Did you take the SSAT Middle Level Math Practice Test? If so, then it’s time to review your results to see where you went wrong and what areas you need to improve.

## SSAT Middle Level Mathematical Reasoning Practice Test Answers and Explanations

1- **Choice C is correct**

If \(\frac{5x}{3}=15\), then \(5x=45→x=9, \frac{3x}{2}=\frac{3×9}{2}=\frac{27}{2}=13.5\)

2- **Choice E is correct**

\(0.3×5=1.5\), all options provided are equal to 1.5 except option E. \(0.15×1=0.15\)

3- **Choice C is correct**

Sara has N books. Mary has 7 more books than Sara. Then, Mary has N\(+7\) books. If Mary gives Sara 3 books, Mary will have: N\(+7-3=\)N\(+4\)

4- **Choice A is correct**

If 25 percent of a number is 45, then the number is: \(25\%\) of \(x=45→0.25=45→x=\frac{45}{0.25}=180\), 15 percent of 180 is: \(15\%\) f \(180=\frac{15}{100}×180=27\)

5- **Choice D is correct**

\(x=45+95=140\)

6- **Choice B is correct**

The diagonal of the square is 8. Let x be the side.

Use Pythagorean Theorem: \(a^2 + b^2 = c^2\)

\(x^2 + x^2 = 82 ⇒ 2x^2 = 82 ⇒ 2x^2 = 64 ⇒x^2 = 32 ⇒x= \sqrt{32}\)

The area of the square is: \(\sqrt{32} × \sqrt{32} = 32\)

7- **Choice C is correct**

The sum of supplement angles is 180.

Let \(x\) be that angle. Therefore, \(x + 5x = 180 \)

\(6x = 180\), divide both sides by \(6: x = 30\)

8- **Choice D is correct**

Use the formula for Percent of Change, \(\frac{New Value-Old Value}{Old Value} × 100 \%\)

\(\frac{30-50}{50} × 100 \% = –40 \% \)(negative sign here means that the new price is less than old price)

9- **Choice D is correct**

\(\frac{1}{3}\) of 27 is 9. Let’s review the options provided:

A. \(0.2×9=1.8 \)

B. \(0.5×4=2 \)

C. \(0.8×7=5.6 \)

D. \(0.5×17=8.5 \)

E. \(0.5×24=12\)

10- **Choice D is correct**

Simplify and solve for \(x\) in the equation. \(3(x −1) = 2(x + 3) + 15 → 3x − 3 = 2x + 6 + 15 \)

\(3x − 3 = 2x + 21\), Subtract \(2x\) from both sides: \(3x – 3 – 2x = 21\), Add 3 to both sides: \(x = 24\)

11- **Choice A is correct**

If the score of Mia was 80, therefore the score of Ava is 40. Since, the score of Emma was half as that of Ava, therefore, the score of Emma is 20.

12- **Choice D is correct**

Let \(x\) be the number. Write the equation and solve for \(x\).

\(\frac{2}{5} ×20= \frac{1}{3} . x ⇒ \frac{2×20}{5}= \frac{1x}{3}\) , use cross multiplication to solve for \(x\).

\(3×40=x×5 ⇒120=5x ⇒ x=24\)

13- **Choice E is correct**

Let \(x\) be the number. Then: \(2x+4=24\)

Solve for \(x: 2x+4=24→2x=24-4=20→x=20÷2=10\)

14- **Choice C is correct**

The perimeter of the trapezoid is 38.

Therefore, the missing side (height) is \(= 38 – 12 – 9 – 7 = 10 \)

Area of the trapezoid: A \(= \frac{1}{2} h (b_1 + b_2) = \frac{1}{2} (10) (9 + 7) = 80\)

15- **Choice B is correct**

Let \(x\) be the number. Write the equation and solve for \(x. (15 – x) ÷ x = 4 \)

Multiply both sides by \(x. (15 – x) = 4x\), then add \(x\) both sides. \(15 = 5x,\)

now divide both sides by \(5. x = 3\)

16- **Choice A is correct**

Let \(x\) be one-kilogram orange cost, then:

\(5x+(3×3.2)=34.6→5x+9.6=34.6→5x=34.6-9.6→5x=25→x=\frac{25}{5}=$5\)

17- **Choice B is correct**

average \(= \frac{sum of terms}{number of terms}\)

The sum of the weight of all girls is: \(27 × 50 = 1,350\) kg

The sum of the weight of all boys is: \(23 × 65 = 1,495\) kg

The sum of the weight of all students is: \(1,350 + 1,495 = 2,845\) kg

Average\( = \frac{2845}{50} = 56.9\)

18- **Choice C is correct**

Solve for \(x\) in the equation.

\(5(x-3)=45→5x-15=45→5x=45+15=60→x=60÷5=12\)

19- **Choice C is correct**

Four years ago, Amy was five times as old as Mike. Mike is 12 years now. Therefore, 4 years ago Mike was 8 years. Four years ago, Amy was: A\(=5×8=40\) ,

Now Amy is 44 years old: \(40 + 4 = 44\)

20- **Choice C is correct**

The red box is \(30\%\) greater than the blue box. Let \(x\) be the capacity of the blue box. Then:

\(x+30\%\) of \(x=26→1.3x=26→x=\frac{26}{1.3}=20\)

## The Absolute Best Book** to Ace the SSAT Middle Level Math** Test

21- **Choice D is correct**

In a group of 5 books, the average number of pages is 55. Therefore, the sum of pages in all 5 books is \((5 × 55 =) 275\). Mary adds a book with 31 pages to the group. Then, the sum of pages in all 6 books is \((5 × 55 + 31) = 306\). The new average number of pages per book is: \(\frac{306}{6}=51\)

22- **Choice A is correct**

Choices A, C, D, and E are incorrect because \(60\%\) of each of the numbers is a non-whole number.

A. \(25 , 60\%\) of \(25 = 0.60×25=15\)

B. \(32 , 60\%\) of \(32=0.60×32=19.2 \)

C. \(38 , 60\%\) of\( 38=0.60×38=22.8 \)

D. \(41 , 60\% \)of\( 41=0.60×41=24.6 \)

E. \(48 , 60\%\) of \(48=0.60×48=28.8\)

23- **Choice A is correct**

\(\frac{1}{3}×36=\frac{36}{3}=12\)

24- **Choice B is correct**

Only option B is correct. \(\frac{5}{2}=2.5→2.5>1.8\)

25- **Choice C is correct**

One lite=1000 cm\(^3\)→ 8 liters=8,000 cm\(^3\)

\(8,000=20×8×\)h→h\(=\frac{8000}{160}=50\) cm

26- **Choice C is correct. **

Four people can paint 5 houses in 8 days. It means that for painting 10 houses in 8 days we need 8 people. To paint 10 houses in 4 days, 16 people are needed.

27- **Choice A is correct**

From the options provided, only A (\(\frac{1}{4}\)) is less than \(\frac{1}{3}\)

28- **Choice B is correct**

Amy earns $40.25 per hour now. $40.25 per hour is 15 percent more than her previous rate. Let \(x\) be her rate before her raise. Then: \(x+0.15x=40.25→1.15x=40.25→x=\frac{40.25}{1.15}=35\)

John earns $34.5 per hour now. $34.5 per hour is 15 percent more than his previous rate. Let \(x\) be John’s rate before his raise. Then: \(x+0.15x=34.5→1.15x=34.5→x=\frac{34.5}{1.15}=30 \)

Amy earned $5.00 more per hour than John before their raises.

29- **Choice D is correct**

\($12×9=$108 \), Petrol use: \(9×2=18\) liters, Petrol cost:

\(18×$1.5=$27\)

Money earned: \($108-$27=$81\)

30- **Choice B is correct**

The width of a rectangle is \(3x\) and its length is \(5x\). Therefore, the perimeter of the rectangle is \(16x\). Perimeter of a rectangle=2(width\(+\)length)\(=2(3x+5x)=2(8x)=16x \)

The perimeter of the rectangle is 64. Then: \(16x=64→x=4\)

31- **Choice B is correct. **

The length of the rectangle is 16. Then, its width is \(4. 16 ÷ 4 = 4\)

Perimeter of a rectangle\(=2×\)width\(+2×\)length\(=2×4+2×16=8+32=40\)

32- **Choice C is correct**

\(α=180^\circ-135^\circ=45^\circ \)

The sum of all angles in a triangle is 180 degrees. Then:

\(x+α+60=180^\circ→x=180^\circ-45^\circ-60^\circ=75^\circ\)

33- **Choice A is correct.**

If \(x∎y=2x-y+3\), Then: \(3∎8=2(3)-8+3=6-8+3=1\)

34- **Choice B is correct. **

\(N×(7-4)=15→N×3=15→N=5\)

35- **Choice D is correct. **

\(30=x×5→x=30÷5=6 \)

\(x\) equals to 6. Let’s review the options provided:

A. \(4x-4→24-4=20, 30\) is not divisible by 20.

B. \(3x+8→3×6+8=26, 30\) is not divisible by 26.

C. \(6x+4→36+4=40, 30\) is not divisible by 40.

D. \(x×5→6×5=30, 30\) is divisible by 30.

E. \(x-10→6-10=-4, 30\) is not divisible by\( -4\).

The answer is D.

36- **Choice B is correct**

0.70 equals 35M. Then: 35M\(=0.70\)→M\(=\frac{0.70}{35}=0.02\)

37- **Choice D is correct**

\(z=2x-4\), then, \(3z=3(2x-4)=6x-12, 3z+7=6x-12+7=6x-5\)

38- **Choice C is correct**

The area of the floor is: 60 cm \(×\) 80 cm \(=\) 4800 cm

The number is tiles needed \(= 4800 ÷ 400 = 12\)

39- **Choice E is correct**

\(\frac{1}{16}=0.0625→C=5\)

\(\frac{1}{25}=0.04→D=4→C×D=5×4=20\)

40- **Choice C is correct. **

\(3000-A+300=2100→3000-A=2100-300=1800→ -A=1800-3000=-1200 →A=1200\)

## Best *SSAT Middle Level* *Math *Prep Resource for 2021

*SSAT Middle Level*

41- **Choice C is correct**

\(𝑥\) is the number of all sales profit and \(1.5\%\) of it is: \(1.5\%×x=0.015x\)

Employee’s revenue: \(0.015x+8,000\)

42- **Choice A is correct**

Number of biology book: 40, total number of books; \(40+55+65=160 \)

the ratio of the number of biology books to the total number of books is: \(\frac{40}{160}=\frac{1}{4}\)

43- **Choice D is correct**

Use cross product to solve for \(x. \frac{x}{x+7}=\frac{3}{4}→4×x=3×(x+7)→4x=3x+21→ x=21\)

\(x-16=21-16=5\)

44- **Choice E is correct**

Let \(x\) be all expenses, then \(\frac{24}{100} x=$768 →x=\frac{100×$768}{24}=$3200 \)

He spent for his rent: \(\frac{26}{100}×$3200=$832\)

45- **Choice C is correct**

let \(x\) be the number of gallons of water the container holds when it is full.

Then; \(\frac{3}{7} x=1.5→x=\frac{7×1.5}{3}=3.5\)

46- **Choice B is correct**

\(\frac{34.3}{100}=0.343\)

47- **Choice C is correct**

The angles on a straight line add up to 180 degrees. Then:

\(x+20+y+x+2y=180\), Then, \(2x+3y=180-20→2(25)+3y=160 →3y=160-50=110→y=36.67\)

48- **Choice C is correct**

\(3×\)M\(-4=- 2→3×\)M\(=-2+4=2→\)M\(=\frac{2}{3}\)

49- **Choice D is correct. **

The ratio of lions to tigers is 7 to 4 at the zoo. Therefore, total number of lions and tigers must be divisible by \(11. 7+4=11 \)

From the numbers provided, only 44 is not divisible by 11.

50-**Choice B is correct**

If \(x\) is greater than 12, then \(\frac{1}{3}\) of \(x\) must be greater than: \(\frac{1}{3}×12=4\).