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Free SHSAT Practice Test: 10 Real Questions
The SHSAT is the exam for New York City's specialized high schools, and from fall 2026 it is computer-adaptive: 100 questions, 50 in English and 50 in math. These ten come straight from our adaptive practice exams.
Question 1
What is 3⁄8 of 240?
- A. 30
- B. 64
- C. 80
- D. 90
Show the answer
The answer is D.
- A is wrong: This is one eighth of 240. The question asks for three of those eighths.
- B is wrong: Neither step gives 64. Divide first: 240 ÷ 8 = 30, then multiply by 3.
- C is wrong: This is 240 ÷ 3 — you used the numerator as the divisor. Divide by the denominator, then multiply by the numerator.
Question 2
A jacket’s price rises from $40 to $50. What is the percent increase?
- A. 25%
- B. 50%
- C. 80%
- D. 125%
Show the answer
The answer is A.
- B is wrong: This looks like $10 out of $20, or the increase compared to half the price. Neither is what the question asks.
- C is wrong: This divides the original price by the new one (40 ÷ 50). A percent increase compares the CHANGE with the original.
- D is wrong: This divides the new price by the original (50 ÷ 40), which gives the new price as a percentage of the old, not the increase.
Question 3
If 5x − 7 = 28, what is the value of x?
- A. 7
- B. 21
- C. 28
- D. 35
Show the answer
The answer is A.
- B is wrong: This is 28 − 7. To undo a subtraction you add — so 28 + 7 = 35, then divide.
- C is wrong: This is the number on the right of the equation, not the value of x.
- D is wrong: This is 5x, not x. One step remains: divide by 5.
Question 4
Two numbers are in the ratio 3 : 5 and their sum is 64. What is the smaller number?
- A. 24
- B. 32
- C. 40
- D. 48
Show the answer
The answer is A.
- B is wrong: This is half of 64, which would only be right if the ratio were 1 : 1.
- C is wrong: This is the larger number. The question asks for the smaller.
- D is wrong: This is six parts of eight. The ratio 3 : 5 makes eight parts in all, and the smaller number is three of them, not six.
Question 5
What is the average (arithmetic mean) of 12, 15, 18, and 23?
- A. 17
- B. 17.5
- C. 18
- D. 23
Show the answer
The answer is A.
- B is wrong: This is the midpoint of the two middle values — that is the median, not the mean.
- C is wrong: This is one of the values in the list, not the average of them.
- D is wrong: This is the largest number in the list, not the average of the four.
Question 6
Which revision corrects the sentence?
The collection of rare coins that belonged to my grandparents were donated to the museum.
The collection of rare coins that belonged to my grandparents were donated to the museum.
- A. were donated (no change)
- B. was donated
- C. have been donated
- D. are donated
Show the answer
The answer is B.
- A is wrong: The plural "were" is being pulled toward "coins" and "grandparents" because they sit right before the verb. Cross out everything between the subject and the verb: "The collection… were donated" is clearly wrong.
- C is wrong: "Have" is also plural, so this repeats the original error and changes the tense on top of it.
- D is wrong: "Are" is plural as well, and the present tense does not fit a donation that already happened.
Question 7
Which choice best corrects the run-on sentence?
The storm knocked out power for six hours, we played board games by candlelight.
The storm knocked out power for six hours, we played board games by candlelight.
- A. power for six hours, we played
- B. power for six hours we played
- C. power for six hours, so we played
- D. power for six hours, playing board games
Show the answer
The answer is C.
- A is wrong: This is the original sentence. A comma alone cannot join two complete sentences.
- B is wrong: Removing the comma makes it a fused sentence — worse than the original, not better.
- D is wrong: This turns the second half into a fragment and loses the cause-and-effect link.
Question 8
Which revision most clearly fixes the ambiguous pronoun?
When Deshawn met Marcus at the library, he had already returned the books.
When Deshawn met Marcus at the library, he had already returned the books.
- A. they had already returned the books
- B. one of them had already returned
- C. he had already returned
- D. Deshawn had already returned
Show the answer
The answer is D.
- A is wrong: “They” makes it plural, changing the meaning. Only one person returned the books.
- B is wrong: “One” is vaguer than “he”, not clearer.
- C is wrong: This is the original — “he” could still be either man.
Question 9
What is the most effective way to combine these sentences?
Amara trained for the marathon all winter. She finished in under four hours.
Amara trained for the marathon all winter. She finished in under four hours.
- A. Amara trained for the marathon all winter, she finished in under four hours.
- B. Amara trained for the marathon all winter; finishing in under four hours.
- C. Amara trained for the marathon all winter, and she finished in under four hours.
- D. Having trained for the marathon all winter, Amara finished in under four hours.
Show the answer
The answer is D.
- A is wrong: A comma splice — two complete sentences joined by only a comma.
- B is wrong: A semicolon must join two complete sentences. “Finishing in under four hours” is a fragment.
- C is wrong: Grammatically fine, but “and” merely lists the two facts. The better version shows the training led to the result.
Question 10
Which sentence contains a misplaced modifier?
- A. Startled by the noise, the birds scattered.
- B. Covered in mud, the dog bounded into the kitchen.
- C. Walking to school, the rain began to fall.
- D. Exhausted from the hike, we set up camp early.
Show the answer
The answer is C.
- A is wrong: Correct as written — the birds are the ones startled.
- B is wrong: Correct as written — the dog is the thing covered in mud.
- D is wrong: Correct as written — we are the ones exhausted.