SAT Math Questions: Quiz! Trivia

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

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

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.

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)

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

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.

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

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

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

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

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.

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.

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

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.

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

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

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

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.

Explanation
a^2+2ab+b^2 = (a+b)^2 = y^2

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.

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|

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

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.

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