Algebra - SAT Math

Card 0 of 9157

Question

If 2 ≤ |t+1|, which number can it not be?

Answer

Explanation: The values of each answer are A)3 B) 2, C) 1, D)4, E)5.

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Question

If z + 2x = 10 and 7z + 2x = 16, what is z?

Answer

Subtract the first expression from the second. That gives you 6z = 6. That simplifies to z = 1.

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Question

If 4_x_ + 5 = 13_x_ + 4 – x – 9, then x = ?

Answer

Start by combining like terms.

4_x_ + 5 = 13_x_ + 4 – x – 9

4_x_ + 5 = 12_x_ – 5

–8_x_ = –10

x = 5/4

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Question

If 3 – 3_x_ < 20, which of the following could not be a value of x?

Answer

First we solve for x.

Subtracting 3 from both sides gives us –3_x_ < 17.

Dividing by –3 gives us x > –17/3.

–6 is less than –17/3.

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Question

Solve for z:

3(z + 4)3 – 7 = 17

Answer

1. Add 7 to both sides

3(z + 4)3 – 7 + 7= 17 + 7

3(z + 4)3 = 24

2. Divide both sides by 3

(z + 4)3 = 8

3. Take the cube root of both sides

z + 4 = 2

4. Subtract 4 from both sides

z = –2

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Question

If 11 + 3_x_ is 29, what is 2_x_?

Answer

First, solve for x:

11 + 3_x_ = 29

29 – 11 = 3_x_

18 = 3_x_

x = 6

Then, solve for 2_x_:

2_x_ = 2 * 6 = 12

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Question

If 4_xs = v, v = ks , and sv ≠_ 0, which of the following is equal to k ?

Answer

This question gives two equalities and one inequality. The inequality (sv ≠ 0) simply says that neither s nor v is 0. The two equalities tell us that 4_xs and ks are both equal to v, which means that 4_xs_ and ks must be equal to each other--that is, 4_xs_ = ks. Dividing both sides by s gives 4_x_ = k, which is our solution.

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Question

If y = 4 and 6y = 10z + y, then z = ?

Answer

Substitute y in the equation for 4.

You now have 6 * 4 = 10z + 4

Simplify the equation: 24 = 10z + 4

Subtract 4 from both sides: 24 – 4 = 10z + 4 – 4

You now have 20 = 10z

Divde both sides by 10 to solve for z.

z = 2.

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Question

If 2_x_ = 3_y_ = 6_z_ = 48, what is the value of x * y * z?

Answer

Create 3 separate equations to solve for each variable separately.

2_x_ = 48

3_y_ = 48

6_z_ = 48

x = 24

y = 16

z = 8

x * y * z = 3072

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Question

A sequence of numbers is: 2, 5, 8, 11. Assuming it follows the same pattern, what would be the value of the 20th number?

Answer

This goes up at a constant number between values, making it an arthmetic sequence. The first number is 2, with a difference of 3. Plugging this into the arithmetic equation you get An = 2 + 3 (n – 1). Plugging in 20 for n, you get a value of 59.

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Question

Simplify x/2 – x/5

Answer

Simplifying this expression is similar to 1/2 – 1/5. The denominators are relatively prime (have no common factors) so the least common denominator (LCD) is 2 * 5 = 10. So the problem becomes 1/2 – 1/5 = 5/10 – 2/10 = 3/10.

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Question

If $\dpi{100} \small \frac{p}{6}$ is an integer, which of the following is a possible value of $\dpi{100} \small p$ ?

Answer

$\dpi{100} \small \frac{0}{6}=0$ , which is an integer (a number with no fraction or decimal part). All the other choices reduce to non-integers.

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Question

Simplify: $\frac{4x^{5}y^{3}z}{12x^{3}y^{6}z^{2}}$

Answer

$\frac{4x^{5}y^{3}z}{12x^{3}y^{6}z^{2}}=\frac{x^{2}}{3y^{3}z}$

First, let's simplify $\frac{4}{12}$ . The greatest common factor of 4 and 12 is 4. 4 divided by 4 is 1 and 12 divided by 4 is 3. Therefore $\frac{4}{12}=\frac{1}{3}$ .

To simply fractions with exponents, subtract the exponent in the numerator from the exponent in the denominator. That leaves us with $\frac{1}{3}x^{2}y^{-3}z^{-1}$ or $\frac{x^{2}}{3y^{3}z}$

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Question

Which of the following fractions is not equivalent to $\frac{6}{45}$ ?

Answer

Let us simplify $\frac{6}{45}$ :

$\frac{6}{45}=\frac{3\times 2}{3\times 15}=\frac{2}{15}$

We can get alternate forms of the same fraction by multiplying the denominator and the numerator by the same number:

$\frac{2\times 2}{15\times 2}=\frac{4}{30}$

$\frac{2\times 1.5}{15\times 1.5}=\frac{3}{22.5}$

Now let's look at $\frac{12}{89}$ :

$6 \times 2 = 12$ , but $45 \times 2 = 90$ .

Therefore, $\frac{12}{89}$ is the correct answer, as it is not equivalent to $\frac{6}{45}$ .

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Question

Which of the following is not equal to 32/24?

Answer

24/32 = 1.33

16/12 =1.33

224/168 =1.33

4/3 = 1.33

96/72 = 1.33

160/96 = 1.67

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Question

Find the root of

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}$

Answer

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}=\frac{(x-\sqrt3)(x+\sqrt5)}{x-\sqrt3}=x+\sqrt5$

The root occurs where . So we substitute 0 for .

$y=x+\sqrt{5}$

$0=x+\sqrt{5}$

This means that the root is at $x=-\sqrt5$ .

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Question

Simplify the fraction below:

$\frac{5}{125}$

Answer

The correct approach to solve this problem is to first write factors for the numerator and the denominator:

The highest common factor is 5. Therefore, you can divide the numerator and denominator by 5 in order to get a simplified fraction.

Thus the numerator becomes,

$\frac{5}{5}=1$ and the denominator becomes $\frac{125}{5}=25$ .

Therefore the final answer is $\frac{1}{25}$ .

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