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PSAT/NMSQT Mock Test
A timed 25-question mock for the Preliminary SAT / National Merit Scholarship Qualifying Test covering algebra, percentages, english grammar, vocabulary & idioms. Answer, submit and review every question with its explanation; set negative marking to match your exam’s current scheme.
PSAT/NMSQT mock test
25 questions · 1 mark each · the timer starts with your first answer and the test submits itself when time runs out.
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Q1.AlgebraSolve: 2x + 2y = 36 and 4x + 2y = 54
Answer: A — x = 9, y = 9
Elimination/substitution gives x = 9, y = 9. Check: 2(9) + 2(9) = 36 ✓ and 4(9) + 2(9) = 54 ✓.
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Q2.PercentagesTwo successive discounts of 10% and 12% are equivalent to a single discount of:
Answer: C — 20.8%
Net discount = a + b − ab/100 = 10 + 12 − 10×12/100 = 20.8%.
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Q3.English GrammarChoose the correct option: She is senior ___ me by two years.
Answer: D — to
Latin comparatives (senior, junior, superior, inferior) take “to”, not “than”.
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Q4.Vocabulary & IdiomsChoose the correctly spelt word.
Answer: B — Accommodation
Accommodation has double c and double m.
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Q5.AlgebraSolve: 2x + 4y = 12 and 4x + 3y = 29
Answer: C — x = 8, y = -1
Elimination/substitution gives x = 8, y = -1. Check: 2(8) + 4(-1) = 12 ✓ and 4(8) + 3(-1) = 29 ✓.
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Q6.PercentagesTwo successive discounts of 25% and 10% are equivalent to a single discount of:
Answer: D — 32.5%
Net discount = a + b − ab/100 = 25 + 10 − 25×10/100 = 32.5%.
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Q7.English GrammarChoose the correct preposition: She is good ___ mathematics.
Answer: B — at
The idiom is “good at” a subject or skill.
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Q8.Vocabulary & IdiomsChoose the synonym of PRUDENT.
Answer: D — Wise
Prudent means acting with care and good judgement.
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Q9.AlgebraSolve: x² + 12x + 35 = 0
Answer: D — -7, -5
Find two roots with sum -12 and product 35: -5 and -7. So x² + 12x + 35 = (x + 5)(x + 7) = 0.
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Q10.PercentagesWhat is 15% of 440?
Answer: A — 66
15% of 440 = 15/100 × 440 = 66.
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Q11.English GrammarChoose the correct option: Let’s discuss ___ the matter tomorrow.
Answer: A — no preposition
“Discuss” is transitive: we discuss the matter (no “about”).
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Q12.Vocabulary & IdiomsChoose the antonym of FRUGAL.
Answer: C — Extravagant
Frugal = sparing with money; extravagant = spending excessively.
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Q13.AlgebraSolve: 5x + 5y = 20 and x + 4y = 10
Answer: B — x = 2, y = 2
Elimination/substitution gives x = 2, y = 2. Check: 5(2) + 5(2) = 20 ✓ and 1(2) + 4(2) = 10 ✓.
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Q14.PercentagesWhat is 35% of 480?
Answer: D — 168
35% of 480 = 35/100 × 480 = 168.
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Q15.English GrammarChoose the correct option: She has been working here ___ 2019.
Answer: C — since
Use “since” with a point in time (2019) and “for” with a duration.
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Q16.Vocabulary & IdiomsMeaning of the idiom “once in a blue moon”.
Answer: B — Very rarely
It means very rarely.
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Q17.AlgebraFind the sum of the first 20 terms of the AP 20, 28, 36, …
Answer: A — 1920
Sₙ = n/2 × [2a + (n − 1)d] = 20/2 × [40 + 152] = 1,920.
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Q18.PercentagesTwo successive discounts of 30% and 5% are equivalent to a single discount of:
Answer: B — 33.5%
Net discount = a + b − ab/100 = 30 + 5 − 30×5/100 = 33.5%.
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Q19.English GrammarIdentify the error: “Each of the students have submitted their assignment.”
Answer: C — have submitted
“Each” is singular, so the verb should be “has submitted”.
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Q20.Vocabulary & IdiomsOne word for: Fear of heights.
Answer: C — Acrophobia
Acrophobia is an extreme fear of heights.
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Q21.AlgebraFind the sum of the first 11 terms of the AP 12, 20, 28, …
Answer: A — 572
Sₙ = n/2 × [2a + (n − 1)d] = 11/2 × [24 + 80] = 572.
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Q22.PercentagesWhat is 5% of 820?
Answer: D — 41
5% of 820 = 5/100 × 820 = 41.
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Q23.English GrammarChoose the passive voice of: “The chef cooked a delicious meal.”
Answer: D — A delicious meal was cooked by the chef.
Simple past active → “was/were + past participle” in the passive.
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Q24.Vocabulary & IdiomsChoose the word closest in meaning to INNOCUOUS.
Answer: C — Harmless
Innocuous means not harmful or offensive.
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Q25.AlgebraFind log₂ 8.
Answer: B — 3
log_2(8) asks “2 to what power gives 8?” → 2^3 = 8, so the answer is 3.
How the mock test works
- The timer starts with your first answer; the test submits itself when time runs out.
- Choose the negative marking that matches your exam (this test has no negative marking by default — check the official notification).
- After submitting you get your score, accuracy, time taken and a topic-wise breakdown, then every explanation.
- “New mock test” builds another paper — calculation questions get new numbers.
About PSAT/NMSQT
Preliminary SAT / National Merit Scholarship Qualifying Test — conducted by College Board & National Merit Scholarship Corporation. The practice SAT that also screens for National Merit Scholarships.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
PSAT/NMSQT practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| English Grammar | English | Question bank |
| Vocabulary & Idioms | English | Question bank |