### All SAT Math Resources

## Example Questions

### Example Question #71 : Expressions

If *x* + *y* = 4, what is the value of *x* + *y* – 6?

**Possible Answers:**

6

4

2

–2

0

**Correct answer:**

–2

Substitute 4 for *x* + *y *in the expression given.

4 minus 6 equals –2.

### Example Question #71 : Expressions

If 6 less than the product of 9 and a number is equal to 48, what is the number?

**Possible Answers:**

6

4

5

3

**Correct answer:**

6

Write an equation for the written expression: 9x – 6 = 48. When we solve for x we get x = 6.

### Example Question #1 : Simplifying Expressions

If x y = (5x - 4y)/y , find the value of y if 6 y = 2.

**Possible Answers:**

4

10

2

5

**Correct answer:**

5

If we substitute 6 in for x in the given equation and set our answer to 2, we can solve for y algebraically. 30 minus 4y divided by y equals 2 **-->**2y =30 -4y **-->** 6y =30 **-->** y=5. We could also work from the answers and substitute each answer in and solve.

### Example Question #1 : Simplifying Expressions

Evaluate: (2x + 4)(x^{2} – 2x + 4)

**Possible Answers:**

4x^{2} + 16x + 16

2x^{3} – 8x^{2} + 16x + 16

2x^{3} + 16

2x^{3} – 4x^{2} + 8x

2x^{3} + 8x^{2} – 16x – 16

**Correct answer:**

2x^{3} + 16

Multiply each term of the first factor by each term of the second factor and then combine like terms.

(2x + 4)(x^{2} – 2x + 4) = 2x^{3} – 4x^{2} + 8x + 4x^{2} – 8x + 16 = 2x^{3} + 16

### Example Question #1 : Simplifying Expressions

Which of the following is equivalent to ?

**Possible Answers:**

ab^{5}c

abc

b^{5}/(ac)

a^{2}/(b^{5}c)

ab/c

**Correct answer:**

b^{5}/(ac)

First, we can use the property of exponents that x^{y}/x^{z} = x^{y–z}

Then we can use the property of exponents that states x^{–y} = 1/x^{y}

a^{–1}b^{5}c^{–1 }= b^{5}/ac

### Example Question #1 : How To Simplify An Expression

Solve for x: 2y/3b = 5x/7a

**Possible Answers:**

7ab/6y

6ab/7y

15b/14ay

14ay/15b

5by/3a

**Correct answer:**

14ay/15b

Cross multiply to get 14ay = 15bx, then divide by 15b to get x by itself.

### Example Question #1 : Simplifying Expressions

Three consecutive positive integers are added together. If the largest of the three numbers is *m*, find the sum of the three numbers in terms of *m*.

**Possible Answers:**

3*m*

3*m* + 3

3*m* + 6

3*m* – 6

3*m* – 3

**Correct answer:**

3*m* – 3

Three consecutive positive integers are added together. If the largest of the three numbers is *m*, find the sum of the three numbers in terms of *m*.

If *m* is the largest of three consecutive positive integers, then the integers must be:

*m* – 2, *m* – 1, and *m*, where *m* > 2.

The sum of these three numbers is:

*m* - 2 + *m* – 1 + *m* = 3*m* – 3

### Example Question #2 : How To Do Distance Problems

Sophie travels *f* miles in *g* hours. She must drive another 30 miles at the same rate. Find the total number of hours, in terms of *f* and *g*, that the trip will take.

**Possible Answers:**

*g* + *f* + 30

*g* + *f*

**Correct answer:**

Using d = rt, we know that first part of the trip can be represented by f = rg. The second part of the trip can be represented by 30 = rx, where x is some unknown number of hours. Note that the rate r is in both equations because Sophie is traveling at the same rate as mentioned in the problem.

Solve each equation for the time (g in equation 1, x in equation 2).

g = f/r

x = 30/r

The total time is the sum of these two times

Note that, from equation 1, r = f/g, so

=

### Example Question #1 : How To Simplify An Expression

If *a* + *b* = 10 and *b* + *c* = 15, then what is the value of (*c* – *a*)/(*a* + 2*b* +* c*)?

**Possible Answers:**

150

1/5

5

3/2

2/3

**Correct answer:**

1/5

Add the two equations:

*a* + *b* = 10

*b* + *c* = 15

------------

*a* + *b* + *b* + *c* = 10 + 15

*a* + 2*b* + *c* = 25 (this is the denominator of the answer)

Subtract the two equations:

*b* + *c* = 15

*a* + *b* = 10

------------

*b* + *c* – (*a* +* b*) = 15 – 10

*c* – *a* = 5 (this is the numerator of the answer)

5/25 = 1/5

### Example Question #1 : Simplifying Expressions

If a = 2b, 3b = c, and 2c = 3d, what is the value of d/a?

**Possible Answers:**

2/3

3

1

2

3/2

**Correct answer:**

1

Eq 1: a = 2b

Eq 2: 3b = c

Eq 3: 2c = 3d

Rewrite Eq. 3 substituting using Eq. 2.

2(3b) = 3d (because c = 3b)

6b = 3d (simplify)

2b = d (divide by 3)

Since a and d both equal 2b, a = d. Therefore, d/a = 1.

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