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PSAT/NMSQT Practice Questions
Original practice questions for the Preliminary SAT / National Merit Scholarship Qualifying Test (College Board & National Merit Scholarship Corporation), mixed across 4 topics with instant answers and explanations. Practise by topic below or take the timed mock test.
PSAT/NMSQT mixed practice
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Q1.AlgebraSolve: x + y = 9 and 3x + 5y = 29
Show answer & explanation
Answer: D — x = 8, y = 1
Elimination/substitution gives x = 8, y = 1. Check: 1(8) + 1(1) = 9 ✓ and 3(8) + 5(1) = 29 ✓.
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Q2.PercentagesThe price of an item changes from $500 to $540. What is the percentage change?
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Answer: D — 8% increase
Change = 40 on a base of 500: 40/500 × 100 = 8% increase. Always divide by the ORIGINAL value.
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Q3.English GrammarChoose the correct tag question: She can swim, ___?
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Answer: C — can’t she
A positive statement takes a negative tag with the same auxiliary: “can’t she?”.
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Q4.Vocabulary & IdiomsChoose the synonym of EPHEMERAL.
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Answer: D — Short-lived
Ephemeral means lasting a very short time.
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Q5.AlgebraFind the sum of the first 29 terms of the AP 15, 21, 27, …
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Answer: C — 2871
Sₙ = n/2 × [2a + (n − 1)d] = 29/2 × [30 + 168] = 2,871.
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Q6.PercentagesTwo successive discounts of 15% and 15% are equivalent to a single discount of:
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Answer: A — 27.75%
Net discount = a + b − ab/100 = 15 + 15 − 15×15/100 = 27.75%.
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Q7.English GrammarChoose the correct option: Hardly had he left ___ it started raining.
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Answer: A — when
The correlative pair is “hardly … when” (also “no sooner … than”).
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Q8.Vocabulary & IdiomsMeaning of the idiom “once in a blue moon”.
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Answer: B — Very rarely
It means very rarely.
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Q9.AlgebraSolve: x² − 6x − 27 = 0
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Answer: C — -3, 9
Find two roots with sum 6 and product -27: 9 and -3. So x² − 6x − 27 = (x − 9)(x + 3) = 0.
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Q10.PercentagesTwo successive discounts of 25% and 12% are equivalent to a single discount of:
Show answer & explanation
Answer: A — 34%
Net discount = a + b − ab/100 = 25 + 12 − 25×12/100 = 34%.
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.
Practise by topic
- Algebra questions — Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution.
- Percentages questions — Convert percentages to fractions you know by heart (12.5% = 1/8, 37.5% = 3/8, 16.67% = 1/6) and always divide a change by the ORIGINAL value.
- English Grammar questions — Find the subject first and make the verb agree with it, ignoring phrases in between.
- Vocabulary & Idioms questions — Learn words in synonym/antonym pairs and by roots (bene = good, mal = bad, chron = time).
- PSAT/NMSQT mock test — 25 timed questions.
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 |