SSAT Practice Test: 25 Quantitative (Math) Questions With Worked Answers

The SSAT math section at a glance (2026-27)

The Middle and Upper Level tests share one format and one timing. Math comes up twice, in Part 3 and again in Part 7. The writing sample is Part 1, before both math sections. Between the two math sections come reading in Part 4, a break, and verbal in Part 6. The whole test runs 3 hours and 10 minutes. The Elementary test runs 2 hours and 5 minutes and is on paper only. Its five-choice format comes from E3n's official Elementary study guides, which date from 2023.

For which Canadian schools ask for the SSAT, what it costs and how to register, see our guide to the SSAT and private school entrance exams in Canada.

What the math section actually tests

E3n, the non-profit that runs the SSAT, says the Middle and Upper Level math sections test the "Ability to solve problems involving arithmetic, elementary algebra, geometry, and other concepts". That sentence is vague, and E3n's own sample score reports are more useful. They split the 50 math questions into five reported topics, 10 questions each. The words in quotation marks below come from the sample Middle Level report. The sample Upper Level report uses the same five topics but describes them in different words:

Those are sample reports, so treat the even split as typical rather than guaranteed on every form. We split our 25 questions five ways to match them, which means a wrong answer points straight at a topic.

The SSAT is not a school test. The official Upper Level study guide says: "The SSAT is not an achievement test, although knowledge of a certain amount of mathematical content is necessary in order to do well on the quantitative sections of the test." No official source maps it to an Ontario grade, so a strong report card does not guarantee a strong math score, and the reverse is true too.

How to use this practice test

Set a timer for 30 minutes. Work on paper, with no calculator and no ruler, because both are on the SSAT's prohibited list. On the paper test your child can write in the blank space of the test book but gets no scrap paper, so practise with all the working on the same sheet as the questions.

Mark an answer, or leave the question blank. Blank matters here, because the real test treats a blank and a wrong answer differently. The scoring section after the answer key shows how.

All 25 questions were written for this article. None is copied from an official SSAT test, guide or practice book. Search for an SSAT practice test and the first page, checked on 19 October 2026, is test-prep companies, most of them selling courses, books or tutoring alongside their free practice. Several free pages keep the answers behind a download or a sign-in. Here the answers and the working are on the page.

Numbers and Operations: questions 1 to 5

Question 1. Which of these is greatest?

(A) 5/8 (B) 0.62 (C) 0.59 (D) 3/5 (E) 0.605

Question 2. What is 3/4 of 2/3 of 48?

(A) 16 (B) 18 (C) 24 (D) 32 (E) 36

Question 3. What is the smallest positive whole number that 4, 6 and 10 all divide into evenly?

(A) 24 (B) 30 (C) 40 (D) 240 (E) 60

Question 4. A jacket costs $80. The store takes 25% off, then takes a further 10% off the reduced price. What is the final price?

(A) $52 (B) $54 (C) $56 (D) $60 (E) $65

Question 5. What is 18 − 3 × (4 + 2) ÷ 9?

(A) 2 (B) 4 (C) 10 (D) 16 (E) 26

Algebra: questions 6 to 10

Question 6. If 3x − 7 = 11, what is x?

(A) 4/3 (B) 4 (C) 6 (D) 12 (E) 18

Question 7. The ratio of boys to girls in a class is 3 to 5. There are 32 students in the class. How many are girls?

(A) 12 (B) 15 (C) 18 (D) 20 (E) 24

Question 8. If 2(a + 3) = a + 10, what is a?

(A) 4 (B) 2 (C) 7 (D) 8 (E) 16

Question 9. Which value of x makes 5 − 2x < −3 true?

(A) 0 (B) 2 (C) 3 (D) 4 (E) 5

Question 10. The price of a book rose from $40 to $50. By what percent did it increase?

(A) 10% (B) 20% (C) 25% (D) 50% (E) 125%

Geometry and Measurement: questions 11 to 15

Question 11. A rectangle has a perimeter of 36 cm and a length of 12 cm. What is its area?

(A) 48 cm² (B) 72 cm² (C) 60 cm² (D) 144 cm² (E) 216 cm²

Question 12. Two angles of a triangle measure 47° and 68°. What is the third angle?

(A) 65° (B) 55° (C) 75° (D) 85° (E) 115°

Question 13. A cube has a volume of 64 cm³. What is its total surface area?

(A) 16 cm² (B) 64 cm² (C) 80 cm² (D) 96 cm² (E) 384 cm²

Question 14. A circle has a diameter of 10. What is its area?

(A) 5π (B) 10π (C) 20π (D) 100π (E) 25π

Question 15. A fish tank is 50 cm long, 40 cm wide and 30 cm high. How many litres of water does it hold when full?

(A) 0.6 (B) 6 (C) 60 (D) 600 (E) 6,000

Data Analysis: questions 16 to 20

Question 16. The mean of five test scores is 82. Four of the scores are 78, 85, 80 and 90. What is the fifth score?

(A) 75 (B) 79 (C) 82 (D) 84 (E) 77

Question 17. What is the median of 7, 3, 9, 3, 12 and 5?

(A) 3 (B) 6 (C) 5 (D) 6.5 (E) 7

Question 18. A bag holds 4 red, 5 blue and 3 green marbles. One marble is picked without looking. What is the probability that it is not blue?

(A) 5/12 (B) 1/2 (C) 7/12 (D) 2/3 (E) 3/4

Question 19. A student has 3 shirts, 4 pairs of pants and 2 pairs of shoes. An outfit is one shirt, one pair of pants and one pair of shoes. How many different outfits can the student make?

(A) 9 (B) 12 (C) 18 (D) 24 (E) 36

Question 20. A bakery sold these numbers of muffins over four days.

What percent of the four-day total was sold on Tuesday?

(A) 15% (B) 25% (C) 30% (D) 35% (E) 40%

Reasoning: questions 21 to 25

Question 21. If n is an odd whole number, which of these must be even?

(A) n + 3 (B) n + 2 (C) 3n (D) n² (E) 2n + 1

Question 22. In the pattern 2, 6, 18, 54, ..., each term is found the same way from the one before. What is the 6th term?

(A) 162 (B) 324 (C) 486 (D) 972 (E) 1,458

Question 23. For any two numbers, a ★ b means a × b − a. What is 4 ★ (2 ★ 3)?

(A) 8 (B) 12 (C) 16 (D) 20 (E) 24

Question 24. If x is between 0 and 1, which of these is greatest?

(A) x (B) x² (C) x³ (D) √x (E) x/2

Question 25. Today is a Wednesday. What day of the week will it be 100 days from today?

(A) Monday (B) Friday (C) Wednesday (D) Thursday (E) Saturday

Answer key, with the working

The working

Question 1. Answer: A. Turn every option into a decimal. 5/8 = 0.625 and 3/5 = 0.6. So the five values are 0.625, 0.62, 0.59, 0.6 and 0.605, and 0.625 is the largest. The traps are (B) and (E): line the decimals up to three places, 0.625 against 0.620 and 0.605, and the order is plain.

Question 2. Answer: C. Work from the inside out. 2/3 of 48 is 32. Then 3/4 of 32 is 24. A quicker route: 3/4 × 2/3 = 6/12 = 1/2, and half of 48 is 24.

Question 3. Answer: E. Write each number as a product of primes: 4 = 2 × 2, 6 = 2 × 3 and 10 = 2 × 5. The smallest number containing all of them needs 2 × 2 × 3 × 5 = 60. Check: 60 ÷ 4 = 15, 60 ÷ 6 = 10, 60 ÷ 10 = 6. Option (D), 240, also works, but it is not the smallest.

Question 4. Answer: B. 25% off $80 leaves 75% of $80, which is $60. Then 10% off $60 leaves 90% of $60, which is $54. The trap is (A): adding the discounts to get 35% off gives $52, but the second discount is taken from the reduced price, not from $80.

Question 5. Answer: D. Brackets first: 4 + 2 = 6. Then multiplication and division, from left to right: 3 × 6 = 18, and 18 ÷ 9 = 2. Last, the subtraction: 18 − 2 = 16. Option (C), 10, is what you get by subtracting first, (18 − 3) × 6 ÷ 9.

Question 6. Answer: C. Add 7 to both sides: 3x = 18. Divide both sides by 3: x = 6. Check: 3(6) − 7 = 11.

Question 7. Answer: D. A ratio of 3 to 5 splits the class into 3 + 5 = 8 equal parts. 32 ÷ 8 = 4 students per part. Girls are 5 parts: 5 × 4 = 20. Check: 12 boys and 20 girls make 32, and 12 to 20 simplifies to 3 to 5.

Question 8. Answer: A. Expand the bracket: 2a + 6 = a + 10. Subtract a from both sides: a + 6 = 10. Subtract 6: a = 4. Check: 2(4 + 3) = 14, and 4 + 10 = 14.

Question 9. Answer: E. Subtract 5 from both sides: −2x < −8. Divide both sides by −2, and flip the sign, because dividing by a negative reverses an inequality: x > 4. Only 5 is greater than 4. Option (D) is the trap: at x = 4 the left side is 5 − 8 = −3, which equals −3 but is not less than it. Check with x = 5: 5 − 10 = −5, which is less than −3.

Question 10. Answer: C. Percent increase is the change divided by the starting value. The change is $10 and the start is $40, so 10 ÷ 40 = 0.25, or 25%. The trap is (B): dividing by the new price, 10 ÷ 50, gives 20%.

Question 11. Answer: B. The perimeter is 2 × length + 2 × width. So 36 = 2(12) + 2w, which gives 2w = 12 and w = 6 cm. The area is 12 × 6 = 72 cm².

Question 12. Answer: A. The angles in a triangle add to 180°. 47 + 68 = 115, and 180 − 115 = 65°. Option (E), 115°, is the sum of the two given angles, not the answer.

Question 13. Answer: D. A cube's volume is side × side × side. 4 × 4 × 4 = 64, so each side is 4 cm. Each face is 4 × 4 = 16 cm², and a cube has 6 faces: 6 × 16 = 96 cm². Option (A) is the area of one face.

Question 14. Answer: E. The area of a circle is π × radius². The diameter is 10, so the radius is 5, and the area is π × 25 = 25π. Option (D), 100π, comes from squaring the diameter instead of the radius.

Question 15. Answer: C. The volume is 50 × 40 × 30 = 60,000 cm³. One litre is 1,000 cm³, so the tank holds 60,000 ÷ 1,000 = 60 litres.

Question 16. Answer: E. A mean of 82 across five scores means the five add to 5 × 82 = 410. The four known scores add to 78 + 85 + 80 + 90 = 333. The fifth is 410 − 333 = 77. Check: 333 + 77 = 410, and 410 ÷ 5 = 82.

Question 17. Answer: B. Put the numbers in order first: 3, 3, 5, 7, 9, 12. With six numbers there is no single middle one, so the median is halfway between the two middle numbers, 5 and 7, which is 6. Option (D), 6.5, is the mean: 39 ÷ 6. Option (A), 3, is the mode.

Question 18. Answer: C. There are 4 + 5 + 3 = 12 marbles. 7 of them are not blue, 4 red and 3 green. The probability is 7/12. Option (A), 5/12, is the probability that the marble is blue.

Question 19. Answer: D. Each choice multiplies the number of outfits: 3 shirts × 4 pants × 2 pairs of shoes = 24. Option (A), 9, comes from adding instead of multiplying.

Question 20. Answer: D. The four-day total is 20 + 35 + 15 + 30 = 100 muffins. Tuesday's 35 out of 100 is 35%.

Question 21. Answer: A. Test it with a number. Take n = 3. Then n + 3 = 6 (even), n + 2 = 5, 3n = 9, n² = 9 and 2n + 1 = 7, all odd. The rule behind it: odd plus odd is always even, and 3 is odd, so n + 3 is even for every odd n.

Question 22. Answer: C. Each term is 3 times the one before: 2, 6, 18, 54. Keep going: the 5th term is 54 × 3 = 162 and the 6th is 162 × 3 = 486. Option (A), 162, is the 5th term.

Question 23. Answer: B. Work the bracket first. 2 ★ 3 = 2 × 3 − 2 = 4. Then 4 ★ 4 = 4 × 4 − 4 = 12. These questions look strange, and they only ask you to follow the rule exactly as written.

Question 24. Answer: D. Try x = 1/4. Then x = 0.25, x² = 0.0625, x³ ≈ 0.0156, x/2 = 0.125, and √x = 0.5. The square root is the largest. For any number between 0 and 1, squaring makes it smaller and taking the square root makes it bigger.

Question 25. Answer: B. The days repeat every 7. 100 ÷ 7 = 14 weeks with 2 days left over. Fourteen full weeks from Wednesday is another Wednesday, and 2 more days is Friday.

Score it the way the SSAT does

On the Middle and Upper Level tests, a right answer earns 1 point, a wrong answer loses ¼ of a point, and a blank neither earns nor loses anything. The rule is on E3n's score-reports page. The Elementary Level gives a point for each right answer and takes nothing off for a wrong one.

So count three numbers, not one. Say your child got 16 right, got 4 wrong and left 5 blank. The raw score is 16 − (4 × ¼) = 15.

The penalty changes the math of guessing. With five choices, a blind guess is right one time in five. Over five blind guesses that averages one right answer (+1) and four wrong ones (−1), which comes to zero. Rule out one wrong choice, and the guess starts to pay, but only a little. The 2023 official Upper Level study guide says to guess "only when you can eliminate at least one (but optimally more than one) answer choice." The 2026-27 Candidate Handbook sets a higher bar. It says students should "avoid random guessing but if you can eliminate 2 of the 5 answer choices, you may be better systematically making an educated guess." On the Elementary test there is no penalty, and the official guide tells students they "should guess on questions where they are unsure."

A raw score on 25 home-made questions does not predict an SSAT result. The real report gives a scaled score and a percentile for math, and the percentile compares your child with first-time test takers in the same grade, in the US and Canada, over the last three years. What this page can show is which topic is short.

What to do with the result

Count the wrong answers by topic, not in total. The topic table above maps every question to one.

Wrong answers spread across all five topics. The topics are probably fine. Look at each wrong answer and find the slip: a sign, a step done in the wrong order, a misread question. Most of the wrong options above were built from exactly those slips, and the working names the common ones.

One topic clearly weaker. That is the useful result. Go back to that topic's skill in the answer key and practise it on its own before the next timed set.

Lots of blanks, few wrong answers. That is a time problem rather than a math problem. E3n calls the SSAT a "virtually unspeeded" test, meaning most students have enough time for every question, but 25 questions in 30 minutes is still a pace a student has to practise. The study guide's advice is to keep moving: skip a hard question, mark it, and come back.

Questions 9, 21 and 24 wrong. These test reasoning about numbers rather than calculation. They are the questions where checking with a small number, as the working does, helps most.

Nearly everything wrong. Stop practising and find out what is going on underneath. More timed tests teach very little when the skills under them are missing, and they can knock a student's confidence before the real thing. If the problem is freezing under the timer rather than not knowing the math, math anxiety in children explains how to tell the two apart. For a study routine that works in the weeks before a test, see how to study for a test.

Where to get more official practice

E3n sells two official practice products: Online Practice at $80 and Guide Books at $70, or both for $130. The practice page says both include four full-length practice tests. It also says those full-length tests are the same in the Guide Books and Online Practice, so buying both still gives four full tests. Online subscriptions last a year from purchase, and Middle and Upper Level materials are sold separately. The prices are in U.S. dollars: the 2026-27 Candidate Handbook says "All amounts are listed in U.S. dollars."

There is also a free 30-question online mini practice test. E3n says it returns an instant report showing the student's ten highest and lowest-scoring topics, and it opens in the SSAT portal. Families who qualify for a fee waiver from a school can get the base registration fee and the online practice covered. A waiver does not cover late or service fees. For the Elementary Level, E3n gives away The Official SSAT Study Guide for grades 3 and 4 as free downloads, with practice questions in each section.

Start at the official SSAT practice page, and use the Elementary guides from E3n's help centre.

When a teacher helps more than another practice test

A practice set shows which kind of question goes wrong. It cannot show why, and the why decides what to do next.

A student who picks (A) on Question 4 knows how to take a percent off a price. They added the two discounts instead of taking them one after the other. A student who picks (D) on Question 14 knows the formula but used the diameter. Both get the question wrong, and both need a different five minutes of teaching.

A teacher who reads the working can see which slip it was. Genie's math page does not mention the SSAT. In answer to whether a math teacher can help with EQAO and exam prep, it says a teacher can work through "practice questions, past unit tests, and provincial-test style problems using the student's own course material". Genie works only with Canadian Certified Teachers, licensed by a provincial governing body such as the Ontario College of Teachers. Before a teacher sees a student profile, their certificate number and issuing body are checked against the provincial registry, with a live government-ID match. Genie calls this the Trust Engine. Students are matched by course, pace and personality, and parents get a per-lesson record of what was covered and what their child understood.