SAT STRATEGY #4 - Replace Variables with Numbers – Pick a number

STRATEGY #4 - Replace Variables with Numbers – Pick a number

Many S.A.T. questions will ask you about a generic situation using variables. Your answer choices will not be numbers.

To make these problems easier:

• Replace each variable with an easy to use number

• Solve the problem using those numbers

• Evaluate each of the 4 choices to see which expression is equivalent to your specific answer

Choose easy to substitute variables.

1. Substitute. 2. Answer question. 3. Check answer choices

Multiple Choice

A boat cost x dollars, and this cost is to be shared equally by a group of people. In terms of x, how many dollars less will each person contribute if there are 4 people in the group instead of 3?

• $$\frac{x}{12}$$

• $$\frac{x}{4}$$

• $$\frac{x}{3}$$

• $$\frac{7x}{12}$$

Multiple Choice

In the figure, z = 50. What is the value of x+y?

• 130

• 180

• 210

• 230

Multiple Choice

For every positive 2-digit number, x, with tens digit t and units digit u, let y be the 2-digit number formed by reversing the digits of x. Which of the following expressions is equivalent to x-y?

• 9(t - u)

• 9(u - t)

• 9t - u

• 9u - t

Multiple Choice

For all numbers a and b, let ab be defined by a ⊙ b = ab + a + b. For all numbers x, y, and z, which of the following must be true?

I. $$x⊙y=y⊙x$$

II. $$(x-1)⊙(x+1)=(x⊙x)-1$$

III. $$x⊙\left(y+z\right)=\left(x⊙y\right)+\left(x⊙z\right)$$

• I only

• II only

• III only

• I and II only

Multiple Choice

1. Mixed Review Problem #1

2. Which of the following letters of the alphabet has at least 1 reflectional symmetry and at least 1 rotational symmetry? (Note: The angle of rotation for rotational symmetry must be less than 360 degrees)

• H

• M

• N

• S

Multiple Choice

2. Mixed Review Problem #2

3. A data set of integers has 5 members. The median of the data set is 6. The mode of the data set is 2. The mean of the data set is 5. Which of the following statements must be true about the data set?

• The sum of the 5 integers is 30.

• The sum of the 5 integers is 10.

• The largest integer is 9.

• The largest integer is 8.