula for the perimeter (P) of a rectangle is given by: P = 2l + 2w Substituting the given perimeter and the expression for l, we get: 30 = 2(2w) + 2w 30 = 4w + 2w 30 = 6w w = 5 meters
    Now that we know the width, we can find the length: l = 2w = 2*5 = 10 meters
    The area (A) of the rectangle is calculated by multiplying the length and width: A = l * w = 10 * 5 = 50 square meters

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  • Current Version
  • Apr 15, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 09, 2007
    Quiz Created by
    Vaibhav Agarwal
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