ACT Math Practice Test 1

The correct answer is (E).

$4x + 3x + 2(x + 5) = 28$

Begin by distributing the 2:

$4x + 3x + 2x + 10 = 28$

Combine like terms:

$9x + 10 = 28$

Subtract 10 from both sides:

$9x = 18$

Divide both sides by 9:

$x = 2$

Note that you can also work backwards and substitute each answer choice for $x$ to see which results in a true statement.

The correct answer is (B). Solve this problem by setting up a proportion. We are told the ratio of milk to juice is 13:$x$ and that there are 39 milk and 18 juice:

$\dfrac{13}{x} = \dfrac{39}{18}$

Cross multiply and solve for $x$:

$(13)(18) = (x)(39)$

$234 = 39x$

Divide both sides by 39:

$6 = x$

The correct answer is (E). The coordinate of T in the original triangle is $(4,1)$.

After the triangle is reflected across the $y$-axis (vertical axis), T’ will be located at $(-4,1)$.

The correct answer is (B). A prime number is a number with no factors other than 1 and itself. Therefore, we can solve this problem by listing the numbers between 20 and 40 and eliminating those which are clearly divisible by some other number.

We only really need to list the odd numbers in this range, since the even numbers are obviously divisible by 2 and therefore not prime. 21, 23, 25, 27, 29, 31, 33, 35, 37, 39

Numbers divisible by 3: 21, 27, 33, 39
Numbers divisible by 5: 25, 35

The remaining numbers are 23, 29, 31, and 37. A quick check will tell us that none of these numbers are divisible by anything other than themselves and 1.

Therefore, 4 of the numbers between 20 and 40 are prime (Choice B).

The correct answer is (D). Substitute the values for $a$ and $b$ into the expression:

$a^3b + 3b$

$(-1)^3(4) + 3(4)$

$(-1)(4) + 12$

$-4 + 12$

$= 8$

The correct answer is (E). The simplest approach is to make a list of the multiples of each of the three numbers, and then find the least multiple that appears in all three lists:

Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 4:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40

Multiples of 8:
8, 16, 24, 32, 40

The least common multiple is 24.

The correct answer is (D). From the chart we can see that Store X had 80 (thousand) in profits and Store Z had 100 (thousand) in profits. Combining these two, we arrive at 180 (thousand) in profits.

The correct answer is (B). In January, Store Y made \$30,000. In February it made \$90,000.

The profit increased by \$60,000 (\$90,000 − \$30,000).

The correct answer is (A). Problems involving similar triangles can be solved using equivalent proportions:

$\dfrac{x}{18} = \dfrac{8}{12}$

Cross multiply and solve:

$(x)(12) = (18)(8)$

$12x = 144$

$x = 12$

The correct answer is (A). The sum of the interior angles of a quadrilateral is 360°:

$84 + 96 + 2x + x = 360$

$180 + 3x = 360$

$3x = 180$

$x = 60$