# SAT Math Questions: Quiz! Trivia

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Vaibhav Agarwal
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Quizzes Created: 58 | Total Attempts: 610,003
Questions: 24 | Attempts: 34,334

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• 1.

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

• A.

-5

• B.

-3

• C.

0

• D.

1

• E.

4

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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• 2.

### How many numbers less than 1000 are divisble by 3?

• A.

300

• B.

310

• C.

311

• D.

333

• E.

500

D. 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.

A^b - c^d = 0

• B.

A^b + c^d = 2 * (a^b)

• C.

(a^b)/(c^d) = 1

• D.

A = c

• E.

A^b * c^d = a^(2*b)

D. 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.

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

• A.

-5x + 2y = 4

• B.

-2x + 5y = -3

• C.

10x - y = 1

• D.

3x + y = 17

• E.

5x - y = -29

E. 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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• 5.

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

• A.

60

• B.

90

• C.

120

• D.

140

• E.

165

D. 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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• 6.

### 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?

• A.

2

• B.

4

• C.

8

• D.

16

• E.

32

C. 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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• 7.

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

• A.

153

• B.

171

• C.

178

• D.

179

• E.

215

B. 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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• 8.

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

• A.

4

• B.

6

• C.

12

• D.

16

• E.

18

C. 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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• 9.

### 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?

• A.

1

• B.

1.5

• C.

2

• D.

2.25

• E.

4

D. 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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• 10.

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

• A.

2

• B.

4

• C.

8

• D.

12

• E.

18

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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• 11.

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

• A.

|a + b| > |b| + |a|

• B.

|a + b| < a - b

• C.

|a| + |b| > 2|b|

• D.

|a - b| > a + b

• E.

None of the above

E. 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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• 12.

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

• A.

6

• B.

18

• C.

64

• D.

118

• E.

120

E. 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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• 13.

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

• A.

1/8

• B.

3/8

• C.

1/2

• D.

2/3

• E.

7/8

E. 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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• 14.

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

• A.

2

• B.

3

• C.

4

• D.

6

• E.

8

B. 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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• 15.

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

• A.

20 square meters

• B.

36 square meters

• C.

40 square meters

• D.

50 square meters

D. 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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• 16.

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

• A.

112

• B.

146

• C.

214

• D.

252

• E.

316

D. 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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• 17.

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

• A.

-3

• B.

-5/2

• C.

-1

• D.

2

• E.

4/3

B. -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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• 18.

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

• A.

-3

• B.

-2

• C.

-1

• D.

0

• E.

1

E. 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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• 19.

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

• A.

Y

• B.

2y

• C.

Y^2

• D.

2y^2

• E.

4y^2

C. Y^2
Explanation
a^2+2ab+b^2 = (a+b)^2 = y^2

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• 20.

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

• A.

12

• B.

15

• C.

18

• D.

24

• E.

28

D. 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.

### Which of the following statements is always true?

• A.

|(a+b)^2| < |a^2| + |b^2|

• B.

|a^2 + b^2| > (a+b)^2

• C.

|a^2 + b^2| >= |a+b|^2

• D.

|a^2 + b^2 - 1|

• E.

|a + b^2| > |a^2 - b|

D. |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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• 22.

### 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?

• A.

1:8

• B.

1:4

• C.

1:1

• D.

4:1

• E.

8:1

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

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• 23.

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

• A.

I only

• B.

II only

• C.

I and II

• D.

I and III

• E.

I, II, and III

B. 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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• 24.

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

• A.

-4

• B.

-2

• C.

0

• D.

2

• E.

4

C. 0
Explanation
(a+b)^2 = (a-b)^2
a^2 + 2 ab + b^2 = a^2 - 2 ab + b^2
2 ab = -2 ab
4 ab = 0
ab = 0

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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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