Practice Test 4

NYC SHSAT Practice Test, Form A (2018) — Math section (questions 58–114). Problems are re-created in the same styles and difficulty, not copied verbatim. · Added Jun 6, 2026

Practice Test 4

The SHSAT runs about 90 seconds per question. This 24-question set ≈ 36 min — the timer counts up so you can track your pace.

Ratios & Proportional Relationships

A landscaper plants maple and birch trees in a ratio of 7 : 4. If she plants 161 maple trees, how many birch trees does she plant?

On a scale drawing of a triangular flag, two sides each measure 9 cm and the third side measures 12 cm. On the actual flag, the two equal sides each measure 24 feet. What is the length of the third side of the actual flag?

16 feet

28 feet

32 feet

36 feet

The sum of three numbers x, y, and z is 50. The ratio of x to y is 1 : 4, and the ratio of y to z is 4 : 5. What is the value of z?

Percents

In a town, 45% of the population is female and 60% of the population commutes to work. Exactly 21% of the total population are females who commute to work. What percent of the total population are males who do NOT commute to work?

15%

16%

24%

39%

A metal washer must have a thickness of 0.04 inch, with an allowable error of 1.5%. What is the greatest allowable thickness of the washer?

0.0406 inch

0.046 inch

0.0454 inch

0.06 inch

The table shows the percent distribution of how long 600 commuters spend traveling to work. How many of the 600 commuters spend at least 30 minutes commuting?

Commute time	Percent
Under 15 min	25%
15–29 min	40%
30–44 min	20%
45 min or more	15%

120

210

330

The Number System

An unmarked stick is laid end over end to measure a distance of exactly 72 feet. The same stick is used the same way to measure a distance of exactly 30 feet. What is the length of the longest possible stick that can measure both distances exactly?

3 feet

6 feet

9 feet

12 feet

How many positive even factors of 72 are greater than 8 and less than 36?

The fraction 10/13 written as a decimal is 0.769230769230…, repeating in a 6-digit block (769230). What is the 391st digit after the decimal point?

10.

In the set of consecutive integers from 12 to 30, inclusive, how many integers are multiples of neither 2 nor 3?

Expressions & Equations

11.

What is the value of the expression (−2)³ + 3 × (5 − 8)² − 12 ÷ 4 ?

12.

If 4x − 3y = 12, what is y in terms of x?

y = (4/3)x + 4

y = (4/3)x − 4

y = −(4/3)x + 4

y = −(4/3)x − 4

13.

The number line above shows a solution set. Which inequality does the graph represent?

−2 < x < 4

−2 ≤ x < 4

−2 ≤ x ≤ 4

−2 < x ≤ 4

Word Problems & Rates

14.

A car is traveling at 45 miles per hour, and 1 mile = 5,280 feet. Which of the following calculations gives the car’s speed in feet per second?

(45 × 5,280) ÷ 3,600

(45 × 3,600) ÷ 5,280

45 × 5,280 × 3,600

45 ÷ (5,280 × 3,600)

15.

Working at constant rates, Maria can fold 4 flyers in 12 minutes and Sam can fold 5 flyers in 10 minutes. Working together, how many flyers can they fold in one hour?

16.

Each week, Leon has fixed expenses of $1,250 at his furniture shop. It costs him $150 to make a chair, and he sells each chair for $275. What is Leon’s profit if he makes and sells 25 chairs in one week?

$1,875

$2,500

$3,125

$4,375

Geometry

17.

In parallelogram PQRS shown above, the measure of angle Q is 72°. What is the value of x, the measure of angle R?

108

118

128

18.

What is the area, in square units, of the shaded triangle shown on the coordinate grid above?

12.5

19.

The figure above shows a right pyramid with a square base measuring 8 centimeters on each side. The slant height of each triangular face is 6 centimeters. What is the total area of the four triangular faces (the surface area excluding the base)?

48 sq cm

96 sq cm

128 sq cm

192 sq cm

20.

On the number line above, the points J, K, L, and M lie in that order. JK = 3½, JM = 9¾, and LM = 1⅛. What is the distance KL? (The figure is not drawn to scale.)

5⅛

5¼

5½

6¼

Statistics & Probability

21.

The table shows the scores of 10 students on a quiz. What is the mean (average) score of the 10 students?

Score	Number of students
90	3
80	4
70	2
60	1

22.

A box contains 4 red marbles, 5 blue marbles, and 6 green marbles. Two marbles are drawn at random, one at a time without replacement. What is the probability that neither marble is blue?

3/7

2/7

9/35

4/9

23.

The same test was given to three sections of a class. The table shows the lowest score and the range of scores in each section. What is the overall range of all the scores in all three sections?

Section	Lowest score	Range
I	64	27
II	60	30
III	68	21

24.

The bar graph above shows the number of students in each after-school club. How many more students are in the two largest clubs combined than in the two smallest clubs combined?