Practice Test 5

SAT Math No Calculator practice test #1 (EASY).

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Question 1
If x is 6 less than y and y is twice of z, what is the value of x when z = 2?

A
10
B
8
C
−2
D
12
Question 1 Explanation: 
The correct answer is (C).

Let's set up some equations to solve for $x$.
Translating from English to math, we get:

"x is 6 less than y" ⇒ $x = y - 6$

"y is twice of z" ⇒ $y = 2z$

Now plug in $z = 2$:

$y = 2z = 2(2) = 4$

$x = y - 6 = 4 - 6 = -2$

Therefore, $x$ is equal to $-2$.
Question 2
If $x + 3 = y$, then $2x + 6 = ?$

A
y
B
2y
C
3y
D
4y
Question 2 Explanation: 
The correct answer is (B).

We can rewrite $x + 3 = y$ as $x = y - 3$

Plugging this value of $x$ into the 2nd equation, we get:

$2(y - 3) + 6$

Simplifying: $2y - 6 + 6 = 2y$

Therefore, $2y$ is the answer.

Alternatively, notice that $2x+6$ is just $2*(x+3)$. Thus, it must be equal to $2*y = 2y$.
Question 3
$3(x - 4) = 18$, what is the value of $x$?

A
$\dfrac{14}{3}$
B
$\dfrac{22}{3}$
C
$6$
D
$10$
Question 3 Explanation: 
The correct answer is (D).

First, distribute:

$3(x - 4) = 18$

$3x - 12 = 18$

$3x = 30$

$x = 10$

Question 4
Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 3. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each person purchased?

A
3, 8, 24
B
7, 9, 17
C
9, 10, 13
D
6, 9, 12
Question 4 Explanation: 
The correct response is (C).

It’s easier for this type of question to use process of elimination. Since all of the answer choices have at least one single-digit number in it, let’s look at the second requirement. If the number of stamps that ONLY ONE of them purchased was divisible by 3, we can eliminate answer choices that contain more than one multiple of 3: (A) and (D).

The third requirement is that we have at least one even number. Between (B) and (C), only (C) satisfies this requirement.
Question 5
For their school uniform, each student can choose from 4 types of tops and 3 types of bottoms. How many combinations of tops and bottoms are there?

A
7
B
12
C
1
D
10
Question 5 Explanation: 
The correct answer is (B).

This is a simple probability question. For every top, there are 3 types of bottoms. We know that there are 4 types of tops.

Thus, there are $3 * 4 = 12$ combinations of tops and bottoms.
Question 6
sm1

The table above represents a relationship between and $x$ and $y$. Which of the following linear equations describes the relationship?

A
$y = x + 3$
B
$y = 3x - 1$
C
$y = 3x$
D
$y = 2x$
Question 6 Explanation: 
The correct answer is (B).

Test each answer choice with the values in the table. (B) is the only option that satisfies all the values of $x$ and $y$.
Question 7
If the average (arithmetic mean) of $2x$ and $4x$ is $18$, what is the value of $x$?

A
2
B
3
C
6
D
9
Question 7 Explanation: 
The correct answer is (C). Use the formula for average:

Average = $\dfrac{Sum~of~all~elements}{Number~of~elements}$

$= \dfrac{(2x + 4x)}{2} = 18$

$\dfrac{(6x)}{2} = 18$

$6x = 18 * 2$

$6x = 36$

$x = 6$
Question 8
In a certain coffee shop, $X$ lattes were sold each hour for 6 hours on Monday, and $Y$ americanos were sold each hour for 7 hours on Monday. What expression represents the total number of lattes and americanos that were sold by the coffee shop on Monday?

A
$13Y + 13X$
B
$13XY$
C
$6Y + 7X$
D
$6X + 7Y$
Question 8 Explanation: 
The correct answer is (D).

$(\dfrac{X}{hour} * 6~hours) + (\dfrac{Y}{hour} * 7~hours) = 6X + 7Y$

Notice that we multiplied the number of each drink by the number of hours that drink was sold, and then added the two totals together: $(6*X) + (7*Y).$

This matches the expression in answer choice (D).

Alternatively, this solution can be verified by testing values. Let’s say $X = 2$ and $Y = 3$. If 2 lattes were sold each hour for 6 hours, then $2 * 6 = 12$ lattes total were sold.

Similarly, if 3 americanos were sold each hour for 7 hours, then $3 * 7 = 21$ americanos were sold.

The total number of lattes and americanos would therefore be $12 + 21 = 33$. Plug in $X = 2$ and $Y = 3$ into the answer choices. The one that yields 33 is correct.
Question 9
If $\dfrac{6}{z+4} = p$, and $p = 12$, what is the value of $z $?

A
−1.5
B
−3.5
C
1.5
D
3.5
Question 9 Explanation: 
The correct answer is (B).

Start by substituting 12 for p in the original equation:

$\frac{6}{z + 4} = 12$

Because the unknown is in the denominator, and the equation represents a simple proportion, we can simplify the problem by cross multiplying and then dividing:

$6 = 12(z + 4)$

Divide both sides by 12:

$\frac{6}{12} = z + 4$

Simplify the fraction:

$\frac{1}{2} = z + 4$

Subtract 4:

$\frac{1}{2} - 4 = z$

$-3.5 = z$
Question 10
If a car averages 36.8 miles per gallon of gasoline, approximately how many kilometers per liter of gasoline does the car average if 1 gallon = 3.8 liters and 1 mile = 1.6 kilometers?

A
16 kpl
B
21 kpl
C
36 kpl
D
49 kpl
Question 10 Explanation: 
The correct answer is (A).

This problem is asking you to do two conversions: miles to kilometers, and gallons to liters. Both conversions can be done simultaneously to ensure correct dimensional analysis.

Set up the expression to yield the proper units:

$\dfrac{36.8~miles}{1~gallon} * \dfrac{1.6~km}{1~mile} * \dfrac{1~gallon}{3.8~L} = 15.49~km~per~liter$

$ ≈ 16~kpl$
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