SSAT Practice Test 2026

About the SSAT exam

The Secondary School Admission Test (SSAT) is a school assessment examination administered in USA. It is designed to assess candidates' knowledge and proficiency across 4 key subject areas including Quantitative, Verbal, Reading Comprehension, Writing. This exam is widely recognized as an essential benchmark for students and professionals.

Use short SSAT practice sets to identify topics to revisit. Choose a subject and difficulty, answer questions, then review the explanations. New accounts get 30 question credits; further new questions use paid credits. Retaking previously seen questions is free.

Whether you're a first-time candidate or retaking the SSAT to improve your score, InfinityMock helps you identify your strengths and weaknesses through detailed performance analytics. Our platform covers Quantitative, Verbal, Reading Comprehension, Writing, with questions available at Easy, Medium, and Hard difficulty levels. Track your progress, review detailed explanations, and build the confidence you need to pass on exam day.

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8 free SSAT practice questions (2026)

Answer these first — no signup, no card. Every answer is explained. For more practice, sign up for 30 free question credits and choose a subject above.

1. If $n$ is an integer and $n^2$ divided by 7 leaves a remainder of 2, which of the following could be the remainder when $n$ is divided by 7?

   • 1
   • 3
   • 5
   • 6
   Show answer & explanation

   Answer: B. 3

   If $n \equiv r \pmod 7$, then $n^2 \equiv r^2 \pmod 7$. Testing the possible remainders $r \in \{0, 1, 2, 3, 4, 5, 6\}$, we find: $0^2 = 0$, $1^2 = 1$, $2^2 = 4$, $3^2 = 9 \equiv 2$, $4^2 = 16 \equiv 2$, $5^2 = 25 \equiv 4$, and $6^2 = 36 \equiv 1$. Thus, the remainder $r$ must be either 3 or 4. Of the options provided, only 3 is correct.

   Topic: Quantitative · hard

2. Pipe A can fill a pool in 6 hours, and Pipe B can fill it in 8 hours. Pipe C can empty the pool in 12 hours. If Pipe A and Pipe B are opened together for 2 hours, and then Pipe C is also opened, how many additional hours will it take to fill the pool completely?

   • 1.5 hours
   • 2 hours
   • 2.5 hours
   • 3 hours
   Show answer & explanation

   Answer: B. 2 hours

   The hourly rates of filling are: A = 1/6, B = 1/8, and C = -1/12. In 2 hours, A and B fill $2 \times (1/6 + 1/8) = 2 \times (7/24) = 14/24 = 7/12$ of the pool. The remaining volume to fill is $5/12$ of the pool. When all three pipes are open, the net rate is $1/6 + 1/8 - 1/12 = 4/24 + 3/24 - 2/24 = 5/24$ of the pool per hour. The additional time needed is $(5/12) / (5/24) = 2$ hours.

   Topic: Quantitative · hard

3. A circle is defined by the equation $x^2 + y^2 - 6x + 8y = 0$. What is the area of a square inscribed in this circle?

   • 25
   • 50
   • 100
   • 25π
   Show answer & explanation

   Answer: B. 50

   Completing the square of the circle equation: $(x-3)^2 - 9 + (y+4)^2 - 16 = 0 \implies (x-3)^2 + (y+4)^2 = 25$. This circle has center $(3, -4)$ and radius $R = 5$. The diameter of the circle is $10$, which is also the diagonal $d$ of the inscribed square. The area of an inscribed square is given by $d^2 / 2 = 10^2 / 2 = 50$.

   Topic: Quantitative · hard

4. In a school of 150 students, 85 take Spanish, 70 take French, and 50 take German. If 30 take both Spanish and French, 25 take both French and German, 20 take both Spanish and German, and 10 students take all three languages, how many students do not take any of these three languages?

   • 10
   • 15
   • 20
   • 25
   Show answer & explanation

   Answer: A. 10

   Using the principle of inclusion-exclusion: $N(S \cup F \cup G) = N(S) + N(F) + N(G) - N(S \cap F) - N(F \cap G) - N(S \cap G) + N(S \cap F \cap G) = 85 + 70 + 50 - 30 - 25 - 20 + 10 = 140$. The number of students who do not take any of these languages is $150 - 140 = 10$.

   Topic: Quantitative · hard

5. If $3^{x+y} = 81$ and $81^{x-y} = 3$, what is the value of $x^2 - y^2$?

   • 1/4
   • 1
   • 4
   • 16
   Show answer & explanation

   Answer: B. 1

   We can rewrite the equations as powers of 3: $3^{x+y} = 3^4 \implies x+y = 4$. Also, $(3^4)^{x-y} = 3^1 \implies 4(x-y) = 1 \implies x-y = 1/4$. Since $x^2 - y^2 = (x+y)(x-y)$, we have $x^2 - y^2 = 4 \times (1/4) = 1$.

   Topic: Quantitative · hard

6. In triangle ABC, a line parallel to BC intersects AB at D and AC at E. If the area of triangle ADE is 16 and the area of trapezoid DBCE is 32, what is the ratio of AD to AB?

   • 1/3
   • √2 / 2
   • √3 / 3
   • 1/2
   Show answer & explanation

   Answer: C. √3 / 3

   Since DE is parallel to BC, triangle ADE is similar to triangle ABC. The area of triangle ABC is Area(ADE) + Area(DBCE) = 16 + 32 = 48. The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding side lengths: Area(ADE)/Area(ABC) = $(AD/AB)^2 = 16/48 = 1/3$. Taking the square root gives $AD/AB = 1/\sqrt{3} = \sqrt{3}/3$.

   Topic: Quantitative · hard

7. How many positive integers less than 1,000 have the property that the sum of their digits is equal to 3?

   • 8
   • 9
   • 10
   • 12
   Show answer & explanation

   Answer: C. 10

   We check integers from 1 to 999. Case 1: Single-digit numbers (sum of digits is 3) -> 3 (1 number). Case 2: Two-digit numbers ($a+b = 3$, where $a \neq 0$) -> 12, 21, 30 (3 numbers). Case 3: Three-digit numbers ($a+b+c = 3$, where $a \neq 0$) -> 102, 111, 120, 201, 210, 300 (6 numbers). In total, there are $1 + 3 + 6 = 10$ such integers.

   Topic: Quantitative · hard

8. A bag contains 4 red marbles, 5 blue marbles, and 6 green marbles. If 3 marbles are drawn at random without replacement, what is the probability that all 3 marbles are of different colors?

   • 4/91
   • 12/91
   • 24/91
   • 36/91
   Show answer & explanation

   Answer: C. 24/91

   The total number of ways to choose 3 marbles from 15 is $\binom{15}{3} = \frac{15 \times 14 \times 13}{3 \times 2 \times 1} = 455$. The number of ways to choose exactly 1 marble of each color (1 red, 1 blue, 1 green) is $4 \times 5 \times 6 = 120$. Thus, the probability is $120 / 455 = 24 / 91$.

   Topic: Quantitative · hard

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SSAT Exam Subjects

Available practice subjects: Quantitative, Verbal, Reading Comprehension, Writing. Select a subject for focused preparation. Coverage is not a guarantee of the complete official syllabus.

📖 SSAT Study Guide

Read our comprehensive How to Pass the SSAT in 2026 — Complete Study Guide for expert preparation tips, study plans, and strategies.

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