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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #2571 : Sat Mathematics

Edward is years old. He is 5 years younger than his sister Francine. In terms of , how old will Francine be in 2 years?

Possible Answers:

e+4

e-7

e-3

e+7

e+3

Correct answer:

e+7

Explanation:

Let f = Francine's age now.

e = f – 5

f = e + 5

In 2 years, Francine will be f + 2. Use our previous calculation to substitute.

f + 2 = (e + 5) + 2 = e + 7

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Example Question #2572 : Sat Mathematics

a # b = (a * b) + a

What is 3 # (4 # 1)?

Possible Answers:

Correct answer:

Explanation:

Work from the "inside" outward. Therefore, first solve 4 # 1 by replacing a with 4 and b with 1:

4 # 1 = (4 * 1) + 4 = 4 + 4 = 8

That means: 3 # (4 # 1) = 3 # 8. Solve this now:

3 # 8 = (3 * 8) + 3 = 24 + 3 = 27

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Example Question #2573 : Sat Mathematics

Simplify the result of the following steps, to be completed in order:

1. Add 7x to 3y

2. Multiply the sum by 4

3. Add x to the product

4. Subtract x – y from the sum

Possible Answers:

29x + 13y

28x – 13y

28x + 13y

28x + 11y

28x + 12y

Correct answer:

28x + 13y

Explanation:

Step 1: 7x + 3y

Step 2: 4 * (7x + 3y) = 28x + 12y

Step 3: 28x + 12y + x = 29x + 12y

Step 4: 29x + 12y – (x – y) = 29x + 12y – x + y = 28x + 13y

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Example Question #405 : Gre Quantitative Reasoning

Which is the greater quantity: the median of 5 positive sequential integers or the mean of 5 positive sequential integers?

Possible Answers:

The median is greater

The quantities are equal

The mean is greater

The relationship cannot be determined

Correct answer:

The quantities are equal

Explanation:

If the first integer is $\dpi{100} \small n$ , then $\dpi{100} \small n+(n+1)+(n+2)+(n+3)+(n+4)=5n+10$

$\dpi{100} \small \frac{5n+10}{5}=n+2$

This is the same as the median.

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Example Question #2574 : Sat Mathematics

You are told that $\dpi{100} \small x$ can be determined from the expression:

Capture7

Determine whether the absolute value of $\dpi{100} \small x$ is greater than or less than 2.

Possible Answers:

$\dpi{100} \small |x|>2$

The quantities are equal

$\dpi{100} \small |x|<2$

The relationship cannot be determined from the information given.

Correct answer:

$\dpi{100} \small |x|>2$

Explanation:

The expression is simplified as follows:

Capture8

Since $\dpi{100} \small 2^{4}=16$ the value of $\dpi{100} \small x$ must be slightly greater for it to be 17 when raised to the 4th power.

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Example Question #2575 : Sat Mathematics

Which best describes the relationship between (x+y)^3 and x^3+y^3 if $x,y\neq 0$ ?

Possible Answers:

$\small (x+y)^{3}>x^{3}+y^{3}$

$\small (x+y)^{3}=x^{3}+y^{3}$

(x+y)^3< x^3 + y^3

The relationship cannot be determined from the information given.

Correct answer:

The relationship cannot be determined from the information given.

Explanation:

Use substitution to determine the relationship.

For example, we could plug in x=2 and y=3 .

(x+y)^3=(2+3)^3=5^3=125

x^3+y^3=2^3+3^3=4+9=13

So far it looks like the first expression is greater, but it's a good idea to try other values of x and y to be sure. This time, we'll try some negative values, say, x=-4 and y=-3 .

(x+y)^3=(-4+-3)^3=-7^3=-343

x^3+y^3=-4^3+-3^3=-64+-27=-91

This time the first quantity is smaller. Therefore the relationship cannot be determined from the information given.

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Example Question #3 : How To Simplify An Expression

If x + y = 5 and 3x - y + z = 3 , then 12x + 3z = ?

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

We have three variables and only two equations, so we will not be able to solve for each independent variable. We need to think of another solution.

Notice what happens if we line up the two equations and add them together.

(x + y) + (3x – y + z) = 4x + z

and 5 + 3 = 8

Lets take this equation and multiply the whole thing by 3:

3(4x + z = 8)

Thus, 12x + 3z = 24.

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Example Question #38 : How To Simplify An Expression

$x^{2} = y$

m + 3 = x

3n = m

Express in terms of . You may assume to be positive.

Possible Answers:

$n = \frac{ \sqrt{y}+3}{3}$

$n = \frac{ \sqrt{y}-3}{3}$

$n = 3 \sqrt{y} + 9$

$n = 3 \sqrt{y} - 1$

$n = 3 \sqrt{y} - 9$

Correct answer:

$n = \frac{ \sqrt{y}-3}{3}$

Explanation:

3n = m

$3n \div 3 = m \div 3$

$n = \frac{m}{3}$

m + 3 = x

m + 3 - 3= x - 3

m = x-3

$x^{2} = y$

$x = \sqrt{y}$ - we throw out the other possible value, $x = -\sqrt{y}$ , since we assume positive.

By substituting:

$n = \frac{m}{3}$

$n = \frac{x-3}{3}$

$n = \frac{ \sqrt{y}-3}{3}$

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Example Question #2573 : Sat Mathematics

$x^{2} + 6x+ 9 = q$

$x^{2} - 4x + 4 = s$

Which of the following could be the relationship between and ?

Possible Answers:

$q = s + 5 \sqrt{s} + 13$

q = s + 5

$q = s + 10 \sqrt{s} + 25$

$q = s + 2 \sqrt{s} + 1$

q = s+1

Correct answer:

$q = s + 10 \sqrt{s} + 25$

Explanation:

In both expressions, the trinomial in can be seen to be a perfect square trinomial:

$q = x^{2} + 6x+ 9$

$q = x^{2} + 2 \cdot 3 \cdot x + 3^{2}$

$q = (x+3)^{2}$

Taking the square root of both sides of this latter equation:

$\pm \sqrt{q} = x+ 3$

and

$x = - 3 \pm \sqrt{q}$

and

$s = x^{2} - 4x + 4$

$s= x^{2} - 2 \cdot 2 \cdot x + 2^{2}$

$s= (x-2)^{2}$

Taking the square root of both sides of this latter equation:

$\pm \sqrt{s} = x-2$

and $x = 2 \pm \sqrt{s}$

By transitivity,

$- 3 \pm \sqrt{q} = 2 \pm \sqrt{s}$

$- 3 \pm \sqrt{q} + 3 = 2 \pm \sqrt{s} + 3$

$\pm \sqrt{q} = 5 \pm \sqrt{s}$

Square both sides:

$(\pm \sqrt{q} )^{2}=( 5 \pm \sqrt{s})^{2}$

$q= 25 \pm 10 \sqrt{s} + s^{2}$

so one of two things is possible:

$q= s^{2} + 10 \sqrt{s}+ 25$

$q= s^{2} - 10 \sqrt{s}+ 25$

This makes

$q= s^{2} + 10 \sqrt{s}+ 25$

the correct choice.

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Example Question #2574 : Sat Mathematics

$a^{2}+ b^{2}= 100$

4c= a

d = b - 5

Express in terms of . You may assume that a > 0 and b > 0 .

Possible Answers:

$c=\frac{ \sqrt{ d^{2}-10d + 125}}{4}$

$c=\frac{ \sqrt{- d^{2}-10d + 75}}{4}$

$c=\frac{ \sqrt{ d^{2}-10d -75}}{4}$

$c=\frac{ \sqrt{ d^{2}-10d + 75}}{4}$

$c=\frac{ \sqrt{- d^{2}-10d + 125}}{4}$

Correct answer:

$c=\frac{ \sqrt{- d^{2}-10d + 75}}{4}$

Explanation:

d = b - 5 , so

b = d+5

$a^{2}+ b^{2}= 100$ , so by substitution,

$a^{2}+ (d+5)^{2}= 100$

$a^{2} = 100 - (d+5)^{2}$

$a^{2}= 100 -( d^{2}+ 10d + 25)$

$a^{2}= 100 - d^{2}-10d -25$

$a^{2}= - d^{2}-10d + 75$

Since is presumed positive,

$a = \sqrt{- d^{2}-10d + 75}$

Since 4c = a ,

$c = \frac{a}{4}$

$=\frac{ \sqrt{- d^{2}-10d + 75}}{c}$

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #2571 : Sat Mathematics

Example Question #2572 : Sat Mathematics

Example Question #2573 : Sat Mathematics

Example Question #405 : Gre Quantitative Reasoning

Example Question #2574 : Sat Mathematics

Example Question #2575 : Sat Mathematics

Example Question #3 : How To Simplify An Expression

Example Question #38 : How To Simplify An Expression

Example Question #2573 : Sat Mathematics

Example Question #2574 : Sat Mathematics

All SAT Math Resources

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