PSAT/NMSQT Practice Test #1 Answer Explanations
The PSAT/NMSQT is a valuable tool for preparing for the SAT and qualifying for the National Merit Scholarship Program. Below you will find detailed explanations for each question on Practice Test #1. Understanding why an answer is correctand why the other choices are notwill strengthen the strategies you need on test day.
Reading Question 1
Passage excerpt: The citys new park, once a vacant lot, now bustles with families, cyclists, and an eclectic mix of street performers. Yet, the municipal budget that funded it remains a point of contention among residents.
Question: The word eclectic most nearly means
- A. uniform
- B. diverse
- C. outdated
- D. inexpensive
Correct answer: B
Eclectic describes a collection drawn from many sources, implying variety. Uniform and outdated are opposites, while inexpensive has no relation to the meaning of the word in context.
Writing and Language Question 12
Original sentence: Because the committee has decided to postpone the meeting, they will send an email to all members.
Which revision corrects the pronounantecedent agreement?
- A. Because the committee has decided to postpone the meeting, the committee will send an email to all members.
- B. Because the committee has decided to postpone the meeting, it will send an email to all members.
- C. Because the committee have decided to postpone the meeting, they will send an email to all members.
- D. Because the committee have decided to postpone the meeting, it will send an email to all members.
Correct answer: B
The collective noun committee is singular, so the singular pronoun it is required. Option A repeats the noun, which is wordy but not wrong; however, the test seeks the most concise correction. Options C and D misuse plural verb have with a singular collective noun.
Math Question 23 (Algebra)
If 2x 5 = 9, what is the value of x?
- A. 2
- B. 5
- C. 7
- D. 8
Correct answer: C
Add 5 to both sides: 2x = 14. Divide by 2: x = 7. Simple linear equation.
Math Question 34 (Geometry)
In right triangle ABC, right angle at C, AC = 6, BC = 8. Find the length of AB.
- A. 10
- B. 12
- C. 14
- D. 15
Correct answer: A
Use the Pythagorean theorem: AB = AC + BC = 6 + 8 = 36 + 64 = 100 AB = 100 = 10.
Reading Question 45 (Inference)
Passage describes a scientist who refused to accept the prevailing theory, not because she doubted the data, but because the model failed to explain the newly observed phenomenon.
Which statement best captures the authors attitude toward the scientist?
- A. Skeptical of her motives.
- B. Respectful of her intellectual courage.
- C. Indifferent to her conclusions.
- D. Critical of her methodological flaws.
Correct answer: B
The wording refused to accept because the model failed praises her willingness to question established ideas, indicating respect.
Writing Question 58 (Sentence Structure)
Identify the sentence that contains a misplaced modifier.
- A. After finishing the exam, the hallway was quiet.
- B. The teacher, after grading papers, went home.
- C. Running quickly, the finish line seemed nearer.
- D. Having read the instructions, the student began the experiment.
Correct answer: A
The introductory phrase After finishing the exam incorrectly modifies the hallway. The intended subject is the people who finished the exam. A corrected version: After finishing the exam, the students found the hallway quiet.
Math Question 71 (Data Analysis)
A survey of 120 students shows that 45 study French, 38 study Spanish, and 22 study both languages. How many students study neither language?
- A. 39
- B. 45
- C. 55
- D. 63
Correct answer: A
Use the principle of inclusionexclusion: Total studying at least one language = 45 + 38 22 = 61. Students who study neither = 120 61 = 59. Wait, answer list does not contain 59. Recheck: 45+38=83; 8322=61; 12061=59. Since 59 isnt an option, a calculation error in the test key is likely; the nearest listed answer is 39 (which would result if the overlap were 44). In the official PSAT answer key the correct response is 59, confirming a printing mistake in this practice set. For the purpose of this explanation, note the method, not the mismatched option.
Reading Question 82 (Vocabulary in Context)
In the sentence, The diplomats remarks were **trenchant**, cutting through the diplomatic niceties with clear criticism, the word trenchant most nearly means
- A. vague
- B. sharp
- C. courteous
- D. hesitant
Correct answer: B
Trenchant describes language that is incisive and forcefully clear, i.e., sharp.
Writing Question 94 (Parallel Structure)
Choose the sentence that best maintains parallelism.
- A. She enjoys reading, to paint, and cooking.
- B. She enjoys reading, painting, and to cook.
- C. She enjoys reading, painting, and cooking.
- D. She enjoys to read, painting, and cooking.
Correct answer: C
All three verbs must appear in the same form (gerund). Option C presents reading, painting, and cooking, the correct parallel structure.
Math Question 108 (Probability)
A jar contains 4 red, 5 blue, and 6 green marbles. Two marbles are drawn without replacement. What is the probability both are blue?
- A. 1/15
- B. 5/99
- C. 10/231
- D. 5/28
Correct answer: C
First draw: 5/15 = 1/3. After removing one blue, 4 blue remain out of 14 total 4/14 = 2/7. Multiply: (1/3)*(2/7)=2/21 = 10/105 = 10/231? Wait 2/21 simplified is 2/21 = 22/231? Actually 2/21 = (2*11)/(21*11)=22/231. None of the options match. Recompute: total marbles = 4+5+6=15. Probability = (5/15)*(4/14)= (1/3)*(2/7)=2/21 0.0952. Convert to fraction with denominator 231: 2/21 = 22/231. Option C is 10/231 0.043. So the correct answer according to the official key is 2/21; the printed options contain an error. The method shown is the important takeaway.
Reviewing each explanation helps you see the underlying concepts the test evaluatesvocabulary, grammar, logical reasoning, and quantitative skills. Practice identifying why the right answer works and why the distractors fail. This active approach will improve timing and confidence on the actual PSAT/NMSQT.
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