SAT Math Questions: Quiz! Trivia
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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
Correct Answer
A. -5Explanation
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 = -5Rate this question:
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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
Correct Answer
D. 333Explanation
Every multiple of three is divisible by 3, so divide 1000 by 3 and take the whole part = 333.3333 = 333Rate this question:
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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)
Correct Answer
D. A = cExplanation
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.Rate this question:
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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
Correct Answer
E. 5x - y = -29Explanation
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)Rate this question:
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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
Correct Answer
D. 140Explanation
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 degreesRate this question:
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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
Correct Answer
C. 8Explanation
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.Rate this question:
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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
Correct Answer
B. 171Explanation
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 = 171Rate this question:
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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
Correct Answer
C. 12Explanation
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 waysRate this question:
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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
Correct Answer
D. 2.25Explanation
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 = 2.25Rate this question:
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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
Correct Answer
A. 2Explanation
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 < 11Rate this question:
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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
Correct Answer
E. None of the aboveExplanation
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.Rate this question:
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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
Correct Answer
E. 120Explanation
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.Rate this question:
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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
Correct Answer
E. 7/8Explanation
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 = 7/8Rate this question:
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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
Correct Answer
B. 3Explanation
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.Rate this question:
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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
Correct Answer
D. 50 square metersExplanation
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 metersRate this question:
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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
Correct Answer
D. 252Explanation
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 = 252Rate this question:
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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
Correct Answer
B. -5/2Explanation
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 = -5/2Rate this question:
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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
Correct Answer
E. 1Explanation
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.Rate this question:
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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
Correct Answer
C. Y^2Explanation
a^2+2ab+b^2 = (a+b)^2 = y^2Rate this question:
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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
Correct Answer
D. 24Explanation
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.Rate this question:
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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|
Correct Answer
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|Rate this question:
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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
Correct Answer
E. 8:1Explanation
F = ma, G = (2m)(4a) = 8ma; 8ma:ma simplifies to 8:1Rate this question:
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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
Correct Answer
B. II onlyExplanation
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.Rate this question:
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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
Correct Answer
C. 0Explanation
(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 = 0Rate this question:
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Apr 15, 2024Quiz Edited by
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Feb 09, 2007Quiz Created by
Vaibhav Agarwal
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