Practice Test 6

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 6

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 florist arranges roses and tulips in a ratio of 9 : 5. If she uses 117 roses, how many tulips does she use?

On a scale drawing of a triangular pennant, the two equal sides each measure 8 cm and the third side measures 14 cm. On the actual pennant, the two equal sides each measure 20 feet. What is the length of the third side of the actual pennant?

28 feet

30 feet

35 feet

40 feet

The sum of three numbers p, q, and r is 80. The ratio of p to q is 3 : 2, and the ratio of q to r is 2 : 5. What is the value of r?

Percents

In a company, 48% of the employees are women and 55% work remotely. Exactly 30% of the employees are women who work remotely. What percent of the employees are men who do NOT work remotely?

18%

25%

27%

30%

A metal spring must have a length of 0.08 inch, with an allowable error of 2.5%. What is the greatest allowable length of the spring?

0.082 inch

0.085 inch

0.10 inch

0.0825 inch

The table shows the percent distribution of how far 450 employees travel to work. How many of the 450 employees travel at least 10 miles to work?

Distance to work	Percent
Under 5 mi	40%
5–9 mi	30%
10–14 mi	20%
15 mi or more	10%

135

150

225

The Number System

An unmarked rod is laid end over end to measure a distance of exactly 90 feet. The same rod is used the same way to measure a distance of exactly 48 feet. What is the length of the longest possible rod that can measure both distances exactly?

3 feet

6 feet

9 feet

12 feet

How many positive even factors of 48 are greater than 2 and less than 24?

The fraction 6/7 written as a decimal is 0.857142857142…, repeating in a 6-digit block (857142). What is the 200th digit after the decimal point?

10.

In the set of consecutive integers from 15 to 35, inclusive, how many integers are multiples of neither 2 nor 3?

Expressions & Equations

11.

What is the value of the expression (−3)³ + 5 × (6 − 2)² − 28 ÷ 7 ?

12.

If 3x − 4y = 24, what is y in terms of x?

y = (3/4)x + 6

y = (3/4)x − 6

y = −(3/4)x + 6

y = −(3/4)x − 6

13.

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

−3 < x < 2

−3 ≤ x < 2

−3 ≤ x ≤ 2

−3 < x ≤ 2

Word Problems & Rates

14.

A snail moves at 9 inches per minute, and 1 foot = 12 inches. Which of the following calculations gives the snail’s speed in feet per hour?

(9 × 60) ÷ 12

(9 × 12) ÷ 60

9 × 60 × 12

9 ÷ (60 × 12)

15.

Working at constant rates, Carla can seal 6 envelopes in 12 minutes and Dan can seal 5 envelopes in 15 minutes. Working together, how many envelopes can they seal in one hour?

16.

Each week, Marcus has fixed expenses of $2,000 at his tailor shop. It costs him $40 to make a jacket, and he sells each jacket for $130. What is Marcus’s profit if he makes and sells 40 jackets in one week?

$1,600

$3,600

$5,200

$2,400

Geometry

17.

In parallelogram PQRS shown above, the measure of angle Q is 58°. What is the value of x, the measure of angle R?

112

122

132

18.

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

19.

The figure above shows a right pyramid with a square base measuring 12 centimeters on each side. The slant height of each triangular face is 5 centimeters. What is the total area of the four triangular faces (the surface area excluding the base)?

60 sq cm

120 sq cm

144 sq cm

240 sq cm

20.

On the number line above, the points W, X, Y, and Z lie in that order. WX = 2⅜, WZ = 9⅛, and YZ = 1¾. What is the distance XY? (The figure is not drawn to scale.)

4¾

5¼

5½

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
100	1
90	2
80	5
70	2

22.

A box contains 6 red marbles, 4 blue marbles, and 2 yellow marbles. Two marbles are drawn at random, one at a time without replacement. What is the probability that neither marble is blue?

14/33

2/3

7/12

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	70	22
II	66	30
III	72	18

24.

The bar graph above shows the number of pieces of each fruit sold at a stand. How many more pieces of the two best-selling fruits combined were sold than the two worst-selling fruits combined?